In 1988 when Maria Klawe moved from IBM in California to the University of British Columbia in Vancouver, along with her theoretical computer scientist husband Nick Pippenger, to become UBC computer science department head, I had received a computer science postdoctoral fellowship offer from the University of Toronto, a fixed-term assistant professorship offer from UBC, and a tenure-track assistant professorship offer from Simon Fraser University, also in the Vancouver region of Canada. My decision to go to UBC led to my subsequent experience of an academic political dispute with my boss Klawe, described in earlier Parts, with an employment aspect involving senior colleagues David Kirkpatrick and Alain Fournier.
As in Part 3, had Klawe and Pippenger chosen not to go to UBC my job offer there would have been upgraded to tenure-track. Thus, my dilemma in choosing a faculty job between UBC or SFU in 1988 had a Klawe-related context.
Then in 1990 when I was again applying for a tenure-track position, Klawe chose not to inform me that 2 of the 5 recommendation letters I had requested did not arrive, one of the two to have been from her close friend, computer science professor Richard “Dick” Karp at the University of California, Berkeley, who had promised to affirm that my recent research was in theoretical computer science – my 1988 Berkeley Ph.D. had been in mathematics.
The deception involving both Klawe and Karp, deployed to my detriment, had started in 1988 at Berkeley when Karp suggested that I choose UBC because of Klawe and Pippenger, as I recalled in a July 2012 blog post:
“The arrival of Maria Klawe and her husband Nicholas Pippenger made UBC Computer Science more important but reduced my prospect of a longer employment, so between ‘fate’ and ‘luck’ – SFU professor Wo-Shun Luk had been particularly interested in my going there – I had chosen fate.
Worse yet, it was a ‘double’ fate: while still at UC Berkeley in April-May 1988 it had been Klawe’s good friend Professor Richard Karp – today the founding director of Simons Institute for the Theory of Computing – informing me of the couple’s decision to go to UBC – thus no immediate chance of tenure-track for me – and also advising me to choose UBC over Simon Fraser because of the new strength; then in 1990 when I applied for a tenure-track position under Head Klawe, “Dick” Karp’s promised reference letter was a no show without my knowledge …”
(“Team Canada female athletes disqualified from Commonwealth silver medal, jailed Chinese democracy activist awarded with Nobel peace prize, and others in between (Part 8) — when political power games rule”, July 6, 2012, Feng Gao’s Blog – Reflections on Events of Interest)
It was in May 1988 that I went to Karp’s office to seek his advice, telling him of Toronto’s postdoc offer, SFU’s tenure-track offer, and UBC’s fixed-term offer that would become tenure-track if Klawe and Pippenger decided not to go there.
Karp expressed surprise that I had a Toronto postdoc offer, i.e., without his help, and then informed me that Maria and Nick had just told him they would be going to UBC. Karp then suggested that I accept the UBC offer because the arrival of Maria and Nick would make it a much stronger department, adding, “Vancouver is a very liveable city. David Kirkpatrick is a very smart guy. Jim Varah is a distinguished numerical analyst; I met him when I visited UBC and he was the department head”.
But Karp also cautioned, “after one year you can go anywhere in Canada” – I would be applying for the Canadian immigrant status – and at some point advised, indirectly, that Pippenger was not to be contradicted, as previously quoted in Part 3:
“Whatever Nick says must be right.”
(“Team Canada female athletes disqualified from Commonwealth silver medal, jailed Chinese democracy activist awarded with Nobel peace prize, and others in between (Part 4) — when power and control are the agenda”, May 24, 2011, Feng Gao’s Blog – Reflections on Events of Interest)
Karp gave me the phone number of Klawe, then manager of the mathematics and related computer science department at IBM Almaden Research Center, telling me that she would like me to contact her. I was disappointed that their going to UBC took away my prospect of a tenure-track job, but felt privileged to get acquainted with the distinguished couple in theoretical computer science prior to her becoming my boss. On the phone I accepted Klawe’s invitation to give a seminar presentation at IBM Almaden, and met her, Nick and a few others there.
My Berkeley Ph.D. was only in mathematics, but my bachelor’s degree from Sun Yat-sen University in Guangzhou, China, had been in computer science, with a concentration in computational mathematics. Computer science had just begun in China in the late 1970s-early 1980s, and Chinese computers of that time were mainframes comparable only to American computers of the 1960s.
(Marshall C. Yovits, ed., Advances in Computers, Volume 27, 1988, Academic Press)
In the academic year 1987-1988, my last at Berkeley, I audited graduate courses taught by computer science professors, such as computer vision by Jitendra Malik, computer architecture by Alvin Despain, parallel processing and pipelining by David Messerschmitt, operating systems by John Ousterhout, and two courses by Richard Karp, on the analysis of probabilistic and random algorithms and on the analysis of parallel algorithms.
Courses in mathematical theories usually did not attract large audiences but Karp’s were exceptional, with his sharp command of mathematical concepts and algorithmic techniques, and his logical organization and articulate presentation of the course materials.
Karp assigned every student, including me who was only auditing, the task of taking notes for at least one lecture, notes that he would review, compile and distribute so that everyone would have a full copy of his course as recorded by the students – reflecting Karp’s confidence in his lectures’ legibility and clarity – in addition to his concise course notes. Later at UBC, I taught these two graduate courses and utilized Karp’s lectures for 2/3 of my course materials.
So at that point in the summer of 1988, I felt confident of integrating into the computer science teaching and research profession in due course.
It had always been in my intellectually youthful personality not to settle on the safest route to personal progress, but on some degree of safety from which I could get into the intrigue of, and make better, the unknown.
In the case of going to Canada, Karp’s advice made sense to me as there should be enough personal security to focus on the scientific prospect: the UBC fixed-term job offer included helping with Canadian immigration, a given part of the SFU tenure-track offer but not in the U of T postdoc offer; UBC had a stronger academic research reputation, also a longer history and a more scenic campus, than SFU, although neither was at the level of overall strength as U of T, Canada’s leading university.
At the previous stage of my career, in 1981-1982 in China applying for Ph.D. study in the United States, I had done similarly with my choices.
I applied to 3 graduate programs: the scientific computing and computational mathematics program in Stanford University’s computer science department, the mathematics department of UC Berkeley, and the applied mathematics department at State University of New York at Stony Brook. Stanford computer science was ranked the best in the world, Berkeley’s mathematics department was the largest – with over 70 faculty members – and one of the very best in the world, while Stony Brook’s applied mathematics was good but did not enjoy a top ranking.
I soon received Stony Brook’s admission, partly because Professor Yung Ming Chen (陳永明), its applied math department chairman at the time, had in 1981 visited our department at Sun Yat-sen university, with me assigned his tour guide, and during his short visit I learned that his father had been an army general and deputy governor of Guangdong province, of which Guangzhou is the capital, during the Nationalist government era, i.e., before the 1949 Communist takeover of China.
My bachelor’s thesis adviser was Professor Yuesheng Li (李岳生), chairman of the computer science department founded after our computational mathematics major class had finished the first year in the mathematics department. Understanding of my ambitiousness Li suggested, as I was thinking, to wait for responses from the other two schools. But having gotten his graduate study, at Moscow State University in the 1950s, after working as a student interpreter for a Soviet mathematics professor fostering research at Jilin University in China’s Northeast, Li also tried to talk me into applying to the University of Wisconsin-Madison, where Professor Carl de Boor at the U.S. Army Mathematics Research Center was a peer of his. I recalled the anecdote in a March 2011 blog post:
“When I applied for graduate study in the United States Professor Li seriously recommended the U. S. Army Mathematics Research Center at the University of Wisconsin, Madison – Dr. Carl de Boor there and his General Motors connection were Professor Li’s favorite and it also had Dr. Grace Wahba – but I preferred the Math program at the University of California, Berkeley, although Computer Science at Stanford was my first choice.”
(“Team Canada female athletes disqualified from Commonwealth silver medal, jailed Chinese democracy activist awarded with Nobel peace prize, and others in between (Part 3) – when violence and motive are subtle and pervasive”, March 29, 2011, Feng Gao’s Blog – Reflections on Events of Interest)
But Berkeley’s politically liberal reputation, its mathematics department’s world leading status and the U.S. West Coast’s mild climate – I had grown up in Guangzhou without any snowy winter – were to my liking, and so I took Li’s respect for Carl de Boor seriously but not so much Wisconsin-Madison as my place of Ph.D. study.
I was accepted by Berkeley but not by Stanford. In a context resembling 6 years later choosing UBC over SFU, I then chose Berkeley over Stony Brook: a more leading Ph.D. program, a university of longer history, and a locality of easier life adjustment.
Berkeley was the original campus of the University of California, founded 90 years before the State University of New York in the 1940s, and a century before SUNY Stony Brook in the 1950s.
(“A brief history of the University of California”, Office of the President, University of California; “History of SUNY”, The State University of New York; and, “Fast Facts”, Stony Brook University)
I had understood that Stanford computer science was hard to get into, its brochure stating that it annually admitted only a small class and few foreign students; also, at the time I wasn’t familiar with the research of its faculty, except some of Prof. James Wilkinson’s in numerical analysis, although I was familiar with some of Stanford math professor Samuel Karlin’s research – more so than with the Berkeley mathematicians’ – as a result of my undergraduate study influenced by Prof. Li.
But the bottom line might be that I wasn’t that strong an applicant; and there was an interesting, related background story.
I had 3 SYSU professors agreeing to provide letters of recommendation: Prof. Li, Prof. Mingjun Chen (陳銘俊), Li’s close associate and former colleague at Jilin University, and Prof. Youqian Huang (黃友謙).
My entrance class of 1977, the first class admitted through a nationwide exam after the 1966-1976 Cultural Revolution, composed mostly of students of mixed school-and-work backgrounds – I had worked as a factory apprentice for over a year – and in our performance wasn’t rated too highly by Chen, whose favorites were the entrance class of 1979, the first composed primarily of fresh middle school graduates.
The Stanford application form asked the professor to rate the applicant as being in the top 2% of the class, the top 10%, or lower, whereas the Berkeley form had a top 5% category. I recall I was cleaning a window on a classroom-cleaning day and Chen was present telling me that he could not rate me as in the top 2% – I had no argument since at least several girls among our graduating class were ahead of me in the grade-point average – but he would rate me as in the top 5% for Berkeley given that it was the school I liked most.
Obviously not a chance for the world’s top computer science department to accept a not-at-the-top graduate from the developing world.
Prof. Huang was more reassuring. An original SYSU graduate and an articulate teacher, Huang was friendly partly because he and my maternal family were from the same Shantou (Swatow) region of Guangdong.
Born and growing up in Cantonese-speaking Guangzhou, I could also speak the Swatow dialect because my maternal grandparents lived with us and helped my parents raise me and my sister, as I have told in a 2010 Chinese blog post.
(“忆往昔，学历史智慧 (Reminiscing the past, learning history’s wisdom)”, April 10, 2010, FengGao.ORG)
Born in Indonesia, Prof. Mingjun Chen died of cancer on July 20, 2008, at the age of 74.
(“讣告”, by 程月华, and, “我们敬爱的陈老师——一路走好”, by Elsa, July 21, 2008, 中山大学, Yat-sen Channel)
A former student reminisced about what a conscientious and demanding teacher Chen had been:
“… 老师上课总是几十年如一日那样从来不迟到！实际上每次八点钟的课他都是七点半就到了！每次七点起身时就看到老师在慢慢向教室走去了！我用十分钟走的路程，想必老师要用半个钟才到吧！从他家里一直走到那，估计至少老师会提前一个小时出发！因为老师有癌症，化疗过，但是身体一直不是很好！每走几分钟就要停下来休息。在中大校道上你常会见到一个满脸皱纹的老头，大清晨带着个装着前晚写的讲义的塑料袋，蹲在路旁休息！每次经过他身边都想上前跟老师说一声：老师您辛苦了，但是一直没有，现在我再也没机会了！一次听同学说他常常五点就起了，或者是为了批改我们的作业会熬通宵！每当老师在评讲作业时说他前一晚的事情，我们都会觉得很心痛！老师看到我们不认真的字迹，错误的运用符号，乱增加言语，就会暴跳如雷，彻夜未眠，第二天仍要赶早去上课！其实如果是助教上课的话他完全可以不来的，因为他没讲一句话，但是他还是静静地做在最左边！不知道大家是不是习惯了，哪天老师不来，我们就会不专心，但是只要老师坐在那，大家就会觉得很安心，才会很认真的听课！”
(Elsa, July 21, 2008, 中山大学, Yat-sen Channel)
English translation of the above quote:
… Everyday in decades Teacher was never late for class! As a matter of fact, for every 8 o’clock class he arrived at 7:30! Each time I got up at 7 I saw Teacher walk slowly toward the classroom! A 10-minute walk for me, I think it took Teacher about half an hour! From his home walking there, I estimate that Teacher would start at least an hour ahead of time! Because Teacher had cancer, he had done chemotherapy, but his health has not been very good! Every few minutes of walk he needed a rest. On Sun-Yat-sen University campus roads you would often see a wrinkled old man, early in the morning carrying a plastic bag filled with lecture notes written the night before, squatting on the roadside resting! Every time walking by him I wanted to come up and say, Teacher your hard work is appreciated, but I never did, and now there is no more chance! I once heard from a classmate that he often got up at 5 o’clock, or staying up all night marking our homework! Whenever Teacher talked about the night before when commenting on our homework, we would all feel heartache! When Teacher saw our careless writings, erroneous used notations and arbitrarily added words, he would fly into a rage and lose sleep all night, but would still attend class early the next morning! Actually, if it was a teaching assistant’s class Teacher would not have to come at all, because he did not say a word, but still he sat quietly at the far left! I do not know if if had become our habit, that any day Teacher did not come, we would not concentrate, but as long as Teacher sat there, we would all feel reassured, and would then very seriously listen to the lecture!
I remember well that in teaching our courses, Chen’s favorite mathematical subject was “inequalities” – like professed by Louis Nirenberg of New York University’ Courant Institute of Mathematical Sciences, John Nash’s co-recipient of the 2015 Abel Prize, as in Part 2.
I have noticed the coincidence that in 1982 Chen’s evaluation ruled out any chance of my attending Stanford, and 8 years later in 1990 the plan of Alain Fournier, who had moved from U of T to UBC, to hire new Stanford Ph.D. Jack Snoeyink as in Part 3, ended my chance of a tenure-track position in theoretical computer science at UBC – and both Chen and Fournier later died of cancer, Chen nearly 8 years after Fournier.
In 1982 at Sun Yat-sen university a more senior, technically solid and practically experienced student, with a master’s degree earned under Prof. Li and closely associated with Prof. Chen, was also going to the U.S. for Ph.D. study. Guanrong Chen (陳關榮) would soon go by his English name of Ron Chen.
During the Cultural Revolution, like many youths of his age Ron was sent to work in a farm, in his case on the big island of Hainan. Like my later Berkeley roommate Kezheng Li (李克正) mentioned in Part 2, Ron studied mathematics on his own; later through a family connection Ron got Mingjun Chen’s tutoring, and after the Cultural Revolution joined Sun Yat-sen University’s first class of graduate students.
Ron was very good at applying what he had mastered. I recall that by the time of his master’s thesis he had found applications for spline functions – Prof. Li’s specialty – in control theory, and soon linked up with Prof. Charles K. Chui of Texas A&M University, College Station, where Chui, as well as Prof. Larry Shumaker, director of Texas A&M’s Center for Approximation Theory, were peers of Li’s.
(“Vita (August 6, 2015): Larry L. Schumaker”, Department of Mathematics, Vanderbilt University)
Along with Texas A&M’s admission Ron secured a teaching assistantship – most of us at SYSU going to U.S. graduate schools in 1982 couldn’t get it prior to attending – and in his Ph.D. study under Chui, continued to apply approximation theory techniques to control theory. One year before my Ph.D., in 1987 Ron received his Ph.D. and co-authored a book on Kalman filters – a mathematical estimation tool in control theory – with his adviser Chui.
(Charles K. Chui and Guanrong Chen, Kalman Filtering with Real-Time Applications, 1987, Springer-Verlag)
After teaching in Houston at Rice University and then at University of Houston, Ron became a tenured professor at the latter. In 1996 he became a fellow of the Institute of Electrical and Electronics Engineers – an honor Nick Pippenger has had as in Part 3 – and the next year he co-authored a book with his former mentor Mingjun Chen and his former SYSU fellow graduate student Zhongying Chen (陳仲英) – three Chens – on approximate solutions of operator equations, a subject I had once audited at Prof. Chen’s SYSU graduate course.
(Mingjun Chen, Zhongying Chen and Guanrong Chen, Approximate Solutions of Operator Equations, 1997, World Scientific; and, “GUANRONG CHEN”, Department of Electronic Engineering, City University of Hong Kong)
Since 2000, Guanrong Ron Chen has been a professor at the City University of Hong Kong, and is an honorary professor at around 30 universities internationally.
( “Guanrong (Ron) Chen, City University of Hong Kong, Hong Kong”, Hindawi Publishing Corporation; and, Department of Electronic Engineering, City University of Hong Kong)
In 2008, Ron missed delivering a keynote speech at a July 18-19 international workshop in Austria, due to attending the “final interview” in China for the 2008 “National Natural Science Award of China”:
“… As the date of final interview coincides with the workshop, he will not be able to attend and give his interesting talk. We wish Professor Chen all the best …”
(“Professor Guanrong Ron Chen, City University of Hong Kong, Hong Kong”, First International Workshop on Nonlinear Dynamics and Synchronization, July 18-19, 2008, Klagenfurt, Austria)
A day later Ron’s former mentor Mingjun Chen died at SYSU in Guangzhou, and a week later on July 25 Ron gave a eulogy at the memorial service.
(“许罗丹教授主持陈铭俊告别仪式”, guosheng.sunbo9.net)
In his tearful reminiscences, Ron told of his own mother’s passing half a year before, his last meeting with his mentor on Father’s Day, and the tale that he had been informed of receiving the National Natural Science Award but been waiting till after the October State Council signing event to give his mentor a surprise, but it was all too late:
“陈铭俊老师：今天我也是60 岁的人了，这几年送走了好几位亲戚朋友，半年前才送走了我母亲，也在这里 ，但都没有觉得像今天那样伤心 。。。(哭泣-编者注) 这里的年轻同学们可能不知道，我和陈铭俊老师的关系非常特殊。简单说来，没有陈铭俊老师的过去，也就没有我陈关荣的今天。。。(哭泣–编者注) 陈铭俊老师：本来，我今年获得了国家自然科学奖，打算到十月份国务院签字以后再告诉您，给您一个惊喜，但都来不及了 。。。(又是哭泣–编者注) 幸好今年父亲节的时候，还见到过您最后一面。当时您对我说的最后一句话是：“陈关荣，只要您还有一口气，就不要停止（工作）。” 陈铭俊老师：我不会停止的……”
(“现场播报:陈关荣致陈铭俊的悼词”, guosheng.sunbo9.net)
English translation of the above quote:
Teacher Chen Mingjun: Today I am also a 60-year-old person, in the last few years I bid farewell to several of my relatives and friends, and six months ago to my mother, also here [at the cemetery’s farewell hall], but none felt as sad as it is today. . . (crying – editor’s note) Young students here may not know, that my relationship with Teacher Chen Mingjun was very special. Simply put, without Teacher Chen Mingjun’s past, there would not be I Chen Guanrong’s today. . . (crying – editor’s note) Teacher Chen Mingjun: Originally, this year I received the National Natural Science Award, and intended to wait until after the October State Council signing before telling you, to give you a surprise, but it is all too late. . . (again crying – editor’s note) Fortunately on Father’s Day this year, I got to see your one last time. At that time the last sentence your said to me was: “Chen Guanrong, as long as you still have a breath, do not stop (working).” Teacher Chen Mingjun: I will not stop……
Ron won one of the second prizes, i.e., second-class awards, in 2008 and went on to win another second-class award in 2012.
(“IAS Benjamin Meaker Visiting Professor: Guanrong Chen, June-August 2013”, Institute for Advanced Studies, University of Bristol; and, “Staff Achievements”, Department of Electronic Engineering, City University of Hong Kong)
Ron has dedicated a 2010 book he co-edited, Evolutionary Algorithms and Chaotic Systems, “to the memory of his mentor Professor Mingjun Chen (1934-2008).”
After his UC Berkeley retirement, in 1995 my former Ph.D. adviser Stephen Smale became a University Distinguished Professor – a type of prominent professorship former U.S. President Jimmy Carter holds at Emory University as in Part 3 – at City University of Hong Kong, before Ron Chen moving there in 2000 and founding the Center for Chaos and Complex Networks – Smale had been a founder of the mathematical theory of chaos in the 1960s.
(“Finding a Horseshoe on the Beaches of Rio”, by Steve Smale, 1998, Volume 20, Number 1, The Mathematical Intelligencer; “Prof. Stephen SMALE (史梅爾)”, City University of Hong Kong; and, “Guanrong (Ron) Chen, Director”, Center for Chaos and Complex Networks, City University of Hong Kong)
By 2003, an international symposium held in Shanghai, China, listed Smale as an honorary chairman of its organizing committee, and Guanrong Chen the vice chairman, and assured international scientists that China, Shanghai especially, was now safe from the SARS epidemic:
“Now SARS is under well control in China. WHO announced on June 24 that WHO had canceled its warning for traveling to Beijing – the last city in the mainland of China, and Beijing now is also not in the list of SARS infected areas again. Thus, people can travel all over China safely now. Even in the worst days, Shanghai has always been lucky. No people were really infected in Shanghai (except one who is the father of a patient coming back from southern China and was infected there). No doctors and nurses were infected in Shanghai. The total number of SARS patients were 8. There is no identified patient or suspect now. …
…
Honorary Chairs:
Chaohao Gu, Fudan University, China
Stephen Smale, University of California at Berkeley, USA
General Chairs:
Gaolian Liu, Shanghai University, China
A. Jameson, Stanford University, USA
Vice Chairman:
Guanrong Chen, City University of Hong Kong, China”
SARS was of course scarier and deadlier than cancer.
Chen and Smale coming together was a tale of convergence of separate figures from my SYSU days and Berkeley days – not known to have been connected back then.
Back in August 1982 when Ron and I went to the United States, there was not yet Smale in the picture. Unlike Ron, I was going to a school where no math professor was an expert in spline function theory or the more general approximation theory, in which Ron had done his masters’ thesis and I my bachelor’s thesis under Yuesheng Li.
I had to start afresh.
In the spring of 1982, Prof. Li had seriously advised that when I got to Berkeley I should pursue my Ph.D. study under Professor Alexandre Chorin, a leading expert on the computation of fluid dynamics, whose “random vortex methods” Li had taught us during his precious teaching time outside of his department chair duties. Influenced by his Soviet math training, Li deemed fluid dynamics very important. He also told me that Chorin was of a Soviet Union-related background and received substantial research funding.
To earn a Ph.D. at a world-leading mathematics program I needed to learn the comprehensive basics in order to have a solid foundation. The mathematics of fluid flows centered on the subject of “partial differential equations”, i.e., equations involving not only derivatives – calculus of variations of mathematical functions – but derivatives in space of 3 dimensions, plus a time dimension. I had learned some at the advanced undergraduate level, but the research specialties of Yuesheng Li and Mingjun Chen had been in “ordinary differential equations”, i.e., in only one spatial dimension.
However, at Berkeley I soon found out that Chorin did not really do the mathematics of partial differential equations: he led a large group of students and researchers doing experimental computing of fluid dynamics equations.
More so than Ron Chen utilizing his specialty since his graduate school days, Chorin had practiced his specialty of fluid-dynamics computing since before graduate school, and his focus was not too mathematical as he has admitted in a recent interview:
“… Born in Poland only a few years before Hitler’s invasion, Chorin is no stranger to a different sort of flight: his family fled through Lithuania and Russia before spending 10 years in Israel and 11 years in Switzerland. By the time Chorin came to the United States for graduate study at the age of 23, he had already started working on the front line of computational mathematics, programming algorithms to solve equations describing ocean tides. Over the last half century, Chorin has tackled questions relating to the motion of fluids—some of the most challenging problems in applied mathematics.
Chorin developed computational methods that are used not only to study the flow of air around aircraft wings, but also the innards of combustion engines, the movement of blood through the heart, and the formation of stars. …
AL: When did you decide to study math?
AC: When I was a small kid, some distant relative of ours (whom I’ve never been able to find as a grown-up) used to ask me math questions, and decided I was good at math. If you asked me when I was seven or eight what I wanted to do, I would have said I wanted to be a mathematician. In Israel I’d been in the gifted program. In Switzerland, I was a fairly mediocre student. My grades did not qualify me to study math. So I studied engineering instead. In college, I did very well in math and got lots of encouragement, so I went back to it.
AL: Do you think that detour into engineering drew you to be in applied math rather than pure math?
AC: Oh, it’s very likely. Actually, at the end of engineering school I intended to be in pure math… but in Israel I was a programmer for someone who did numerical analysis for physics problems, and I got enamored with it.
AL: I’m sure you’ve seen the field of applied math change over the course of your career.
AC: It’s changed tremendously! The words “applied math” are too vague—I do mostly computational mathematics, and that has changed a lot. In fact, it is getting more distant from math. When I was a student, the computational issue was “How do you approximate [this] partial differential equation?” That’s a math question. Nowadays, we’ve been successful, so you can ask much more specific questions which are less mathematical. …”
(“ALEXANDRE CHORIN”, by Anna Lieb, April 29, 2015, Berkeley Science Review)
As quoted above, Chorin wasn’t from the Soviet Union but a Polish Jew escaping Nazi occupation by way of the Soviet Union. Nevertheless I wasn’t the only one with a misconception about his origin, as even his former Ph.D. adviser, Professor Peter Lax – a colleague of Louis Nirenberg’s – at NYU’s Courant Institute, had mistaken Chorin for a Hungarian compatriot:
“… In a fateful chance encounter on the street, he met his former teacher, de Rham, who advised him to pick a school in the United States and wrote letters on his behalf. De Rham counseled him, in particular, to study with another famous mathematician, Peter Lax, at New York University’s Courant Institute. Courant was then what Chorin calls the “mother ship” of computational and applied math. …
Lax, now 87 and a professor emeritus at Courant, recollects being initially drawn to Chorin because of a misunderstanding. Lax thought that Chorin was a fellow Hungarian emigré because there was a very prominent family named Chorin in Hungary. But Chorin’s original Polish surname was Choroszczański; the family had changed it in Israel. (In contrast, he never Anglicized his French first name because he wanted to avoid being confused with another fluid-mechanics researcher whose first name was “Alexander” and whose surname was similar to Chorin.)”
(“Science Lives: Alexandre Chorin”, by Douglas Steinberg, May 8, 2014, Simons Foundation)
In contrast to Stephen Smale whose anti-war history had risked his eligibility for U.S. National Science Foundation grants as in Part 2, Chorin’s research received substantial U.S. military funding, such as acknowledged in his 1973 papers, partly collaborated with his Berkeley student Peter S. Bernard, that established his “vortex methods”:
“… the Office of Naval Research under Contract no. N00014-69-A-0200-1052.”
(“Numerical study of slightly viscous flow”, by Alexandre Joel Chorin, 1973, Volume 57, Part 4, Journal of Fluid Mechanics, and, “Discretization of a vortex sheet, with an example of roll-up”, by Alexandre Joel Chorin and Peter S. Bernard, November 1973, Volume 13, Issue 3, Journal of Computational Physics, in Alexandre Joel Chorin, Computational Fluid Mechanics: Selected Papers, 1989, Academic Press)
That was a navy grant, a type mentioned in Part 2 about John Nash’s former MIT senior colleague, former Communist party member Norman Levinson, who in the 1960s held both NSF and navy grants.
Still, Lax described Chorin as “very independent”:
“Even though Chorin turned out not to be Hungarian, Lax recounts that once he got to know him, “I thought highly of him. He had a very lively mind.” Lax also notes that Chorin “was always very independent.” …”
In my impression Chorin was a proud loner, often strolling alone with his German Shepherd or a pet like it. His “lively” comment about the United States, “as if I belonged”, drew remarks from President Barack Obama on November 20, 2014, when awarding the National Medal of Science to Chorin and others:
“After he came here as a foreign student from Israel, Eli Harari co-founded SanDisk with two colleagues, one from India, another from China. Alexandre Chorin, whose accomplishments led to a sea change in the way a generations of mathematicians use computers, sums up his experience this way: “I came here as a foreigner on an American fellowship, received the opportunity to study at great schools and work at great universities, and have been treated as if I belonged.”
Treated as if I belonged. You do belong — because this is America and we welcome people from all around the world who have that same striving spirit. We’re not defined by tribe or bloodlines. We’re defined by a creed, idea. And we want that tradition to continue. But too often, we’re losing talent because — after the enormous investment we make in students and young researchers — we tell them to go home after they graduate. We tell them, take your talents and potential someplace else.”
(“Remarks by the President at National Medals of Science and National Medals of Technology and Innovation Award Ceremony”, November 20, 2014, The White House)
Look, “a foreigner on an American fellowship” was clearly treated better than ones like Ron Chen arriving on a teaching assistantship, let alone others like me.
In fact, receiving a National Medal at 76 while active as one of only 24 University Professors in the entire University of California, including UC Berkeley, UCLA, UC San Diego and UC Riverside mentioned in earlier Parts, and other campuses, Chorin has belonged to the U.S. more than Smale.
Smale received a National Medal of Science after he had retired from Berkeley and gone to CityU of Hong Kong – in 1996 along with Richard Karp and 6 others nationally, from President Bill Clinton:
“Also receiving a medal was Stephen Smale, 66, a professor, emeritus, of mathematics at the University of California, Berkeley. Smale, who now conducts research and teaches at the City University of Hong Kong, was cited “for four decades of pioneering work on basic research questions which have led to major advances in pure and applied mathematics. He is responsible for formulating key definitions, proofs, and conjectures which have energized an ever-growing number of mathematicians and scientists.””
(“Eight Researchers Accept The National Medal Of Science For 1996”, by Thomas Durso, August 19, 1996, The Scientist)
Nonetheless, Obama chose a well-suited example to make his point, which must have felt personal because his own father, Barack Obama, Sr., had studied at the University of Hawaii in Honolulu and then earned a graduate degree at Harvard University but eventually returned to Kenya, where his intellectual goals were never realized. I wrote about this history in a November 2009 blog post:
“Barack Obama, Sr. had left Kenya at age 23 to study at the University of Hawaii (the same age also for me when I went to study in the U.S., but I later taught at the University of Hawaii…), where he met and married President Obama’s mother and produced a future U.S. president – the only one from Hawaii; he then went to study at Harvard, met Mark Ndesandjo’s mother and returned to Kenya with her, where Mark was born.
…
In 1963 when his father left him and his mother Stanley Ann Dunham, a white student at the University of Hawaii born in Kansas and grown up in various parts of the continental United States, Barack Obama was only two-years-old; neither side of his parents’ families had approved of the interracial marriage, which at the time was legally permitted in Hawaii but not in 22 other states in the United States. Barack’s mother later remarried an Indonesian student and took Barack to that country after her husband was summoned back to his home country following the rise to power of military strongman Suharto, sending Barack back to Hawaii to live with the grandparents when she wanted a good education for her son at the prestigious Punahou School in Honolulu, which Barack liked better than schooling in Indonesia.
It could be Kenyan presidential politics as Barack Obama described in his 1995 book, or the economy of life in Africa, or still something more, that his ambitious, U.S.-educated economist father later suffered career setback in Kenya and became an alcoholic and physical abuser…”
(““Nairobi to Shenzhen”, and on to Guangzhou (Part 1)”, November 22, 2009, Feng Gao’s Blog – Reflections on Events of Interest)
Another well-suited reason for Obama’s remarks on Chorin’s lively comment, from my vantage point, is that Chorin had been the Ph.D. adviser of Nathaniel Whitaker I knew at Berkeley, one of the few African-American mathematics Ph.D. students in the U.S., as I noted in a February 2013 blog post:
““Whitaker” is reputed to be one of the most ancient Anglo-Saxon names, traceable in the written records to the 11th-12th centuries or earlier, with “white acre” and “wheat acre” being its origin…
Back in my UC Berkeley days there was a fellow graduate student one year ahead of me by the name of Nathaniel Whitaker, except that he was African American so I don’t know how his name had been inherited. …
Nate and my classmate friend Paul Wright … were among a very small number of African American Mathematics Ph.D. students in the United States.”
(“Guinevere and Lancelot – a metaphor of comedy or tragedy, without Shakespeare but with shocking ends to wonderful lives (Part 2)”, February 28, 2013, Feng Gao’s Posts – Rites of Spring)
At Berkeley I continued to think of Chorin as of Russian Jewish background, and that the only Polish mathematician I knew in the early 1980s was a visiting assistant or associate professor whose name I have not been able to recall, who taught the first-semester graduate course on set theory and topology, was very friendly and wrote a strong letter of recommendation for my application for the foreign student tuition waiver and teaching assistantship.
Another basic course, on measure theory and functional analysis, was a second-semester continuation of it and was taught by a strict Prof. William Bade, the department’s vice chair of graduate affairs from whom obtaining the tuition waiver and teaching assistantship was not easy for me.
My Berkeley roommate Kezheng Li, as in Part 2 a senior math graduate student who gave me considerable help, for his Ph.D. studied algebraic geometry, a specialty field within algebra, the latter an important basic subject on which I took another 2-semester course.
The first semester of algebra was taught by a retired professor, Gerhard Hochschild, an easygoing teacher from whom most students expected good grades.
The second semester was taught by another senior professor, Abraham Seidenberg, a demanding teacher who gave a final exam so long that it came like a shock; learning the Galois theory for the first time I could not finish the exam, but the final grade wasn’t too bad as many students didn’t finish.
An interesting episode about Seidenberg, a narcissistic version of Albert Einstein in his looks, happened near the end of the last class when students were filling out teaching evaluation forms, a time when the professor was supposed to be absent and a student would bring the evaluations to the department: Seidenberg not only stayed in the classroom but took peeks into the filled-out forms on the lectern, sometimes as a form was being placed there by a student.
I would encounter this kind of intimidating antic only one more time, as in Part 1 by UBC computer science department head Maria Klawe in February 1992, when she insisted on staying in the room for a faculty meeting that would hear my grievance about her management.
The first time was easier and the second time harder – that seemed to be a pattern in my experience, not just for these two 2-semester courses.
The other 2-semester course I took was partial differential equations – as mentioned important for my anticipated future study – taught by Professor Tosio Kato.
An exemplary scholar, Kato’s presentation was detailed and thorough, yet covering a broad range of topics of interest, especially impressive when his own education had been in physics. S. T. Kuroda, a former physics student of Kato’s at the University of Tokyo, had had a similar experience:
“My recollection of Kato goes back to my younger days when I attended his course on mathematical physics at the Department of Physics, University of Tokyo. It was 1953–54. The course covered, thoroughly but efficiently, most of the standard material from the theory of functions through partial differential equations. The style of his lecture never gave an impression that he went quickly, but at the end of each class I was surprised by how much he had covered within one session.”
(“Tosio Kato (1917–1999)”, by Heinz Cordes, Arne Jensen, S. T. Kuroda, Gustavo Ponce, Barry Simon, and Michael Taylor, June/July 2000, Volume 47, Number 6, Notices of the American Mathematical Society)
Recall, as in Part 2, the tale of John Nash’s Princeton Ph.D. work in game theory in the early 1950s, that later won him the Nobel Prize in Economics: Nash’s original idea was dismissed by John von Neumann, a powerful mathematician who had founded game theory but become preoccupied with nuclear bomb development and advising U.S. military leaders; David Gale, later a UC Berkeley math professor I worked as a teaching assistant for, then encouraged Nash to pursue the idea for his Ph.D. thesis.
Half a world away in Japan, Kato’s entrance into advanced mathematical research also had a von Neumann factor, in this case von Neumann’s acceptance of Kato’s work on Hamiltonian operators, and a World War II wartime factor. The story was told by the mathematical physicist Barry Simon in 2000, in memory of Kato who had passed away in October 1999:
“Kato’s most celebrated result is undoubtedly his proof, published in 1951 [K51a], of the essential self-adjointness of atomic Hamiltonians:
…
In a case of scientific serendipity, J. von Neumann concluded his basic work on the theory of unbounded self-adjoint operators just as quantum theory was being invented, and he had realized by 1928 that the critical question was to define the Hamiltonian as a self-adjoint operator. Kato proved that the operator … defined initially on smooth functions of compact support, has a unique self-adjoint extension (and he was even able to describe that extension).
I have often wondered why it took so long for this fundamental question to be answered. As Kato remarks in his Wiener Prize acceptance [K80], the proof is “rather easy.” … I would have expected Rellich or K. O. Friedrichs to have found the result by the late 1930s.
One factor could have been von Neumann’s attitude. V. Bargmann told me of a conversation he had with von Neumann in 1948 in which von Neumann asserted that the multiparticle result was an impossibly hard problem and even the case of hydrogen was a difficult open problem (even though the hydrogen case can be solved by separation of variables and the use of H. Weyl’s 1912 theory, which von Neumann certainly knew!). Perhaps this is a case like the existence of the Haar integral, in which von Neumann’s opinion stopped work by the establishment, leaving the important discovery to the isolated researcher unaware of von Neumann’s opinion.
Another factor surely was the Second World War. … In [K80] Kato remarks dryly: “During World War II, I was working in the countryside of Japan.” In fact, from a conversation I had with Kato one evening at a conference, it was clear that his experiences while evacuated to the countryside and in the chaos immediately after the war were horrific. He barely escaped death several times, and he caught tuberculosis. …
Formally trained as a physicist, Kato submitted his paper to Physical Review, which could not figure out how and who should referee it, and that journal eventually transferred it to the Transactions of the American Mathematical Society. Along the way the paper was lost several times, but it finally reached von Neumann, who recommended its acceptance. The refereeing process took over three years.”
(Heinz Cordes, Arne Jensen, S. T. Kuroda, Gustavo Ponce, Barry Simon, and Michael Taylor, June/July 2000, Notices of the American Mathematical Society)
I can understand the “von Neumann’s attitude” factor leading to a long delay of a mathematical discovery, as can be glimpsed also in Nash’s case. But I can’t quite agree with Simon’s take of the “Second World War” factor: Kato’s difficult life during that time no doubt was a delay to Japanese research in mathematical physics, but wouldn’t that have allowed researchers in the West to achieve Kato’s “most celebrated result” first – had it not been for von Neumann’s oppressive or authoritarian influence?
A different biography of Kato seemed to deemphasize the devastation of World War II to his research career:
“… In 1941 he earned his bachelor’s degree from the University of Tokyo, commencing a relationship that would last two more decades. After a year away Kato rejoined the University of Tokyo in 1943 to start his teaching career while also pursuing a doctorate there. In 1944 he married Mizue Suzuki. In 1951 he became a doctor of science, and the same year he became a full professor. In 1962 he immigrated to the United States to accept a professorship at the University of California at Berkeley from which he retired in 1989.
In 1949, while still working on his doctorate, Kato published one of his early important papers, “On the Convergence of the Pertubation Method, I, II” in Progressive Theories of Physics. …”
(Elizabeth H. Oakes, Encyclopedia of World Scientists, 2007, Infobase Publishing)
In 1942, the year of the Midway naval battles and the year Kato was away from his university, there was no real war in Japan proper, whatever the reason for his evacuation to the countryside; and in the year 1944 when war was closing in on Tokyo, Kato got married.
Having studied with Prof. Kato, I would not make the kind of leap of logic Prof. Barry Simon did.
Well, unless there was no choice, I suppose. As in the pattern of the second being harder, near the end of the second semester Kato gave the students a list of, I have forgotten how many, probably 7 or 8 problems, and several weeks of time for each to independently solve 3 of them. One of them, in topology, had been posed in class weeks earlier and a few days later I had gone to his office and communicated a solution to him; and another I soon solved; but for a third problem, I went around the rest, worked on several of them in some details, and did not obtain any complete solution with full confidence – in the end I also handed in what I got for one of the others, no doubt with leap of logic somewhere.
As the first year ended, I liked partial differential equations well enough that I was contemplating Ph.D. study under Kato.
In the summer of 1983, on July 11-29 at UC Berkeley there was a major international conference partially funded by the NSF, Summer Research Institute on Nonlinear Functional Analysis and Its Applications, on a subject with deep connections to partial differential equations. The organizing committee consisted of Kato, Felix Browder and Louis Nirenberg – 2 senior mathematicians mentioned in Part 2 in relation to John Nash – French mathematicians Haim Brezis and Jacques-Louis Lions, and Paul Rabinowitz of the University of Wisconsin.
I attended the plenary presentations and paid special attention to one by Paul Rabinowitz, partly because he was a Wisconsin-Madison colleague of Carl de Boor whom my undergraduate adviser Yuesheng Li had highly recommended, and he had the same last name as Philip Rabinowitz in the numerical analysis field of my undergraduate study. Later in 1997 when de Boor was elected to the National Academy of Sciences and Rabinowitz received the George David Birkhoff Prize in Applied Mathematics, their department’s newsletter gave informative introductions of the two:
“Carl de Boor, Professor of Mathematics and Computer Sciences, was among the 60 scholars elected this year to the National Academy of Sciences. Carl grew up in East Germany and received the PhD from the University of Michigan in 1966. …
… Splines were introduced in the 40’s (by the late I.J. Schoenberg of Wisconsin) as a means for approximating discrete data by curves. Their practical application was delayed almost twenty years until computers became powerful enough to handle the requisite computations. Since then they have become indispensible tools in computer-aided design and manufacture (cars and airplanes, in particular), in the production of printer’s typesets, in automated cartography… Carl is the worldwide leader and authority in the theory and applications of spline functions. His contributions have been more fundamental and numerous than any other researcher in this field, ranging from rigorous theories through highly efficient and reliable algorithms to complete software packages. Carl has made Wisconsin-Madison a major international center in approximation theory and numerical analysis…
…
Professor Paul Rabinowitz has been awarded by the American Mathematical Society (AMS) and the Society for Industrial and Applied Mathematics (SIAM), the 1998 G.D. Birkhoff Prize for his outstanding contributions to mathematics. … Paul received the PhD in Mathematics from New York University in 1966…
The citation for the Prize reads in part:
“Perhaps more than anyone else Paul Rabinowitz has deeply influenced the field of non linear analysis. His methods for the analysis of nonlinear systems has changed the way we think of them. … Paul Rabinowitz broke new ground to invent general mini-max methods for problems not necessarily satisfying the Palais-Smale [compactness] condition and that are indefinite. …
He has also introduced the use of sophisticated topological tools to obtain multiple solutions of nonlinear problems. Rabinowitz is a powerful mathematician who combines abstract mathematics with concrete applications to problems arising in various fields.””
(“Van Vleck Notes: Dedications, Honors and Awards …”, Fall 1997, Department of Mathematics, University of Wisconsin)
At the summer 1983 Berkeley conference, Rabinowitz’s powerful mathematical theorem, the “Mountain-Pass Lemma”, was a focus of interest, even though the conference proceedings’ titles showed that term only in another researcher’s paper, “The topological degree at a critical point of mountain-pass type” by Helmut Hofer; the titles also referred to the “Palais-Smale condition” bearing the name of Berkeley’s Stephen Smale, in one paper, “A generalized Palais-Smale condition and applications” by Michael Struwe.
(Felix E. Browder, ed., Nonlinear Functional Analysis and Its Applications, 1986, Volume 45, Part 1, Proceedings of Symposia in Pure Mathematics, American Mathematical Society)
As I recall, Peking University professor and Berkeley visiting scholar Gongqing Zhang (張恭慶) attended the conference. Several Chinese mathematicians presented papers, prominent among them Jilin University professor Zhuoqun Wu (伍卓群) – a 1950s classmate of Yuesheng Li’s.
(Felix E. Browder, ed., 1986, American Mathematical Society)
Just prior to the Fall 1983 semester I passed the Preliminary Examination, the required written exam for the Ph.D. program. Kezheng had helped me over the summer by having me study previous prelim exam problems, discuss with him and hear his insights on the fine points. Kato happened to be the examiner, and though I did not fully solve all the problems in a long list, I did pretty well.
The oral Qualifying Examination remained, to be taken in front of a committee after a Ph.D. adviser was chosen.
Prof. Kato was generous. When I went to his office, likely shortly after passing the Prelim Exam, to ask him to be my Ph.D. adviser, he told me that he was retiring, but would give me a research assistantship for one semester while I looked for a younger, more research active Ph.D. adviser – it was very helpful as my teaching assistantship did not start until the spring semester of the 1983-1984 academic year – and he also advised that, given my interest in the mathematics of computation more than in computing, Andrew Majda or Stephen Smale would be the choice.
Except the more junior Polish visiting professor, it had been a distinguished group of senior professors teaching these basic graduate courses in 1982-1983: Tosio Kato was a 1980 winner of the Norbert Wiener Prize, a leading prize in applied mathematics awarded jointly by the American Mathematical Society and the Society for Industrial and Applied Mathematics – Alexandre Chorin later received it in 2000 – while Gerhard Hochschild was a 1980 winner of the Leroy P. Steele Prize for his research, a leading prize awarded by the AMS – John Nash later received it in 1999.
(“The Leroy P Steele Prize of the AMS”, MacTutor History of Mathematics archive; and, “The Norbert Wiener Prize”, Society for Industrial and Applied Mathematics)
So 5 years before taking Karp’s advice regarding a faculty job at UBC or SFU, I followed Kato’s advice in finding a Ph.D. adviser.
Kato’s advice was sensible. From a background in partial differential equations and computation, Chorin would have been the choice had I liked programming and computing more than the mathematics.
The next professor who did research in mathematics in relation to fluid dynamics computation was Ole Hald. In 1978, Hald and collaborator Vincenza Mauceri Del Prête were the first to prove some desirable property of convergence, i.e., that the computed approximate solutions would converge to the true solution, for Chorin’s random vortex methods:
“Introduction. In this paper we will prove the convergence of Chorin’s vortex method for the flow of a two dimensional, inviscid fluid. …
…
The convergence of Chorin’s method has already been considered by Dushane [4]. However, his proof is incorrect… Our proof follows the general outline of Dushane but introduces two new ideas. …
In one respect our result is less than satisfying. It can be shown that the solution of the Euler equations for a two dimensional flow exists for all time (see Wolibner [14], McGrath [7] and Kato [6]). However, we have only been able to prove the convergence of Chorin’s method for a small time interval. …”
(“Convergence of Vortex Methods for Euler’s Equations”, by Ole Hald and Vincenza Mauceri Del Prête, July 1978, Volume 32, Number 143, Mathematics of Computation)
Look, someone else did the mathematics for Alexandre Chorin.
I recall it was also in the Fall of 1983 that I took a numerical matrix computation course taught by Hald, did erratically with the large amount of hand calculations, and received a B-level grade – any C-level grade would disqualify a student from the Ph.D. program.
Something I heard might give insight to Ole Hald’s conscientiously demanding attitude about subtle details. My classmate Mei Kobayashi, daughter of Prof. Shoshichi Kobayashi – as cited in Part 2 in the 1960s he had applied for NSF grants together with Smale – told me that Hald’s wife was a former fashion model and their car was not only vacuumed very clean but delicately treated with fragrance.
I don’t know if Mei’s observation was accurate but like Chorin, Hald had earned his Ph.D. from NYU’s Courant Institute; also, Catherine Willis, Hald’s Ph.D. graduate prior to Mei, became a financial analyst at the Wall Street investment firm Kidder-Peabody after working for the U.S. Geological Survey.
(“Catherine Willis: Modeling the World of High Finance”, 1991, Association for Women in Mathematics; Anna Lieb, April 29, 2015, Berkeley Science Review; and, “Ole Hansen Hald”, Mathematics Genealogy Project)
Mei’s Ph.D. thesis, which I helped proofread, was titled “Discontinuous Inverse Sturm-Liouville Problems with Symmetric Potentials”. I had first encountered inverse problems for partial differential equations in Stony Brook professor Yung Ming Chen’s lecture at SYSU; at the time, Ron’s master’s classmate Luoluo Li (黎羅羅) worked on trigonometric spline functions, but my bachelor’s thesis turned out to do better in that subject, and Li then switched to the inverse problems.
Mei was a Princeton graduate and liked to boast she had been a Princeton cheerleader, adding, “actually I was a pom pom” – I obviously knew about cheerleaders, but Mei would explain that “pom poms” were ones lifted up by the cheerleaders.
After Hald, the next professor who came to Berkeley and did research in the mathematics of fluid dynamics equations was Andrew Majda.
Like Hald, Majda did research related to Chorin’s vortex methods; in the early 1980s he and collaborator J. Thomas Beale introduced a new class of vortex methods improved over Chorin’s, and proved their excellent convergence property:
“… The methods of Leonard and Del Prête require a large amount of detailed information … On the other hand, the three-dimensional vortex blob method recently introduced by Chorin [4], [5] is more flexible and requires less information. … Can such a “crude” three-dimensional vortex algorithm accurately represent fluid flows?
In the work presented here, we answer this question affirmatively. We formulate below a new class of three-dimensional vortex methods and then prove that these 3-D vortex methods are stable and convergent with arbitrarily high order accuracy. In these new algorithms, we update the velocity crudely in a fashion completely analogous to the 3-D vortex blob method of Chorin; however, unlike the algorithm in [4], we incorporate the vortex stretching through a Lagrangian update. …”
(“Vortex Methods. I: Convergence in Three Dimensions”, and, “Vortex Methods. II: Higher Order Accuracy in Two and Three Dimensions”, by J. Thomas Beale and Andrew Majda, July 1982, Volume 39, Number 159, Mathematics of Computation)
Majda’s sense of ‘smarterness’ – than Chorin, that is – was brimming in the above quote.
As in Part 2, in the fall of 1983 I asked Smale to be my Ph.D. adviser and he said yes. At the time I was taking Smale’s graduate topics course, and I was also taking Majda’s seminar course, who said he was in the process of moving to Princeton and would not accept new students – unless taking me to Princeton along with his current Ph.D. students, that he might.
I told Smale that I would opt for Princeton if I could but otherwise at Berkeley he would be my adviser, and it was okay with him.
In an October 2010 blog post I recalled Majda’s strong temperament:
“Prof. Andrew Majda was known for his strong temperament, and the year I was auditing a graduate class from him he was in the process of moving to Princeton which had made him an important job offer. Near the Berkeley classroom there was construction work going on at the time and the noise sometimes got really loud, and Majda would burst into tantrums like, “It’s driving me crazy, they are driving me out of Berkeley.””
(“Team Canada female athletes disqualified from Commonwealth silver medal, jailed Chinese democracy activist awarded with Nobel peace prize, and others in between (Part 1) — when democracy can be trumped by issue-based politics”, October 8, 2010, Feng Gao’s Blog – Reflections on Events of Interest)
The show of temper cited above was during a graduate class on solutions of partial differential equations, not the seminar course.
The seminar course saw Majda present the basics of equations for fluid flows with shock waves, pose a long list of open problems, and then schedule the students to give presentations, either on their research or surveying other researchers’ works.
To me who had not studied shock waves before, Majda handed a paper by Tai-Ping Liu, a University of Maryland mathematician, pointed to the last paragraph that had claimed a result without giving the proof, and asked me to present the proof.
Prof. Tai-Ping Liu had done significant pioneering work on shock waves, such as in a 1982 paper titled, “Nonlinear Stability and Instability of Transonic Flows Through a Nozzle”, that also referenced past key papers in the field.
(“Nonlinear Stability and Instability of Transonic Flows Through a Nozzle”, T.-P. Liu, 1982, Volume 83, Communications in Mathematical Physics)
I went through the thrust of the paper Majda provided, the relevant references listed in the paper, and what I thought were relevant sections of a book Majda lent me, Shock Waves and Reaction-Diffusion Equations by Joel Smoller, in search of mathematical lemmas and theorems that might serve as basis to prove that claim. I did not find any obviously useful ones, and settled on trying to tackle it through some mathematical techniques I had learned.
What I came up with was not a full proof, but I decided to present it in the seminar course as my result. As scheduled my presentation was the last of the semester, and I started with an overview on the physics background, the differential equations, the problem and the claim, and only halfway into my proof the class time was up; others left, Majda asked me what the rest was, I mentioned the techniques to him, and he said, “That’s an original idea, but the proof is harder than that” – I knew but just hadn’t reached the end to show the deficiency.
Majda then said, “since you want to study with Smale, I am not going to take you to Princeton”.
Something about “inequalities”, perhaps? It might be Majda’s polite way to say that I wasn’t technically strong enough for his liking.
Nevertheless, previously when I mentioned to him that if he did not take me to Princeton I would study with Smale, Majda would become visibly uncomfortable, and once stated, “Steve Smale is a great mathematician, but he knows nothing about numerical analysis”.
Majda might not care much about Smale, but what choices did I have at Berkeley?
At the time other than Chorin, Hald and Majda, there were only two Berkeley mathematics professors with significant research in computational mathematics of differential equations: Paul Concus and Keith Miller, both with Ph.D. earlier than Chorin’s.
Paul Concus was not active at all when it came to producing Ph.D. students. A senior scientist at Lawrence Berkeley National Laboratory but only an adjunct professor, in his entire academic career since receiving his Harvard Ph.D. in 1959 under adviser George Francis Carrier, Concus has produced only one Ph.D. graduate: Anne Greenbaum in 1981.
(“Capillary Surfaces in Microgravity”, by Paul Concus and Robert Finn, in Jean N. Koster and Robert L Sani, eds., Low-Gravity Fluid Dynamics and Transport Phenomena, 1990, American Institute of Aeronautics and Astronautics, Inc.; and, “Paul Concus”, Mathematics Genealogy Project)
In contrast, from 1986 to 1995 Chorin served as head of the LBNL mathematics department where Concus was a senior scientist, and in that period at least 11 Ph.D.s graduated under his Berkeley professorship from 1987 to 1995.
(“Alexandre Chorin”, Lawrence Berkeley National Laboratory; and, “Alexandre Joel Chorin”, Mathematics Genealogy Project)
Keith Miller was better than Paul Concus in producing Ph.D. students, 4 of them in the 1970s after receiving his Ph.D. in 1963 from Rice University. But during the entire 1980s Miller produced only one Ph.D. student: Steve Oslon in 1986.
(“C. Keith Miller”, Mathematics Genealogy Project)
So shouldn’t Miller have time to take in another Ph.D. student or two? Not necessarily. The personal experience my classmate Robert Rainsberger told me, that of Miller’s rejection of his quest to be Miller’s Ph.D. student, revealed something stern yet preferential.
Miller specialized in the finite element method for solving partial differential equations, fluid dynamics in particular, and was the only Berkeley math professor to have the finite elements as the primary expertise.
Robert was a returning student, with prior U.S. air force experience, a University of Illinois degree in 1979, and computational work background at the Lawrence Livermore National Laboratory, about 40 miles from Berkeley. He enrolled at Berkeley mathematics department’s Ph.D. program while continuing to work part-time at LLNL, and we took Kato’s course together; he told me he was interacting with Miller, possibly doing some project if I recall correctly.
Then at some point after I had become Smale’s Ph.D. student, Robert told me that Miller stated if he continued to work at LLNL Miller would not be his Ph.D. adviser, because the national lab was involved in weapons research.
Disappointed, Robert eventually found Heinz Cordes, who like Kato was an older professor and whose expertise was in differential equations and operators, but not in computation, as his adviser. A 1987 book by Cordes on differential operators acknowledged Rainsberger’s help in proofreading; and Rainsberger’s thesis was titled, “On L2 Boundedness of Pseudo-Differential Operators”.
(Heinz Otto Cordes, Spectral Theory of Linear Differential Operators and Comparison Algebras, 1987, Cambridge University Press; and, “Robert Bell Rainsberger”, Mathematics Genealogy Project)
Robert’s Ph.D. study turned out to be mostly pure-math labor. Before and after, Robert’s work was in computation, particularly mesh generation applicable to CAD in general, according to his current biography at Stanford:
“Robert Rainsberger spent his earliest 4 years in the U.S. Air Force before entering the University of Illinois to earn his B.S. in mathematics in 1979. He was then employed by Lawrence Livermore National Laboratory for two years as a computer scientist before entered the University of California, Berkeley. In 1988 he received his Ph.D in mathematics. After completing his Ph.D., Dr. Rainsberger returned to Lawrence Livermore National Laboratory to continue working on 3D hexa mesh generation. During this same period, Dr. Rainsberger contracted to Control Data Corporation to develop the first versions of ICEM CFD. In 1991, Dr. Rainsberger founded XYZ Scientific Applications, Inc. where he remains the principle code developer of TrueGrid, President, and CEO of the corporation.”
(“Our People: Robert Rainsberger”, Stanford Composites Manufacturing Innovation Center)
A 2003 presentation by him at U.S. National Institute of Standards and Technology showed that a usage of Rainsberger’s mesh generation was in the finite element method for fluid dynamics:
“The first part of this expository talk is an introduction on some of the elementary and advanced techniques of mesh generation for finite element analysis. The second part describes a technique to form nearly orthogonal meshes based on the solution to various systems of elliptic partial differential equations in fluid dynamics, hydrodynamics, heat transfer, solid and structural mechanics in order to minimize lower order error terms. …
… He is currently a consultant to NIST Mathematical and Computational Sciences Division on developing finite element analysis codes for applications in the NIST World Trade Center (WTC) investigation project.”
(“MESH GENERATION FOR NON-LINEAR FINITE ELEMENT ANALYSIS”, by Robert Rainsberger, December 4, 2003, Information Technology Laboratory, National Institute of Standards and Technology)
The fall of the World Trade Center towers, which Robert studied in 2003, was not like fluid flow, though, but like crumbling rocks.
Some may comment that, given UC Berkeley’s strong anti-war tradition, Keith Miller was probably like Stephen Smale, in this case taking a stand against weapons research.
It appeared that way, until one learns about Miller’s next Ph.D. student, Andrew Kuprat, whose 1992 Ph.D. thesis was titled, “Creation and Annihilation of Nodes for the Moving Finite Element Method” – the kind of topic Rainsberger had wanted for his Ph.D. study.
(“Andrew Paul Kuprat”, Mathematics Genealogy Project)
What about Kuprat? Right after receiving his Ph.D. he became a computational scientist at Los Alamos National Laboratory in New Mexico, working extensively on high-energy physics:
“Dr. Kuprat is an expert at computational geometry, mesh generation, and the solution of partial differential equations using finite elements. His current interests include generation of optimized meshes for computational fluid dynamics simulations on human and animal airway and cardiovascular geometries, efficient schemes for conservatively mapping quantities in multiphysics simulations, and moving finite element methods for materials microstructure modeling. Dr. Kuprat was a primary developer of LaGriT (Los Alamos Grid Toolbox) at Los Alamos between 1994 and 2005. …
Education
- B.Sc., Mathematics and Physics – University of Victoria, Victoria Canada – 1984
- Ph.D., Mathematics – University of California, Berkeley – 1992
- Post-Doc, Plasma Physics – Los Alamos National Laboratory – 1992–1995
- Post-Doc, Mechanics of Materials – Los Alamos National Laboratory – 1995–1996
Positions and Employment
- 1996–2005 – Scientist, Los Alamos National Laboratory, Los Alamos, NM
- 2005–Present – Senior Scientist, Battelle/Pacific Northwest Division (PNNL), Richland, WA”
(“Andrew Kuprat, Ph.D., Adjunct Professor”, The Gene & Linda Voiland School of Chemical Engineering and Bioengineering, Washington State University, Pullman)
Much more than LLNL in weapons research, LANL was the original birthplace of atomic bombs, including the ones exploding over Hiroshima and Nagasaki, Japan, in 1945, and is the world’s leading nuclear weapons lab.
(“The U.S. Nuclear Weapons Complex: Major Facilities”, Union of Concerned Scientists)
Still, some may argue that Kuprat was a math and physics graduate from the University of Victoria, Canada, and so he might not have any prior weapons background – unlike Rainsberger – and if with his Berkeley Ph.D. he chose to work in LANL, his adviser Miller might not have expected that.
Well, Miller greeted his new Ph.D. graduate’s LANL job with acceptance and further collaboration, as indicated in the proceedings of a “physics computing” conference in Albuquerque, New Mexico, in 1993:
“Physics Computing ’93
The Division of Computational Physics will host Physics Computing’93 in Albuquerque, New Mexico, May 31 – June 4, 1993. Co-sponsors of the meeting, which will also be known as The 5th International Conference on Computational Physics, are the AIP journal Computers in Physics and the European Physical Society. The venue will be the Albuquerque Convention Center.
…
Tutorial Subjects
…
2D Moving Finite Elements: An Adaptive Grid Method for Computational Fluid Dynamics, Alan H. Glasser, Los Alamos National Laboratory, C. Keith Miller, University of California, Berkeley, and Andrew P. Kuprat, Los Alamos National Laboratory”
(“PHYSICS COMPUTING NEWS – SPRING 1993, Newsletter of the Division of Computational Physics”, American Physical Society)
See, Keith Miller went all the way to LANL’s heartland to participate in a tutorial on his specialty, surrounded by the nuclear weapons lab experts.
Even if Andrew Kuprat’s academic origin from Canada’s Victoria carried a magical aura of ‘peace’ – in contrast to Rainsberger’s U.S. air force and Illinois backgrounds – it wouldn’t be sufficient ground to justify his going all the way to become an expert at the world’s leading nuclear weapons lab and still enjoying (his Berkeley Ph.D. adviser’s) blessing of ‘peace’!
Perhaps not coincidentally, UC Berkeley had had a historical role in the invention of nuclear weapons, when the physicist Robert Oppenheimer founded LANL and led the atomic bomb development, as noted in my February 2013 blog post:
“The physicist Robert Oppenheimer, the director of IAS at Princeton with whom von Neumann discussed his pending move in 1956, had hailed from UC Berkeley to become “father of the atomic bomb”, leading the development of nuclear bombs at Los Alamos National Lab founded by him in northern New Mexico; Oppenheimer later also died of cancer, at the age of 63.”
(“Guinevere and Lancelot – a metaphor of comedy or tragedy, without Shakespeare but with shocking ends to wonderful lives (Part 2)”, February 28, 2013, Feng Gao’s Posts – Rites of Spring)
This was the Robert Oppenheimer who, as in Part 2, brought the Chinese mathematician Shiing-shen Chern and his family to the IAS in Princeton in December 1948 when China was on the verge of being taken over by the Communists.
The former Berkeley physicist who had led the development of the atomic bomb later opposed the development of the hydrogen bomb, and presumably by that virtue became a victim of McCarthyism:
“In April of 1954, Robert Oppenheimer, the former head of the Manhattan Project, the director of the Institute for Advanced Study, and the most famous scientist in America, was declared a security risk by Eisenhower and stripped of his security clearance in the full glare of national publicity. The ostensible reason was Oppenheimer’s youthful left-wing association, but the real reason, as von Neumann and most scientists testified at the time, was Oppenheimer’s refusal to support the development of the H-bomb.”
(Sylvia Nasar, A Beautiful Mind, 1998, Simon & Schuster)
Hmm, “the most famous scientist in America” wasn’t Albert Einstein? Oh well, at least it wasn’t Norman Levinson, like in Nasar’s book as discussed in Part 2.
J. Robert Oppenheimer’s brother Frank, also a physicist involved in the original atomic bomb development, was also a victim of McCarthyism and became an activist for “nuclear disarmament and peace”:
“Here’s a look at the past. Items have been culled from The Chronicle’s archives of 25, 50, 75 and 100 years ago.
1985
Feb. 3: Frank Oppenheimer, the distinguished physicist who founded San Francisco’s famed Exploratorium, died in his Sausalito home Feb. 2 after a long illness. He was 72. In his varied career, Dr. Oppenheimer pioneered research in radiation and cosmic rays, conducted secret studies on uranium isotope separation during the Manhattan Project of World War II, spent years in university teaching and finally created and directed the unique museum whose imaginative presentation of science has earned it worldwide renown. He was the younger brother of J. Robert Oppenheimer, who won fame as the director of the Los Alamos laboratory, which designed and built America’s first atomic bombs. Frank Oppenheimer was passionately committed to the cause of nuclear disarmament and peace. As a graduate student during the Depression, he briefly joined the Communist Party, and that short-lived membership cost him dearly later in life. In 1949, he was summoned before the House Un-American Activities Committee, then forced to resign his assistant professorship at the University of Minnesota. …”
(“Exploratorium founder Frank Oppenheimer dies”, by Johnny Miller, January 31, 2010, SFGate.com)
So one shouldn’t take the weapons-or-peace logic too orthodoxly, or even too seriously, but should do so with a grain of salt when one realizes that the famous activists opposing the weapons of mass destruction, like the Oppenheimer brothers, could well be the ones who had invented them in the first place.
On the other hand, the scientific institutions created and/or shaped by these talented physicists could be treasures, like the Exploratorium founded by Frank Oppenheimer at San Francisco’s Palace of Fine Arts:
“After the war, Frank became a physics professor at the University of Minnesota. But in 1949, he was forced to resign as a result of harassment by the House Un-American Activities Committee. Blackballed by McCarthy-era paranoia, Frank was unable to continue his physics research, and spent the next ten years as a cattle rancher in Pagosa Springs, Colorado.
…
With improvement in the political climate, Frank was offered an appointment at the University of Colorado in 1959. There, he revamped the teaching laboratory, creating a “library of experiments” that was in many ways a prototype for the Exploratorium.
In 1965, while in Europe on a Guggenheim fellowship, Frank explored and studied European museums and became convinced of the need for science museums in the United States that could supplement the science taught in schools. When he returned home, Frank was invited to plan a new branch of the Smithsonian, but he declined, preferring instead to work on what he called his “San Francisco project”— a museum of his own.
Frank proposed to house his new museum in the vacant Palace of Fine Arts in the Marina district of San Francisco. The proposal was accepted by the city, and in 1969, with no publicity or fanfare, the doors opened to Frank’s Exploratorium. Frank nurtured and shaped the growing museum until 1985, when he died from lung cancer.”
(“Dr. Frank Oppenheimer”, The Exploratorium)
The Palace of Fine Arts is the only surviving structure from the 1915 Panama Pacific International Exhibition hosted in a grandiose and palatial group of buildings made from temporary materials.
(“His Castles Outlive Their Kings: How Cal’s Architect Shaped and Scraped the Skyline”, by Cirrus Robert Wood, November 2, 2015, California Magazine, shared on Arts and the Community, and Fashion Statements)
So getting the famous mathematician Steve Smale, instead of one of the numerical analysts, as my Ph.D. adviser did not feel bad. In fact, in the early 1960s after he had moved from Berkeley to Columbia, Smale was offered a professorship by Princeton after he had solved the Generalized Poincare Conjecture, bettering the work of Princeton professor John Milnor, who then brought him the Princeton job offer. But Smale was more interested in negotiating for a higher salary at Berkeley to return to California.
(Steve Batterson, Stephen Smale: The Mathematician Who Broke the Dimension Barrier, January 2000, American Mathematical Society)
Smale also had fine tastes beyond mathematics, assembling and owning one of the world’s best private collections of mineral rocks.
(“The Very Model of a Modern Mineral Dealer”, May 20, 2015, Priceonomics)
My fellow math Ph.D. student friend William Geller cautioned me that Smale might not have much time for his students; but I felt that I was intellectually independent, anyway.
Smale was to go on sabbatical for the academic year 1984-1985, which he would spend in Paris, France, and so he scheduled my Qualifying Exam to be in the late spring, May 1984, not long before his departure.
In around February-March 1984 I moved out of the apartment shared with Kezheng Li and into an apartment rented by computer science Ph.D. student David Chin, mentioned in my March 2011 blog post:
“By the spring of 1984 I had moved to an apartment in Richmond near Albany and my new roommate David (Ngi) Chin was a Computer Science Ph.D. student specializing in a subfield of Artificial Intelligence – focusing on the role of intelligent agents in natural language systems. An MIT grad from Boston, born in Hong Kong, David played some chess and softball but I only played tennis and volleyball regularly with him. His previous roommate and fellow Computer Science student Vincent Lau had left school early for the computer industry.
By late spring I also passed the Ph.D. qualifying exam, marking the start of research-oriented Ph.D. study under my thesis adviser.”
(March 29, 2011, Feng Gao’s Blog – Reflections on Events of Interest)
The move was related to the upcoming qualifying exam. Kezheng was an active leader in the community of the Berkeley graduate students and visiting scholars from China, and so his place was busy, like an informal social activity center.
Kezheng had kindly offered to share his apartment with me before I had even left China:
“… a computer systems technician at Sun Yat-sen university who was also a friend and South China Teacher’s College’s affiliated middle school alumnus of my roommate “Jie Wang”, was from the circle of kids at South China Institute of Technology and knew a professor there whose son was a fellow Berkeley Math graduate student and former roommate of “Li”’s, and so before my journey a new connection was already made.”
(March 29, 2011, Feng Gao’s Blog – Reflections on Events of Interest)
It was in a gated apartment complex on Durant Avenue, with a small but representative group of math Ph.D. students living there, and a larger number of Chinese graduate students and some scholars.
Kezheng’s former roommate who had arranged for my sharing was Guojun Liao (廖國鈞), studying for his Ph.D. in the pure math field of differential geometry. Guojun’s late grandfather in the 1910s was the president of Guangdong Higher Normal College, one of the colleges that later in 1924 were combined to constitute National Guangdong University – I noted in a November 2010 blog post that it was soon renamed Sun Yat-sen University in honor of the father of the Chinese Republican Revolution, whose government founded the university at the provisional national capital Guangzhou, and who had been born in a village only 60 miles away.
(“Team Canada female athletes disqualified from Commonwealth silver medal, jailed Chinese democracy activist awarded with Nobel peace prize, and others in between (Part 2) – when violence is politically organized”, November 22, 2010, Feng Gao’s Blog – Reflections on Events of Interest; and, “寻访梅州籍大学校长廖道传 梁启超称他为“嘉应健生””, July 15, 2015, 梅州日报)
In the 1990s, a professor at the University of Texas at Arlington, Guojun shifted his research focus to mesh generation related to the finite element method, i.e., to the same field as Keith Miller. A SIAM 45th anniversary meeting session at Stanford in July 1997, which Guojun co-organized with Paul Zegeling of Utrecht University – the place new Stanford Ph.D. Jack Snoeyink spent a postdoc year at in 1990 after getting an UBC tenure-track position I unsuccessfully sought, as in Part 3 – listed 4 presentations: one by R. D. Russell, W. Huang, and Weiming Cao of Simon Fraser University in Canada, one by Keith Miller of UC Berkeley, one by Andrew Kuprat of LANL, and one by Feng Liu of UC Irvine and Guojun G. Liao.
(“Moving-Grid Methods for Partial Differential Equations (Part II of II)”, July 17, 1997, SIAM’s 45th Anniversary Meeting, Stanford University)
After Guojun, Kezheng’s roommate in the 1981-1982 academic year was math Ph.D. student Xiaolu Wang (王曉麓), who then moved to another unit in the same complex to share with a Caucasian graduate student. After his Ph.D., Xiaolu went to work in the U.S. East Coast and eventually ended up on Wall Street.
After Xiaolu, in the summer before my late August 1982 arrival, Kezheng’s roommate was Zhaowei Meng (孟昭偉) – as spelled by the Chinese Pinyin – who was on his way to attend Stanford’s business school, as mentioned and referred to as “ZWM” in my November 2009 blog post.
(November 22, 2009, Feng Gao’s Blog – Reflections on Events of Interest)
A couple of white math Ph.D. students, my classmate Peter Detre and his wife Catherine Carroll, lived in the apartment complex. In late 1999 when I was looking for work in Silicon Valley I ran into Catherine, originally from Britain as I recall; she was teaching at Texas A&M University at Kingsville – a different campus of Ron Chen’s alma mater – and said that she and Peter had parted ways, and that Peter had gotten a Yale law degree and was a “practicing lawyer somewhere”. Peter was Canadian and William Bade’s Ph.D. graduate, but I would not have expected to see a The New York Times wedding announcement of his – without Catherine.
(“WEDDINGS; Claire O. Finkelstein, Peter A. Detre”, June 5, 1994, The New York Times; and, “ccarroll”, wikidot)
In comparison to where Zhaowei, Xiaolu and Peter later got to, in 1984 my move ended only with sharing with a Ph.D. student in computer science – my undergraduate discipline even if AI was a newer field – and a Chinese American who could speak his family’s native tongue Taishanese (Toisan) – a variant of Cantonese.
Steve Smale was quite pleased to accept me as his first Ph.D. student from the People’s Republic of China – as noted in Part 2 – and with a prior background in numerical analysis, a field he had recently moved into.
As in Part 2, Smale was a prominent mathematician who had received the Fields Medal, the highest honor of the mathematical community, in 1966 at the International Congress of Mathematician held that year in Moscow’s Kremlin Palace.
Smale had moved from one area of mathematics to another, discovering and proving original results and founding new theories. In his topics courses I took over the several years, Smale would present most of his core achievements, in fields ranging from differential manifolds to dynamical systems, from mathematical economics to models of population growth, and from the simplex method in linear programming to Newton’s method for solving equations – with the exception of his early work in topology and the generalized Poincare conjecture.
But from time to time criticisms could be heard from some experts, especially ones in more applied fields, as to whether Smale really understood their issues when making mathematics there.
For one, Smale concentrated on the mathematics of it, and experts he conversed with tended to be the highly mathematical types. For example, in 1981 he published an important paper studying some mathematics related to numerical analysis, and acknowledged several persons:
“1. The main goal of this account is to show that a classical algorithm, Newton’s method, with a standard modification, is a tractable method for finding a zero of a complex polynomial. Here, by “tractable” I mean that the cost of finding a zero doesn’t grow exponentially with the degree, in a certain statistical sense. …
…
Before stating the main result, we note that the practice of numerical analysis for solving nonlinear equations, or systems of such, is intimately connected to variants of Newton’s method; these are iterative methods and are called fast methods and generally speaking, they are fast in practice. The theory of these methods has a couple of components; one, proof of convergence and two, asymptotically, the speed of convergence. But, not usually included is the total cost of convergence.
…
There is a final comment on the spirit of the paper. I feel one problem of mathematics today is the division into the two separate disciplines, pure and applied mathematics. Oftentimes it is taken for granted that mathematical work should fall into one category or the other. This paper was not written to do so.
I would like to acknowledge useful conversations, with a number of mathematicians including L. Blum, S. S. Chern, G. Debreu, D. Fowler, W. Kahan, R. Osserman, R. Palais, G. Schober and H. Wu.
Special thanks are due Moe Hirsch and Mike Shub.”
(“The fundamental theorem of algebra and complexity theory”, by Steve Smale, 1981, Volume 4, Number 1, Bulletin of the American Mathematical Society)
For the quote above I have selected several points Smale made in the paper: with standard modification, Newton’s method is a “tractable” algorithm in a statistical sense; the “total cost of convergence” had not been well addressed by the theory of numerical analysis; and, a problem of mathematics today was “the division into the two separate disciplines, pure and applied mathematics”, but his paper “was not written to do so”.
These were good points and worthwhile goals to pursue. But looking at the names Smale acknowledged, 9 for “useful conversations” plus 2 with special thanks to, a total of 11, only William Kahan was in the field of numerical analysis, even though other established Berkeley professors were acknowledged, such as mathematicians Shiing-shen Chern and Hung-Hsi Wu, and mathematical economist Gérard Debreu.
If Smale had not actually interacted with numerical analysts much, how could he be sure, given that his earlier background had not been in numerical analysis, that the progress he made would be useful for that field?
But the separation may have been the other way around; in other words, when Majda asserted that Smale knew nothing about numerical analysis, it wasn’t due to Smale’s lack of trying but the numerical analysts’ dismissive attitudes toward his efforts.
The Ph.D. oral qualifying exam committee would consist of several professors within the department, including the adviser, and one from outside the department. For my committee, Smale suggested: Prof. Charles Pugh, a close colleague in his former field of dynamical systems, whose graduate course on that subject I was taking; Alexandre Chorin, for my background in numerical analysis; and an engineering professor; and I suggested Andrew Majda.
The two numerical analysts took a little explanation to persuade.
I went to Chorin’s office to ask and his reaction, which I can only recall vaguely, was like, “You want to study with Smale; then why do you ask me to be on your committee?” I explained that my undergraduate background had been in numerical analysis and I would be doing related research, and Chorin responded with something like, “Smale doesn’t understand numerical analysis”, but grudgingly agreed.
This would become a pattern in my remaining years at UC Berkeley interacting with the professors in numerical analysis, that I had to emphasize my prior background for them to take me more seriously, and also had to ignore their comments about Smale.
I asked Majda to be on my committee and also to write a support letter for my application for a graduate fellowship, and his response was like, “since you want to study with Smale, you should not ask me for either”. After my explanation that his seminar course had been important and my research would be related to numerical analysis, Majda grudgingly agreed, wrote a letter on the spot, handed it to me – it was supposed to be confidential – and said, “this is the last I can do for you; from now on you should not ask me for more”.
With Majda’s letter, and confidential letters from Kato and Smale if I remember correctly, I later received my only fellowship, the Earl C. Anthony graduate fellowship, for the academic year 1984-1985.
It was a fellowship, even if not as much in prestige or amount as Kezheng received, which was either a UC Regents or UC Berkeley Chancellor’s graduate fellowship, not to mention the multi-year National Science Foundation fellowship my friend Will Geller received. But being sensitive, I sometimes wondered: my fellowship’s name had a “C.”.
In the spring of 1984, my former undergraduate adviser Yuesheng Li came by Berkeley on his way back to Sun Yat-sen University to assume its presidency. Prof. Li had spent some time at Texas A&M where his former master’s student Ron Chen was and where Prof. C. K. Chui and Prof. Larry Schumaker were peers of his in spline function theory and approximation theory as mentioned earlier.
Li told me he had also visited the mathematician Garrett Birkhoff at Harvard – son of the mathematician George David Birkhoff for whom the Birkhoff Prize for applied mathematics, which Wisconsin’s Paul Rabinowitz later won in 1997, had been named.
My Qualifying Exam was a near disaster. Since childhood I had had problems with shyness and nervousness, although I was okay with teaching when preparations ahead of time would enable me to present contents in structured and orderly fashions. When caught in an unprepared situation and I was nervous, for the moment I could sometimes be at a loss. In an oral exam in front of professors who could determine my fate added to my anxiety.
A part of the exam time was spent on my answers going in wrong directions. In one instance, Chorin asked a basic question but I misunderstood it as a question about something less well-defined and went on a long discussion, arguing with him before realizing it was my misinterpretation. In another instance, Pugh asked about the proof of a theorem from his dynamical systems course, I embarked on something halfway before realizing that it was a proof for another theorem, and said oh I should do it over, Pugh smiled and the committee deemed it enough time spent on that question.
After the exam I waited in the hallway for the committee’s decision; eventually Majda emerged first from the room, said with a stern look, “congratulations you passed”, and walked away; then the others came out and congratulated me. A few days later I met Majda, thanked him, and he said, “what you did was crazy. Your adviser was the only one who insisted on letting you pass”.
The Prelim Exam had been easier for me but the Qualifying Exam was harder partly due to my own fault, and it became etched in my mind that I passed because Smale was about to go to Paris for sabbatical and told other committee members he had no time for a second exam try – normally several months down the road.
For the Ph.D. degree two foreign languages were required, by passing exams translating math literature. I chose French first, passing easily as most French math terms had similar English versions. Then I took the German exam and failed, and subsequently spent much more time learning before passing on the second try. I later wondered if I could have gotten my Ph.D. had I chosen the third foreign language option, Russian, with its alien alphabet – I had looked at it back in my teenage days as my father knew some, and of course my undergraduate adviser had studied at Moscow State University.
After passing the two exams a Ph.D. student would file for the Ph.D. candidacy, in Mathematics or Applied Mathematics depending on the research field. Smale could be viewed as in math or applied math, as an earlier quote from his 1981 paper showed he did not consider himself separated by the two disciplines; the department’s graduate secretary, Janet Yonan, also said that as Smale’s student I could choose one or the other; so I filed for candidacy in “Applied Mathematics”. But when the certificate was issued to me, it was in “Mathematics”, I went to Janet, and she sort of said it just happened this way and if I wanted to change I would need to write a request letter to the department.
Given the hostility toward Smale I had encountered from the numerical analysts, I had the sense that for the applied mathematics category it would need to be approved by someone close to them and especially to Chorin, someone like Prof. Alberto Grünbaum, soon to become director of the Center for Pure and Applied Mathematics, 1985-1989, and later department chairman, 1989-1992. Originally from Argentina and with a Rockefeller University Ph.D., Grünbaum had taught at NYU’s Courant Institute – the “mother ship” Chorin, Hald and Majda had gone through either in Ph.D. study or teaching.
(“Francisco Alberto Grünbaum”, Department of Mathematics, University of California, Berkeley)
I decided it wasn’t worth the trouble, that mathematics was fine.
My classmate Mei Kobayashi had Ole Hald as her Ph.D. adviser, as described earlier, and her Ph.D. candidacy and later Ph.D. degree were in applied mathematics. At Berkeley most math graduate students went for their Ph.D. directly but Mei, whose Princeton bachelor’s degree had been in chemistry, felt the need to also get a master’s degree in mathematics prior to her Ph.D. in applied mathematics.
(“Class Notes”, November 11, 1987, Volume 88, Princeton Alumni Weekly; and, “Mei Kobayashi”, prabook)
Another classmate Paul Wright, previously cited in a quote in Part 3, was one of two African-American math Ph.D. students I knew at Berkeley – Chorin’s student Nate Whitaker being the other – and he also earned a master’s degree in mathematics, which he told me was useful because being originally from Jamaica he had only U.S. permanent residency at the time. Paul did his master’s thesis under Smale as I can recall, and then chose Grünbaum as his Ph.D. adviser; so like Mei, Paul’s Ph.D. was most likely in applied mathematics.
(“Paul Emerson Wright”, Mathematicians of the African Diaspora, Department of Mathematics, University at Buffalo; and, Nathaniel Dean, ed., African Americans in Mathematics: DIMACS Workshop, June 26-28, 1996, 1997, American Mathematical Society)
Grünbaum’s field, partial differential equations with soliton solutions, was among the trendiest in the department, like Chorin’s, with a large number of graduate student followers. A more recent presentation by Grünbaum described it as follows:
“The study of nonlinear partial differential equations of mathematical physics such as those of Korteweg-deVries, Toda, nonlinear Schroedinger, etc starting around 1970 has given a unifying push to several parts of mathematics … All of these equations exhibit solitons. a nonlinear version of the superposition principle going back at least to Fourier in the case of linear equations. I run myself into this enchanted land while studying a concrete problem in medical imaging: X-ray tomography with a limited angle of views, and I am definitely not an expert on this grand scheme.”
(“Colloquium – F. Alberto Grünbaum – Soliton mathematics as a unifying force”, April 11, 2012, Department of Mathematics, Boğaziçi University)
Once, a student who regularly attended Chorin’s seminars commented to me that several famous computational fluid dynamics methods, including Chorin’s, were run on the same equations and same data, and their resulting flow graphs were drastically different from one another; “but it was the same flow so at most one of them was correct”, he said.
Chorin’s Ph.D. student Jim Shearer told me he found the soliton tunneling effect, presented in Grünbaum’s graduate course on nonlinear partial differential equations, quite hard to believe, that a same soliton could disappear and reappear on different sides of a barrier.
Having come from Communist China, during my Berkeley years I was keen at familiarizing myself with the broader modern intellectual curriculum. After the Preliminary Exam and after the Qualifying Exam were times when I could afford more time studying other subjects.
As mentioned in Part 2, besides the ideological indoctrination of the Cultural Revolution my father was a university philosophy teacher, and so I had read much of Mao Zedong’s published works, a selection of which I more recently surveyed in a blog post; and I had also read some of the works of Vladimir Lenin, Karl Marx, Friedrich Engels and Joseph Stalin.
(“Power, avengement, ideological cementation — Mao Zedong’s class politics in great forward leaps, tactical concessions”, April 6, 2015, Feng Gao’s Posts – Rites of Spring)
In another recent blog post, originally posted on my website in 2011, I mentioned that I got to read some Chinese classics starting at the elementary-school age, during the Cultural Revolution time.
(“Some Chinese Cultural Revolution politics and life in the eyes of a youth”, November 7, 2015, Feng Gao’s Posts – Rites of Spring)
In fact, Sun Yat-sen University’s library collections were one of the best among the libraries in China, as I remember my father said, that the several million volumes might be smaller than that of the National Library and that of Peking University Library but probably none else. In my November 2010 blog post, I mentioned that some Western reports of burning of library books during the Cultural Revolution were inaccurate.
(November 22, 2010, Feng Gao’s Blog – Reflections on Events of Interest)
In my middle-school days in the early to mid-1970s, using my father’s library card I read a good selection of Chinese editions of Western classics, including Greek philosophy, Roman history, and the Renaissance and Enlightenment thinkers. What the Chinese publications really lacked was in modern Western thoughts, most not available until the 1980s.
So at Berkeley sometime during 1983-1985, I audited several upper-division undergraduate courses at the philosophy department, covering the philosophy of mind, meaning, language, etc., one probably taught by Prof. John Searle. I recall writing home telling my father, that UC Berkeley philosophy department’s graduate courses were mostly seminars and the Ph.D. curriculum used the upper-division courses as requirements.
One philosophy course I audited was taught by a visiting lecturer from Harvard University, on the Austrian philosopher Ludwig Wittgenstein. The lecturer was unusually energetic – reminding me a little of Lenin – and I sometimes saw him take fast strides between campus locations, cutting a standout figure from the culturally more reserved west-coast professors. I forgot his name at some point but believe it was Warren Goldfarb, today the Walter Beverly Pearson Professor of Modern Mathematics and Mathematical Logic, and a founder of Harvard’s gay and lesbian movement in 1984 although I have not found public info of his visiting Berkeley – an internationally leading city of gay and lesbian movements – around that time.
(“Stories Transform Goldfarb Into Activist”, by Anna D. Wilde, June 10, 1993, and, “Nine Secondary Fields Approved”, by Peter R. Raymond, November 17, 2006, The Harvard Crimson; and, “Who’s Who: Members of the Board and leadership team of the HGSC”, Harvard Gender and Sexuality Caucus)
One of my keenest interests while in my middle-school senior and university undergraduate years was in the history of science and philosophy of science. Unfortunately, neither seemed to be among the research focuses at the world famous UC Berkeley, but I continued reading, without auditing courses, including books by Karl Popper and radical Berkeley philosopher Paul Feyerabend, and attending the occasional seminar talks of relevance.
On one occasion, the MIT philosopher of science Thomas Kuhn returned to give a lecture at Berkeley, where he was once a professor when publishing his most famous book, The Structure of Scientific Revolutions, before moving to Princeton and then MIT. So I got to hear the author of one of my two most favorite books as an undergraduate – the other being Mathematical Thought from Ancient to Modern Times by Morris Kline.
Kuhn stated in the 1962 book:
“If science is the constellation of facts, theories, and methods collected in current texts, then scientists are the men who, successfully or not, have striven to contribute one or another element to that particular constellation. Scientific development becomes the piecemeal process by which these items have been added, singly and in combination, to the ever growing stockpile that constitutes scientific technique and knowledge. And history of science becomes the discipline that chronicles both these successive increments and the obstacles that have inhibited their accumulation. …”
(Thomas S. Kuhn, The Structure of Scientific Revolutions, 1962, Volume II, Number 2, International Encyclopedia of Unified Science, The University of Chicago Press)
The accumulative growth of scientific knowledge described above is probably what the public typically think of scientific research. But according to Kuhn, some historians of science found it untrue:
“In recent years, however, a few historians of science have been finding it more and more difficult to fulfil the functions that the concept of development-by-accumulation assigns to them. As chroniclers of an incremental process, they discover that additional research makes it harder, not easier, to answer questions like: When was oxygen discovered? Who first conceived of energy conservation? Increasingly, a few of them suspect that these are simply the wrong sorts of questions to ask. Perhaps science does not develop by the accumulation of individual discoveries and inventions. Simultaneously, these same historians confront growing difficulties in distinguishing the “scientific” component of past observation and belief from what their predecessors had readily labeled “error” and “superstition.” … If these out-of-date beliefs are to be called myths, then myths can be produced by the same sorts of methods and held for the same sorts of reasons that now lead to scientific knowledge. If, on the other hand, they are to be called science, then science has included bodies of belief quite incompatible with the ones we hold today.”
(Thomas S. Kuhn, 1962, The University of Chicago Press)
Indeed, as I have described in the case of the Berkeley math professors’ research in numerical analysis, which I was learning at the time, they could be dismissive of one another, and though aware that their work was not always scientific each of them and the followers marched on.
Kuhn wrote that historians of science began to pay attention to such scientific research:
“… Gradually, and often without entirely realizing they are doing so, historians of science have begun to ask new sorts of questions and to trace different, and often less than cumulative, developmental lines for the sciences. Rather than seeking the permanent contributions of an older science to our present vantage, they attempt to display the historical integrity of that science in its own time. They ask, for example, not about the relation of Galileo’s views to those of modern science, but rather about the relationship between his views and those of his group, i.e., his teachers, contemporaries, and immediate successors in the sciences. Furthermore, they insist upon studying the opinions of that group and other similar ones from the viewpoint—usually very different from that of modern science—that gives those opinions the maximum internal coherence and the closest possible fit to nature. …”
(Thomas S. Kuhn, 1962, The University of Chicago Press)
Kuhn referred to this type of scientific research as “normal science”, i.e, it was actually the norm:
“… Normal science, the activity in which most scientists inevitably spend almost all their time, is predicated on the assumption that the scientific community knows what the world is like. Much of the success of the enterprise derives from the community’s willingness to defend that assumption, if necessary at considerable cost.”
(Thomas S. Kuhn, 1962, The University of Chicago Press)
“Normal science” tended to suppress other things that contradicted it:
“Normal science, for example, often suppresses fundamental novelties because they are necessarily subversive of its basic commitments.”
(Thomas S. Kuhn, 1962, The University of Chicago Press)
I can agree with that, given my experience discussed in earlier Parts, that at the University of British Columbia even the faculty association would take part in suppressing issues that might unravel the politically correct appearance of the academia.
But Kuhn argued that such suppression would not last very long:
“Nevertheless, so long as those commitments retain an element of the arbitrary, the very nature of normal research ensures that novelty shall not be suppressed for very long. … The extraordinary episodes in which that shift of professional commitments occurs are the ones known in this essay as scientific revolutions. They are the tradition-shattering complements to the tradition-bound activity of normal science.”
(Thomas S. Kuhn, 1962, The University of Chicago Press)
“So long as those commitments retain an element of the arbitrary” – that was a big “so long as”.
Prof. Kuhn might not have expected that contemporary political correctness could easily give a “revolutionary” label to a vested power status, thus usurping the notion of “scientific revolutions”. In my case as in Part 1, the faculty association was official not “arbitrary”, and an anti-Reagan and anti-Thatcher stereotype posture by its president William Bruneau was, by political correctness, “revolutionary” enough to exclude me of any political merit.
Thomas Kuhn’s The Structure of Scientific Revolutions has been purchased or read by more people in the world than any other book on the history and philosophy of science – books by Aristotle and René Descartes included:
“Thomas S. Kuhn was the most important, and the most famous, historian and philosopher of science within living memory. The Structure of Scientific Revolutions has been read, or purchased, by more people than any book on either subject ever written—the closest competitors in philosophy must be the Posterior Analytics and the Discourse on Method…”
(“Thomas S. Kuhn 1922-1996”, by N. M. Swerdlow, 2013, U.S. National Academy of Sciences)
But in his Berkeley talk I attended, sometime in 1986-1988, probably 1987, Kuhn did not speak on the scientific revolutions. In the room packed to its full seating and standing capacity, I noticed a familiar figure standing not far from Prof. Kuhn at the lectern: Betul Tanbay, a fellow math Ph.D. student from Istanbul, Turkey, and officemate of my friends Will Geller and Samy Zafrany, both Jewish and all three studying mathematical logic at the time.
Of the three, Samy, an Ethiopian Israeli Jew with a congenial personality, had been my officemate for my first period of TA stints. But by no later than 1985 my assigned officemates became more senior Ph.D. students Jeff McIver and Steve Pomerantz, both interested in financial banking; Steve studied under Prof. Murray Protter, a colleague of Kato’s in partial differential equations, and Jeff under Prof. Jack Wagoner, who later would also be Will’s adviser and the department chairman after Grünbaum, though in 1987 Will was probably studying mathematical logic under Prof. Leo Harrington as I recall.
Will was the fellow math graduate student I knew best outside of the Chinese student circle, as I recalled in a January 2013 blog post:
“… In UC Berkeley student days a classmate and good friend of mine had been William Geller, whose fiancee and later wife, Stephanie Montague, received her Ph.D. in 1989 from California School of Professional Psychology…
From a Italian American garment business family in New York City, Stephanie had liked to say, “My family name is that of Romeo’s in Romeo and Juliet”.”
(“Guinevere and Lancelot – a metaphor of comedy or tragedy, without Shakespeare but with shocking ends to wonderful lives (Part 1)”, January 29, 2013, Feng Gao’s Posts – Rites of Spring)
Prof. Alfred Tarski, founder of UC Berkeley’s group in mathematical logic and methodologies of science, who had died in 1983, had been on the advisory committee that published Kuhn’s book in 1962. Tarksi has sometimes been compared to Kurt Gödel as the two most influential mathematical logicians of the 20th century.
(Thomas S. Kuhn, 1962, The University of Chicago Press; and, “Book Review: Alfred Tarski. Life and Logic”, by Hourya Benis Sinaceur, August 2007, Volume 54, Number 8, Notices of the American Mathematical Society)
I did not really study mathematical logic at Berkeley. As an undergraduate I had acquainted with some basics of Gödel’s work, which shed light on mathematics as a discipline by fundamentally clarifying the scopes of mathematical systems; but I had done so by independent reading, such as a book by NYU Courant Institute’s Prof. Martin Davis. My SYSU roommate Jie Wang (王潔) and his master’s adviser, Soviet Union-educated professor Guangkun Hou (侯廣坤), “Teacher Hou” as in my March 2011 blog post, did some research in that field.
(Martin Davis, Computability and Unsolvability, 1958, McGraw-Hill; and, March 29, 2011, Feng Gao’s Blog – Reflections on Events of Interest)
Another intellectual subject of my interest, which I became fascinated with at Berkeley, was cultural anthropology, especially structuralism. I spent time reading literature available at the anthropology department library.
In the late 19th century and early 20th century, the Columbia University anthropologist Franz Boas was the champion of cultural relativism:
“Boas outlined his views denying the importance of nature and emphasizing the influence of culture in several books, including The Mind of Primitive Man, published in 1911 and now considered a classic. Boas argued that the development of Western civilization was not the consequence of intrinsic genius on the part of the white race but simply owing to favorable circumstances. Other cultures could not be termed inferior, he declared, only different. …
…
Boas’s arguments were greatly strengthened because of a kind of linguistic revolution he launched in American social science by his novel use of the term “culture.” Before the nineteenth century, European writers spoke only of “civilization.” The term civilization comes from the Latin word civis meaning citizen. Used in the singular, civilization implies a certain form of government and a certain level of achievement. In the nineteenth century, Matthew Arnold used the term “culture” in contrast with “civilization.” … The word culture comes from the Latin term cultura meaning to grow or cultivate. “Culture” arises out of “agriculture.” Arnold used culture in an elevated sense, however; culture was represented by the high traditions of Athens and Jerusalem. …
Boas, however, used a new definition, one that was initiated by the English anthropologist Edward Tylor, who defined culture as the “knowledge, belief, arts, morals, customs and any other capabilities and habits acquired by man as a member of society.” … Only some people may be considered to have civilization, but all people in the Boasian sense have culture, in that they have customs and beliefs. … Through the democratization of the term, Boas found it much easier to suggest the essential relativity of cultures… Over time, even Americans who did not espouse relativism began to speak of “culture” in the Boas sense of the term, which is the way we commonly use the term today.
Historically, one of the strongest arguments for Western civilizational superiority has been the spectacular political and economic successes of modern industrial society. According to George Stocking in The Ethnographer’s Magic, Boas qualified but never abandoned his belief in the concepts of modernity, technology, rationality, and civilization. … Boas was not a strict cultural relativist, although he moved increasingly in that direction over the years. He emphasized that his main argument with the scientific racists was not that they were wrong, but that their case was unproven.”
(Dinesh D’Souza, The End of Racism: Finding Values In An Age Of Technoaffluence, 1995, Simon & Shuster)
UC Berkeley’s anthropology department was founded at the beginning of the 20th century by Prof. Alfred Kroeber, and strongly influenced by Kroeber and Prof. Robert Lowie:
“Lowie was attracted to anthropology because it represented intellectual fulfillment without the difficulties of physical manipulation of objects. He was also no doubt attracted to it because Boas represented a liberal point of view and had devoted himself to fighting the prejudices directed toward Jews and other ethnic and racial minorities as well as toward the teaching of anthropology. Lowie never became a political activist but his sympathies were definitely on the liberal side and he wrote extensively on racist problems.
…
During 1917—1918 Lowie was invited to become visiting lecturer in anthropology at the University of California at Berkeley by A. L. Kroeber, who had founded the department fifteen years earlier. In 1921, Lowie was appointed a permanent member of the staff at Berkeley and remained such until his retirement, although he held many visiting professorships and lectureships.
(“Robert Harry Lowie 1883—1957”, by, Julian H. Steward, 1974, U.S. National Academy of Sciences)
Kroeber and Lowie were former Ph.D. students of Franz Boas, and brought cultural relativism further to a level free of racism:
“As often happens with an influential teacher, however, Boas’s students extended his principles to construct a radically new framework for understanding race in the modern world. The names of Boas’s students at Columbia University read like a Who’s Who of early American anthropology: Margaret Mead, Ruth Benedict, … Alfred Kroeber, Robert Lowie, …
- Alfred Kroeber and Robert Lowie insisted that culture should be studied entirely independent of biology or heredity, which went far beyond anything Boas wrote.
- Margaret Mead virtually denied that human nature had anything to do with heredity: “Human nature is almost unbelievably malleable, responding . . . to contrasting cultural conditions.”
- …”
(Dinesh D’Souza, 1995, Simon & Shuster)
Also influenced by Franz Boas, the French anthropologist Claude Lévi-Strauss took a different intellectual route he deemed more scientific, that of discovering and analyzing hidden social relational patterns in human cultures, even the most primitive ones. In his influential book I read, Structural Anthropology, Lévi-Strauss compared structural anthropology to the study of language grammars, crediting the motivation and inspiration to Franz Boas but asserting that the anthropology study was vastly underdeveloped:
“… We propose to show that the fundamental difference between the two disciplines is not one of subject, of goal, or of method. They share the same subject, which is social life; the same goal, which is a better understanding of man; and, in fact, the same method, in which only the proportion of research techniques varies. They differ, principally, in their choice of complementary perspectives: History organizes its data in relation to conscious expressions of social life, while anthropology proceeds by examining its unconscious foundations.
…
Boas must be given credit for defining the unconscious nature of cultural phenomena with admirable lucidity. By comparing cultural phenomena to language from this point of view, he anticipated both the subsequent development of linguistic theory and a future for anthropology whose rich promise we are just beginning to perceive. He showed that the structure of a language remains unknown to the speaker until the introduction of a scientific grammar. Even then the language continues to mold discourse beyond the consciousness of the individual, imposing on his thought conceptual schemes which are taken as objective categories. Boas added that “the essential difference between linguistic phenomena and other ethnological phenomena is, that the linguistic classifications never rise to consciousness, while in other ethnological phenomena, although the same unconscious origin prevails, these often rise into consciousness, and thus give rise to secondary reasoning and to reinterpretations.” …
…
In the light of modern phonemics we can appreciate the immense scope of these propositions, which were formulated eight years before the publication of Cours de linguistique générale by Ferdinand de Saussure, which marked the advent of structural linguistics. But anthropologists have not yet applied these propositions to their field. …”
(Claude Lévi-Strauss, trans. by Claire Jacobson and Brooke Grundfest Schoepf, Structural Anthropology, 1963, Basic Books, Inc.)
Referring to the social relational patterns as “social structure”, Lévi-Strauss ambitiously declared that understanding a society’s social structure would lead to, in particular, comprehension of the culture and prediction of the results of changes:
“The term “social structure” has nothing to do with empirical reality but with models which are built up after it. This should help one to clarify the difference between two concepts which are so close to each other that they have often been confused, namely, those of social structure and of social relations. It will be enough to state at this time that social relations consist of the raw materials out of which the models making up the social structure are built, while social structure can, by no means, be reduced to the ensemble of the social relations to be described in a given society. …
The question then becomes that of ascertaining what kind of model deserves the name “structure.” This is not an anthropological question, but one which belongs to the methodology of science in general. Keeping this in mind, we can say that a structure consists of a model meeting with several requirements.
First, the structure exhibits the characteristics of a system. It is made up of several elements, none of which can undergo a change without effecting changes in all the other elements.
Second, for any given model there should be a possibility of ordering a series of transformations resulting in a group of models of the same type.
Third, the above properties make it possible to predict how the model will react if one or more of its elements are submitted to certain modifications.
Finally, the model should be constituted so as to make immediately
intelligible all the observed facts.”
(Claude Lévi-Strauss, 1963, Basic Books, Inc.)
Lévi-Strauss gave credits to Kroeber and Lowie, as well as other cultural anthropologists, for the structuralist aspects of their studies.
Credits were given to Kroeber on women’s fashion studies:
“Some of the researches of Kroeber appear to be of the greatest importance in suggesting approaches to our problem, particularly his work on changes in the styles of women’s dress. Fashion actually is, in the highest degree, a phenomenon that depends on the unconscious activity of the mind. We rarely take note of why a particular style pleases us or falls into disuse. Kroeber has demonstrated that this seemingly arbitrary evolution follows definite laws. These laws cannot be reached by purely empirical observation, or by intuitive consideration of phenomena, but result from measuring some basic relationships between the various elements of costume. The relationship thus obtained can be expressed in terms of mathematical functions, whose values, calculated at a given moment, make prediction possible.”
(Claude Lévi-Strauss, 1963, Basic Books, Inc.)
And credits were given to Lowie on kinship studies:
“… When he became active in research as well as in theoretical ethnology, the latter field was fraught with philosophical prejudices and an aura of sociological mysticism; therefore, his paramount contribution toward assessing the subject matter of social anthropology has sometimes been misunderstood and thought of as wholly negative. … However, it is Lowie who, as early as 1915, stated in modern terms the role of kinship studies in relation to social behavior and organization: “Sometimes the very essence of social fabric may be demonstrably connected with the mode of classifying kin.” …
… Thus he was laying the foundations for a structural analysis of kinship on two different levels: that of the terminological system, on the one hand, and, on the other, that of the correlation between the system of attitudes and terminology, thus revealing which later on was to be followed by others.”
(Claude Lévi-Strauss, 1963, Basic Books, Inc.)
Lévi-Strauss compared his structuralist views of anthropology to Karl Marx’s views on history, on the analysis of societies and on primitive societies:
“… the famous statement by Marx, “Men make their own history, but they do not know that they are making it,” justifies, first, history and, second, anthropology. At the same time, it shows that the two approaches are inseparable.
…
Marx himself, therefore, suggests that we uncover the symbolic systems which underlie both language and man’s relationship with the universe. …
…
If we grant, following Marxian thought, that infrastructures and superstructures are made up of multiple levels and that there are various types of transformations from one level to another, it becomes possible—in the final analysis, and on the condition that we disregard content—to characterize different types of societies in terms of the types of transformations which occur within them. …
…
Actually, Marx and Engels frequently express the idea that primitive, or allegedly primitive, societies are governed by “blood ties” (which, today, we call kinship systems) and not by economic relationships. If these societies were not destroyed from without, they might endure indefinitely. …”
(Claude Lévi-Strauss, 1963, Basic Books, Inc.)
Professor Claude Lévi-Strauss sounded more than my father later did, who, mentioned in Part 2, started as a Chinese literature student and ended as a professor in the history of Marxist philosophy.
(November 7, 2015, Feng Gao’s Posts – Rites of Spring; and, “High [Gao] Qiyun Self Selection (Chinese Edition)”, by Gao Qiyun, 2000, Abe Books)
Lévi-Strauss also credited the mathematician John von Neumann’s game theory for bringing the economist and the anthropologist closer together, and closer to Marxian thought:
“The complete upheaval of economic studies resulting from the publication of Von Neumann and Morgenstern’s book ushers in an era of closer cooperation between the economist and the anthropologist, and for two reasons. First—though economics achieves here a rigorous approach—this book deals not with abstractions such as those just mentioned but with concrete individuals and groups which are represented in their actual and empirical relations of cooperation and competition. Surprising though the parallel may seem, this formalism converges with certain aspects of Marxian thought.”
(Claude Lévi-Strauss, 1963, Basic Books, Inc.)
My reading cultural anthropology without auditing courses meant missing two public lectures in September 1984 by Lévi-Strauss, who was in Berkeley for the academic year 1984-1985 as the Charles M. and Martha Hitchcock Visiting Professor.
(“UCSF News”, 1984, The University of California, San Francisco; and, “Charles M. and Martha Hitchcock Lectures”, Berkeley Graduate Lectures)
But I did not miss it completely because later, sometime in 1986-1988, Prof. Lévi-Strauss gave a huge public lecture at the Crown Zellerbach Hall, the leading performing-arts venue at UC Berkeley, and I attended.
I have found one online reference, albeit anecdotal by a former Berkeley student, to that lecture:
“The first time I set foot into this huge hall was in my freshman year of college, to hear a talk by Claude Levi-Strauss. Sure, I thought, I’d love to hear the founder of Levi’s! I wear Levi’s after all! Actually, I went b/c I had met a hot anthro major in a miniskirt who invited me to the talk, for, truth be told, I don’t give a whit about the jeans industry.
I found soon that Claude Levi-Strauss, among the last great intellectuals of his generation, right up there with Michel Foucault (who did NOT write Foucault’s Pendulum, apparently), has nothing to do with denim.
That didn’t keep the 5 level hall from being completely full that warm afternoon. And I don’t quite know whatever happened to the lovely anthropologist in the miniskirt.”
(“Cal Performances: Recensioni Consigliate”, by T. W., January 25, 2007, yelp)
Michel Foucault mentioned above was a famous French philosopher who became a visiting professor at UC Berkeley in the 1980s, contracted HIV/AIDS in the San Francisco Bay Area and died in France in June 1984:
“… The original reports about the cause of death were ambiguous and contradictory. … Foucault’s fondness for San Francisco bath houses was widely discussed at the time. What we knew about AIDS, however, was not entirely clear. Nor was it clear what exactly was at stake in thinking AIDS was the cause of Foucault’s death. In 1984, it was possible (it still seems plausible, today) to believe in an AIDS conspiracy, in campaigns of disinformation disseminating news about the “gay plague,” and in a practiced neglect of AIDS cases because they were reported by homosexuals. …”
(“Fact and Fiction: Writing the Difference Between Suicide and Death”, by John Carvalho, 2006, Volume 4, Contemporary Aesthetics)
That was the same year when philosophy professor Warren Goldfarb co-founded Harvard’s gay and lesbian movement, who if I am not mistaken sometime in that period was a Berkeley visiting lecturer whose course I audited.
My experience with that Lévi-Strauss lecture had a similarity to the Cal freshman’s quoted above, that helped me remember when it took place: waiting in line at the Zellerbach Hall I saw and went in together with “Karen”, an undergraduate student who had been in my calculus TA class; a returning white student, Karen and her young Chinese American friend Kevin Mah, and their classmates were supportive of my teaching and I received an Outstanding TA Award for the academic year that I taught them, 1985-1986; so it could not have been the September 1984 Lévi-Strauss lectures.
As for the namesake of Levi Strauss jeans, a fame of San Francisco, they were too pricey for me then. Living in America I soon liked wearing jeans, but for my budget they started out Wranglers, and later mostly of the inexpensive start-up brand Gap from the Levi Strauss retailer The Gap.
Across Durant Avenue from the anthropology building was Cafe Roma, its patio the most popular hangout around campus. I often saw Alexandre Chorin, in his air of authority, walk in for a cup. Some math graduate students liked to hang around their bikes in the open space across the street, near the anthropology building, ones like Eric Kostlan, more senior than me and the only Ph.D. student of Smale’s also in Chorin’s circle.
The anthropology building was named after Alfred Kroeber, and the impressive anthropology museum after Robert Lowie, two late professors who had given prominence to UC Berkeley’s cultural anthropology:
“When a new anthropology building, which had been Kroeber’s lifelong ambition, was finally built at the University of California at Berkeley, it was officially named the Robert H. Lowie Museum of Anthropology. This museum, together with the Museum of Art, was part of the A. L. Kroeber Hall, but the honor paid Lowie was especially significant in that Lowie was never identified with or personally attracted to museum work. His early connections with the American Museum of Natural History were mainly a means whereby he had the opportunity to do fieldwork under the direction of Clark Wissler, and he relinquished this job in 1921 to accept the more congenial role of Professor of Anthropology at the University of California.”
(Julian H. Steward, 1974, U.S. National Academy of Sciences)
Today the anthropology museum is no longer the Robert H. Lowie Museum. After my departure from Berkeley, in the early 1990s it was renamed Phoebe A. Hearst Museum of Anthropology in honor of the museum’s original founder, according to the museum’s official history:
“Museum Founding and Growth
The Phoebe A. Hearst Museum of Anthropology, formerly the Lowie Museum of Anthropology, was founded in 1901. Its major patron, Phoebe Apperson Hearst, supported systematic collecting efforts by both archaeologists and ethnographers to provide the University of California with the materials for a museum to support a department of anthropology. …
… The Museum’s collections have grown from an initial nucleus of approximately 230,000 objects gathered under the patronage of Phoebe Hearst to an estimated 3.8 million items. The Museum was accredited by the American Association of Museums in 1973, and re-accredited in 1990.
Museum Locations
The Museum was physically housed from 1903 to 1931 in San Francisco, where exhibits opened to the public in October, 1911. A key figure during these years was Ishi, a Yahi Indian who lived at the Museum from 1911 until his death in 1916 and worked with the anthropologists to document the ways of his people. When the Museum moved back to the Berkeley campus in 1931, there was no space for public exhibitions, and the Museum focused on research and teaching. With the construction of a new building housing the Museum and anthropology department in 1959, space for exhibition again became available. The building, which the Museum continues to occupy, was named Kroeber Hall, and the Museum was named in honor of Robert H. Lowie, a pioneer in the Berkeley anthropology department. In 1991, the Museum’s name was changed to recognize the crucial role of Phoebe A. Hearst as founder and patron.”
(“History of the Museum”, Phoebe A. Hearst Museum of Anthropology)
Who said “economic successes”, or wealth, in this case of the Hearst family fame discussed in Part 2, and love of the museum did not matter? In the end, the millions in the museum collections and the thousands of visitors meant a more important law to the UC Berkeley anthropology museum than the laws of cultural anthropology Professor Robert Lowie may have discovered.
The Charles M. and Martha Hitchcock lectures that had featured Claude Lévi-Strauss in 1984, in 1988 featured the physicist Stephen Hawking, the Lucasian Professor of Mathematics at Cambridge University, a title once held by Isaac Newton.
I attended one of these March-April lectures by Hawking, and this time a familiar person I saw there, and chatted with, was my adviser Steve Smale.
During the timespan of his Berkeley lectures, on April Fool’s Day Prof. Hawking’s bestselling popular book, A Brief History of Time, was published. 8 years earlier in 1980, Smale had published a collection of articles under an interestingly similar title, The Mathematics of Time, on dynamical systems and mathematical economics. And 5 years before that in 1975, Hawking and co-author G. F. R. (George) Ellis had published an astrophysics textbook – his first book while the 1988 one his second – under a related but more advanced title, The Large Scale Structure of Space-Time.
(S. W. Hawking and G. F. R. Ellis, The Large Scale Structure of Space-Time, 1975, Cambridge University Press; Steve Smale, The Mathematics of Time, 1980, Springer-Verlag; “Origin of the Universe”, March 21, 1988, “Black Holes, White Holes, and Worm Holes”, April 5, 1988, and, “Direction of Time”, April 7, 1988, by Stephen Hawking, Berkeley Graduate Lectures; and, “Excerpt from ‘A Brief History of Time’”, by Stephen Hawking, April 5, 2007, USA Today)
Theories of physics had always been among my interests since my middle-school days, when browsing through the Sun Yat-sen University central library bookshelves I liked to read the Scientific American magazine. In the 1977 national university entrance exams I didn’t do as well on the physics exam as on the math exam, and my hands-on experimental ability was rather poor; so that prospect did not become a reality.
A reason I focused on partial differential equations in my first year at Berkeley and wanted to do my Ph.D. study under Tosio Kato was that these equations were a major mathematical foundation of physics. I recall Prof. David Gale, whose math specialty was in ordinary differential equations, making an even stronger statement in a colloquium talk, asserting that the universe was governed by differential equations – as in Part 2 Gale had helped John Nash start Ph.D. study in game theory despite von Neumann’s dismissal of Nash’s idea.
So in 1984-1985 while Smale was away on sabbatical, I made an unsuccessful attempt at starting some research in mathematical physics.
In 1983 Professor Robert Anderson, originally Canadian and a U of T graduate, had moved from Princeton to Berkeley, and my first TA job was for his introductory calculus course. A professor of both mathematics and economics, Bob was nonetheless not a particularly electrifying speaker and would soon focus his teaching at the graduate level.
During the 1984-1985 academic year Anderson gave a graduate course on nonstandard analysis, a specialty of his since his Yale Ph.D. study, and Will Geller and I were two loyal students among the small class, Will being especially impressed that Bob was an openly gay faculty member active in community politics.
Formulated using mathematical logic, nonstandard analysis is a mathematical system that includes infinitesimals, i.e., infinitely small numbers and infinitely large numbers, a system constructed to be an equivalent and alternative to the standard calculus-based mathematical analysis, which handles infinity via the notion of limits.
Historically, the need for the infinite calculus had arisen from physics and astronomy, and the infinitesimals were used intuitively, without sufficient mathematical rigor:
“The concept of infinitesimal was beset by controversy from its beginnings. The idea makes an early appearance in the mathematics of the Greek atomist philosopher Democritus c. 450 B.C.E., only to be banished c. 350 B.C.E. by Eudoxus in what was to become official “Euclidean” mathematics. We have noted their reappearance as indivisibles in the sixteenth and seventeenth centuries: in this form they were systematically employed by Kepler, Galileo’s student Cavalieri, the Bernoulli clan…
However useful it may have been in practice, the concept of infinitesimal could scarcely withstand logical scrutiny. Derided by Berkeley in the 18th century as “ghosts of departed quantities”, in the 19th century execrated by Cantor as “cholera-bacilli” infecting mathematics, and in the 20th roundly condemned by Bertrand Russell as “unnecessary, erroneous, and self-contradictory”, these useful, but logically dubious entities were believed to have been finally supplanted in the foundations of analysis by the limit concept which took rigorous and final form in the latter half of the 19th century. …”
(“Continuity and Infinitesimals”, by John L. Bell, July 27, 2005 (revised September 6, 2013), Stanford Encyclopedia of Philosophy)
The German philosopher Gottfried Wilhelm Leibniz developed a special liking for the infinitesimals, but their mathematical use was later replaced by the theory of limits started by Leibniz’s contemporary, the physicist Isaac Newton, until the 1960s when nonstandard analysis was invented by the mathematician Abraham Robinson:
“Newton developed three approaches for his calculus, all of which he regarded as leading to equivalent results, but which varied in their degree of rigour. The first employed infinitesimal quantities which, while not finite, are at the same time not exactly zero. Finding that these eluded precise formulation, Newton focussed instead on their ratio, which is in general a finite number. If this ratio is known, the infinitesimal quantities forming it may be replaced by any suitable finite magnitudes—such as velocities or fluxions—having the same ratio. This is the method of fluxions. Recognizing that this method itself required a foundation, Newton supplied it with one in the form of the doctrine of prime and ultimate ratios, a kinematic form of the theory of limits.
…
Among the best known of Leibniz’s doctrines is the Principle or Law of Continuity. In a somewhat nebulous form this principle had been employed on occasion by a number of Leibniz’s predecessors, including Cusanus and Kepler, but it was Leibniz who gave to the principle “a clarity of formulation which had previously been lacking and perhaps for this reason regarded it as his own discovery” …
The Principle of Continuity also played an important underlying role in Leibniz’s mathematical work, especially in his development of the infinitesimal calculus. … Given a curve determined by correlated variables x, y, he wrote dx and dy for infinitesimal differences, or differentials, between the values x and y: and dy/dx for the ratio of the two, which he then took to represent the slope of the curve at the corresponding point. …
…
… The first signs of a revival of the infinitesimal approach to analysis surfaced in 1958 with a paper by A. H. Laugwitz and C. Schmieden. But the major breakthrough came in 1960 when it occurred to the mathematical logician Abraham Robinson (1918–1974) that “the concepts and methods of contemporary Mathematical Logic are capable of providing a suitable framework for the development of the Differential and Integral Calculus by means of infinitely small and infinitely large numbers.” This insight led to the creation of nonstandard analysis, which Robinson regarded as realizing Leibniz’s conception of infinitesimals and infinities as ideal numbers possessing the same properties as ordinary real numbers.”
(John L. Bell, July 27, 2005 (revised September 6, 2013), Stanford Encyclopedia of Philosophy)
In studying nonstandard analysis I was also intrigued by two facts, that the axiomatic framework can lead to different mathematical systems containing infinitesimals, and that in mathematical physics certain conventional use of infinities was quite common.
A well-known example of infinity use has been the Dirac delta function, originated from physics where when a charge is concentrated at an infinitely small local point, its magnitude is infinitely large:
“DIRAC DELTA FUNCTION
In electromagnetic field analysis we come across the source density and the point source. Take the situation of a point charge q and the corresponding charge density ρv. Obviously the charge density must be zero everywhere in space and become infinite at the location …”
(Devendra K. Misra, Practical Electromagnetics: From Biomedical Sciences to Wireless Communication, 2007, John Wiley & sons)
Such a one-point distribution in standard mathematical analysis is defined as a “generalized function”, and is a useful tool in approximation and solutions of differential equations.
(Philip J. Davis, Interpolation and Approximation, 1975, Dover Publications, Inc.; and, Sadri Hassani, Mathematical Physics: A Modern Introduction to Its Foundations, 2013, Springer)
I found two classical books, one by Paul Adrien Maurice Dirac on quantum mechanics and one by Robert Davis Richtmyer on mathematical physics, to be well written, suitable readings for me who had studied some relevant mathematics through Kato’s course on partial differential equations.
(P. A. M. Dirac, The Principles Of Quantum Mechanics, 1958, Oxford University Press; and, Robert D. Richtmyer, Principles of Advanced Mathematical Physics, 1978, Springer-Verlag)
The mathematics of quantum mechanics employed differential operators, related to differential equations, in a central role. Recall that my classmate Robert Rainsberger’s Ph.D. thesis under Heinz Cordes was related to differential operators; in fact, Cordes has written a book on quantum theory in the spirit and approach of Dirac.
(Heinz Otto Cordes, Precisely Predictable Dirac Observables, 2007, Springer)
But neither Dirac’s book nor Richtmyer’s book really covered a type of infinity I was most interested in: “divergence” occurring in the calculations of physical quantities in particle physics – related to Dirac delta function – and “regularization” and “renormalization” – procedures to remove the infinity, involving ad hoc rules that lack a rigorous and comprehensive mathematical foundation.
(“Ultraviolet divergence”, Wikipedia)
I needed directly relevant references; but in the 1980s there were few published resources accessible to non-specialists on quantum divergence. As I recall I settled on trying to understand the book, Quantum Mechanics and Path Integrals, by Richard Feynmann and Albert Hibbs.
(R. P. Feynmann and A. R. Hibbs, Quantum Mechanics and Path Integrals, 1965, McGraw-Hill)
I found Feynman’s mathematics very different from those of Dirac and Richtmyer, not to mention his particle physics-centered presentation. I gained some sense of the occurrence of divergence but not any thorough understanding of either the physics or the particular mathematics to proceed with my attempt.
I spoke with a Berkeley biophysics Ph.D. student friend, Dar-Chone Chow (周達仲), who gave me an informal interpretation of quantum states and state transitions, as in ‘quantum leaps’, drew my attention to Feynmann’s notion of path integrals where divergence could occur, and otherwise said it was “too fundamental” to try.
I realized that on my own I was unable to really proceed, and soon put it on the backburner of my studies.
Later in 1987, Berkeley physics professor Eyvind Wichmann gave a math graduate course on von Neumann algebra. I audited, and at some point went to his office to try to gain a better understanding of divergence. I recall Prof. Wichmann drawing an unbounded stationery potential and a bounded moving potential, stating that their interaction was where divergence would occur. Somehow I felt that, even if so, the real physics was not truly captured at this level of mathematical modeling.
Dodging my interest in learning more about the physics, Wichmann said instead, quite seriously, “John von Neumann understood quantum physics, better than the physicists did”.
Given my limited knowledge I could not argue with Prof. Wichmann. I had read some literature on von Neumann’s mathematical formulation of quantum mechanics, who supposedly proved that his probabilistic model was complete for the physics and “hidden parameters” could not exist, that in this sense “causality in nature” was highly unlikely – a claim I felt very questionable – and whose highly abstract, algebraic approach Wichmann espoused was mathematically elegant but of little pragmatic interest to me.
(Miklós Rédei and Michael Stöltzner, eds., John von Neumann and the Foundations of Quantum Physics, 2001, Springer Science and Business Media; and, “Quantum Theory: von Neumann vs. Dirac”, by Fred Kronz, 2012, Stanford Encyclopedia of Philosophy)
In contrast to me, the more senior Xiaolu Wang, who later went to Wall Street as mentioned earlier, did his math Ph.D. thesis in the field of C*-algebra related to von Neumann algebra, with the title, “On the C*-algebras of a family of Solvable Lie Groups and Foliations”.
(“Xiaolu Wang”, Mathematics Genealogy Project)
So in 1984-1985 my months of efforts, on and off, did not lead to any progress in starting research in mathematical quantum physics.
I also needed to find Ph.D. research topics that would be of interest to my adviser Steve Smale.
Recall Smale’s comment in his 1981 paper regarding the theory of numerical analysis, that it was lacking in the total cost of convergence:
“The theory of these methods has a couple of components; one, proof of convergence and two, asymptotically, the speed of convergence. But, not usually included is the total cost of convergence.”
(Steve Smale, 1981, Bulletin of the American Mathematical Society)
I felt that an important component of the total cost was due to arithmetic round-off errors in the numerical computation. UC Berkeley had an expert, Professor William Kahan, a professor of both mathematics and computer science, in floating-point arithmetic and round-off error analysis; he had been the only numerical analyst acknowledged in Smale’s 1981 paper, as quoted earlier.
I approached Kahan, who gave me a few papers to read, and I began to attend seminars he led. I became aware of the research of Kahan’s former Ph.D. student James Demmel, an earlier part of which employed interval analysis to estimate fixed-point arithmetic round-off errors in solving systems of linear equations.
(“An interval algorithm for solving systems of linear equations to prespecified accuracy”, by James W. Demmel and Fritz Krückeberg, July 6, 1983, Computer Science Division (EECS), University of California, Berkeley)
However, for practical efficiency floating-point arithmetic was the choice of numerical computation. I looked into whether interval analysis, in which error intervals for the operands of an arithmetic operation lead to an error interval for the result, was applicable to floating-point arithmetic error analysis, and concluded that interval analysis did not seem useful for floating-point arithmetic error estimation in a worst-case model generally, i.e., without more concrete, problem-dependent assumptions about the possible distribution of actual error.
Kahan was popular with students wanting to get a master’s degree in computer science before going to the computer industry; his Ph.D. student from Hong Kong, Ping Tak Peter Tang, was in the mathematics department and Kahan asked that I helped read his thesis before he graduated to join Intel Corporation; and Demmel, a computer science professor at NYU’s Courant Institute before returning to Berkeley, was of course Kahan’s protégé.
Kahan’s office at the electrical engineering and computer science department’s computer science division, located in the same Evans Hall as the mathematics department, was next-door to the office of Prof. Lofti Zadeh, famous for his theory of fuzzy sets and fuzzy logic that he applied to artificial intelligence. So I also did some reading on Zadeh’s theory, in relation to my interest in arithmetic round-off errors, probabilistic analysis and interval analysis.
(“Fuzzy Probabilities”, by Lofti A. Zadeh, 1984, Volume 20, Number 3, Information Processing & Management)
As earlier, by this time my roommate was computer science Ph.D. student David Chin, who specialized in artificial intelligence.
Like with quantum physics, I continued to maintain an interest in arithmetic round-off error issues, which were relevant to my research in numerical analysis. In the early 1990s when I met NASA scientist David Bailey, who had been pioneering multiprecision arithmetic, I felt it was a promising direction toward variable-precision arithmetic in general, that would bridge fixed-point arithmetic and floating-point arithmetic; so I requested and eagerly went over a preprint of his paper.
(“A Portable High Performance Multiprecision Package”, by David H. Bailey, (revised) May 18, 1993, RNR Technical Report RNR-90-022)
When Smale notified me that he would be back during the Christmas season in 1984 and would like to learn about my progress, I had little to show but a formulation of the observation that as a numerical algorithm’s accuracy of approximation increases, floating-point arithmetic errors become dominant and a limit to the total accuracy – thus raising an issue of the optimal choice of approximation relative to the precision of floating-point arithmetic.
In the note of several pages I sketched for a problem to illustrate the above, there was no advanced mathematics involved. When I met him, Smale was unhappy with what I had submitted, and asked me to look into a different matter instead: he had drafted a paper that included some average analysis of the cost of approximation of integrals, and encountered rebuttal from some researchers.
I studied it, and communicated my findings to Smale in the spring of 1985. When he returned in the summer, Smale was more encouraging: he had made appropriate changes, and the paper was being published in October 1985 and would be the main basis of his graduate topics course in Fall 1985.
(“On the efficiency of algorithms of analysis”, by Steve Smale, October 1985, Volume 13, Number 2, Bulletin of the American Mathematical Society)
In this paper, Smale acknowledged conversations with, among others, A. Grunbaum, as discussed earlier the powerful new director of Center for Pure and Applied Mathematics, close to Alexandre Chorin and the numerical analysts:
“ACKNOWLEDGMENT. Conversations with L. Blum, A. Grunbaum, E. Kostlan, and A. Ocneanu were helpful to me in developing the ideas in this section.”
(Steve Smale, October 1985, Bulletin of the American Mathematical Society)
Unlike in his 1981 paper, this time Grünbaum was the only established Berkeley professor acknowledged by Smale.
Apparently during his sabbatical Steve did not only spent time in Paris, as in this paper he mentioned that in July 1984 he was in Caracas, Venezuela:
“Besides the help of Traub and Wozniakowski, conversations with A. Calderon, P. Collet, J. Franks, M. Shub, and especially David Elworthy in Caracas, July 1984 (where I found these results) were important for me. …”
(Steve Smale, October 1985, Bulletin of the American Mathematical Society)
After the mention of Caracas in July 1984, Steve acknowledged conversations with me and his son Nat, also a Berkeley math Ph.D. student:
“… So also were conversations with Feng Gao and Nat Smale.”
(Steve Smale, October 1985, Bulletin of the American Mathematical Society)
In the section of the paper where I was mentioned, Smale deployed Gaussian measure as the setting for his average analysis of approximation of integrals, mentioning the related Wiener measure.
Gaussian measure is named after the 19th-century German mathematician Carl Friedrich Gauss, whose name is also associated with the Fundamental Theorem of Algebra in the title of Smale’s 1981 paper; Wiener measure is named after the late MIT mathematician and founder of cybernetics, Norbert Wiener, as is the Wiener Prize in Applied Mathematics Tosio Kato had received in 1980. These probability measures later became the settings for my Ph.D. thesis as well.
Later in 1988, this paper of Smale’s in Bulletin of the American Mathematical Society – the U.S. mathematical research community’s leading journal that had also published Smale’s 1981 paper – was awarded the Chauvenet Prize by the Mathematical Association of America for the outstanding exposition.
(“Chauvenet Prizes”, Mathematical Association of America)
During his Fall 1985 course, Smale also presented his α-theory, to be published in 1986, on computable convergence estimates for his modified Newton’s method-type algorithm for finding zeros of complex polynomials. The inspiration I got from Smale’s α-theory later led to the main body of my Ph.D. thesis.
Smale was quite pleased with my work in progress; in the paper for his plenary address at the 1986 International Congress of Mathematicians, he also acknowledged me when he acknowledged Lenore Blum and Jim Curry:
“… Lenore Blum’s MSRI talk on a condition number for linear programming via the LCP helped put the LCP back in my mind. Her comments and those of Jim Curry and Feng Gao have been generally useful to me.”
(“Algorithms for Solving Equations”, by Steve Smale, 1986, Proceedings of the International Congress of Mathematicians, Berkeley, California)
Steve’s collaborator Lenore has previously been mentioned in Parts 2 & 3.
Jim Curry, who preferred to be referred to as “James”, not “Jim”, was a rare African-American math Ph.D. graduate of Berkeley originally from Oakland, a neighboring city mentioned in Part 2. James was an associate chairman of the mathematics department at the University of Colorado, Boulder, on sabbatical at Berkeley’s Mathematical Sciences Research Institute; he had done computational research in dynamical systems using a Cray supercomputer, and was doing research related to Smale’s analysis of Newton’s method.
(“On zero finding methods of higher order from data at one point”, by James H. Curry, June 1989, Volume 5, Issue 2, Journal of Complexity; “James Howard Curry”, Mathematical Association of America; and, “James H. Curry”, Department of Applied Mathematics, University of Colorado, Boulder)
The International Congress of Mathematicians, as in Part 2, was the once-in-4-years international gathering of the mathematical community that in 1966 was held at the Kremlin Palace in Moscow where Smale and 3 others were awarded the Fields Medal.
20 years later in 1986, the ICM was held at UC Berkeley, and Smale led its 15 plenary speakers:
“Since the “World Congress of Mathematicians,” held in Chicago in 1893, the mathematicians of the world – as urged then by Felix Klein – have gone far in forming unions and holding international congresses. In the summer of 1986 the twentieth such congress took place at the University of California (Berkeley).
The city of Berkeley from which the University takes its designation was named for the Anglican bishop, George Berkeley (1685-1753), not for his perceptive comments regarding the newly invented calculus, but for another perceptive comment – “Westward the course of empire takes its way” – which occurs in a work entitled “On the Prospect of Planting Arts and Learning in America.”
…
The Congress itself was distinguished by an increasing emphasis on computer science. The New York Times headlined MATHEMATICIANS FINALLY LOG ON. Steve Smale, Berkeley’s own Fields Medalist (Moscow 1966), led off the stellar lineup of fifteen plenary speakers with a lecture on “Complexity aspects of numerical analysis” —a far cry from his Moscow lecture on “Differentiable dynamical systems.” …”
(Donald J. Albers, G. L. Alexanderson and Constance Reid, International Mathematical Congresses: An Illustrated History 1893-1986, 1987, Springer-Verlag)
Actually, the 1986 ICM Proceedings listed 16 plenary speakers, only that the speech of one of them, Jürgen Fröhlich, supposed to be on the mathematics of quantum mechanics, was listed as a no show:
“FRÖHLICH, JÜRG (Paper not read at the Congress. No manuscript received.), Analytical approaches to quantum field theory and statistical mechanics”.
(“PROCEEDINGS OF THE INTERNATIONAL CONGRESS OF MATHEMATICIANS AUGUST 3-11, 1986”, 1987, Berkeley, California, American Mathematical Society)
Haha! I wasn’t the only one who had spent time on quantum mechanics but come up with nothing to show.
It’s unclear why Fröhlich’s talk was a no show. The Swiss mathematical physicist’s official resume lists an invited address at the 1978 ICM in Helsinki and a plenary address at the 1994 ICM in Zurich, with no mention of the 1988 Berkeley ICM halfway in between.
(“Mathematical Physics — Prof. Jürg Fröhlich: CURRICULUM VITAE”, Institute for Theoretical Physics, Swiss Federal Institute of Technology Zurich)
In 1990, in my paper contributed to the Smalefest conference celebrating Smale’s 60th birthday – as in Part 2 at that conference Smale gave a speech on his former Communist history – I recalled the inspiration of Smale’s α-theory to my Ph.D. research:
“In fall 1985 at Berkeley, when Steve Smale was disseminating this α-theory in his graduate course and also in one Mathematics Department colloquium talk, I was at the preliminary stage of my Ph.D. research under his supervision. Smale’s observation on computable error estimates struck me as pointing out a potentially important direction for the analysis of numerical approximation algorithms. … ”
(“On the Role of Computable Error Estimates in the Analysis of Numerical Approximation Algorithms”, by Feng Gao, in Morris W. Hirsch, Jerrold E. Marsden and Michael Shub, eds., From Topology to Computation: Proceedings of the Smalefest, 1993, Springer-Verlag)
Smale was pleased with the progress of my Ph.D. research. In the fall of 1986 when I asked him to be a reference for my academic job search, Smale responded, “Apply to the top-20 or so math departments, tenure-track positions, and I will write a letter for you”.
I applied to well over 20, mathematics as well as computer science departments. Then interestingly, all the job interviews – a total of 3 – came at computer science departments: at Princeton University, State University of New York at Buffalo, and University of Maryland at College Park – it resembled the 3 schools, Stanford, SUNY Stony Brook and UC Berkeley, 5 years earlier when I applied for Ph.D. study, as well as the 3 Canadian schools, U of T, SFU and UBC that offered me jobs in the following year.
An obvious reason for their all being in computer science in 1988 was that many of the university CS departments were much newer than their math counterparts and the needs for computer science teaching and research were fast growing.
A second possible reason, pointed out by Smale’s collaborator Lenore Blum, a professor at the all-women Mills College – mentioned in Part 3 in the context of 5 new college graduates featured in Life magazine in 1969 – in Oakland, was that Smale’s research was not universally accepted by mathematicians and none of his Ph.D. graduates had become professors at leading math departments in the United States.
I had heard something like it, from none other than Professor Shiing-shen Chern, founding director of Berkeley’s MSRI and a mathematical patriarch who, as in Part 2, had co-organized research activities with Smale. On one private occasion after I had become Smale’s Ph.D. student, Chern cautioned me that mathematicians might not always view Smale’s work as genuine mathematics.
Yet another possible reason, mentioned by Will Geller as discussed earlier, was that Smale might not have given a lot of attention to his students. Smale’s Ph.D. graduate James Renegar, who had taught mathematics for several years at the remote Colorado town of Fort Collins then returned for postdoctoral research at MSRI and at Stanford, before getting a job at the operations research department of Cornell University – a leading U.S. university that as in Part 3 has named its medical college after businessman Sanford Weill – lamented to me that Smale did not necessarily write strong support letters for his students, and that Smale’s collaborator Michael Shub wasn’t easy to get to know: Jim had lobbied Mike for a job at IBM Thomas J. Watson Research Center in New York State, where Mike was a scientist, but got an offer only after Cornell had offered.
As cited in Part 2, Mike Shub had been Smale’s Ph.D. student in the 1960s following Smale into the Berkeley anti-war movement. In his 1986 ICM paper, right after mentioning Lenore, Jim Curry and me as quoted earlier, Smale gave special thanks to Renegar and, especially, Shub:
“Especially important through all of this has been the work of, and conversations with, Jim Renegar and Mike Shub. That contribution from Mike Shub, to me, has persisted over many years indeed.”
(Steve Smale, 1986, Proceedings of the International Congress of Mathematicians, Berkeley, California)
Jim was very bright. During his postdoctoral time at Berkeley’s MSRI and Stanford he combined inspiration from Smale’s focus on Newton’s method with Stanford operations research department’s focus on linear programming, and came up with an innovative Newton’s method-type algorithm for the latter.
(“LINEAR PROGRAMMING (1986)”, by Nimrod Megiddo, 1987, Volume 2, Annual Review of Computer Science)
Still, Mike Shub’s contribution had persisted for much longer as Smale said. Shub had started following Smale in the early 1960s as a Columbia University undergraduate student. An anecdote discussed in Part 2 that, fearing a nuclear war and angry with President John Kennedy during the October 1962 Cuban Missile Crisis, Smale abandoned his Columbia class and headed with his family towards Mexico, happened when Shub was taking Smale’s graduate course.
(Steve Batterson, January 2000, American Mathematical Society)
But even Lenore expressed to me sentiments similar to Jim’s, that Steve was a great mathematician but he did not provide much help for his students. In that respect, Lenore filled much of that void for Steve’s younger followers.
James Curry also told me his experience similar to Jim Renegar’s, though not about Steve. After his Berkeley Ph.D., James went to a tenure-track assistant professorship at Howard University, a private, leading black U.S. university located in Washington, D.C., only to find that faculty members there were not into math research; so after 2 years, James left for postdoctoral research at MIT, starting over looking for a faculty job.
James was very driven. I recall his reminiscence that as a graduate student he had seen familiar persons chat all the time in the department’s common coffee room, and after becoming a faculty member elsewhere he returned to visit and saw the same persons still hang out in the coffee room – “they did not accomplished much”, James said.
That might be the case, but the department coffee room was popular, especially at 3-4 in the afternoon on weekdays when free refreshments, like cookies, were available.
It’s a matter of one’s ambitions and standards, I guess. I remember David Witte, a tall, handsome and popular postdoctoral fellow who brought his bicycle everywhere, including to the coffee room, and who in around 1987-1988 told me he had a tenure-track assistant professorship offer from the University of Wisconsin-Madison but chose to go to MIT next as a short-term instructor; David said that in a few years some senior professors at the top universities would retire and positions would be open, but if one settled into a university at the next level it would be harder to move up.
Wow! For me, had there not been a famously liberal UC Berkeley with nice weather on the U.S. West Coast, I would have been happy to get into Wisconsin-Madison for graduate study as advised by my undergraduate adviser in China.
In the case of my seeking an academic job, Smale phoned his friend James Yorke, director of the Institute for Physical Sciences and Technology at the University of Maryland, before the institute contacted me for a joint-candidacy interview with the computer science department at College Park. So Steve did provide real help.
Steve’s phone lobbying for me happened after my February 1987 interviews at Princeton and Buffalo, likely in March as the Maryland interview took place in April; he dampened my enthusiasm of the Princeton interview experience – in 1984 Andrew Majda had talked about bringing me there as a Ph.D. student – by informing me that his other graduating Ph.D. student, Joel Friedman, was also being interviewed by Princeton.
Joel solved a conjecture of Smale’s, a feat few graduate students achieved. He had hailed from Harvard in 1984 with a multitude of fellowships, and was someone Will raved about, that Joel was also doing research at IBM Almaden Research Center with prominent theoretical computer scientist Nick Pippenger – in comparison, at the time I didn’t even know about Pippenger’s wife Maria Klawe, the IBM research group’s manager.
(“On the convergence of newton’s method”, by Joel Friedman, March 1989, Volume 5, Issue 1, Journal of Complexity)
I was also informed that Joel was son of the mathematician Avner Friedman, who was well known, in that year 1987 the new director of Institute for Mathematics and its Applications at the University of Minnesota – Berkeley’s MSRI and Minnesota’s IMA were the only U.S. math research institutes financed by the National Science Foundation.
(“Avner Friedman: Mathematician in Control”, Interview of Avner Friedman by Y.K. Leong, 2007, Issue 10, Newsletter of Institute for Mathematical Sciences, National University of Singapore; and, “DMS Mathematical Sciences Research Institutes Update”, November 1, 2015, Amstat News)
So in 1987 Jim Renegar landed a tenure-track job in operations research at Cornell, and Joel Freidman landed a tenure-track job in computer science at Princeton – Smale’s students were getting tenure-track positions at leading U.S. universities in various departments, just not mathematics.
As for me, 3 interviews were not bad; that none led to a tenure-track job offer probably had to do with the fact that I was in the U.S. on a foreign student-visiting scholar type visa and the extra requirements for such a hiring were not something academic institutions would easily undertake.
At College Park, I met a mathematician and numerical analyst I had great respect for. In a February 2013 blog post I quoted about Professor Ivo Babuska, when comparing pure mathematicians and applied mathematicians:
“Politically, the personalities in the fields of pure mathematics and those in the fields of applied mathematics were quite different. A large number of academicians in pure math were known to be political left-wings, active to various degrees as political dissidents, international human-rights activists, or in the case of Americans, anti-war activists.
…
But despite my Ph.D. adviser’s pure math pedigrees, my professional interests and studies were more in applied and computational mathematics, in fields where politics was usually not openly discussed as much, not the least because research was substantially funded by industry and by military-related sources.
…
Babuska’s background had a link to a major political event… he came to the United States from Czechoslovakia in 1968. But here is one biography that offered more details about his 1968 move:
“… The Communists had seized control of the country in 1948 and it was under strong Soviet influence over the following years. Mathematics was allowed to develop without interference, however, and the applied and computational methods developed by Babuska found favour. Beginning in 1964 reformers had won many concessions which became more clear-cut in early 1968 when the country began to implement “socialism with a human face”. The reforms came to a sudden end, however, in August 1968 when Soviet tanks rolled into Prague. Babuska had just been appointed as a professor at the Charles University of Prague but, given the political situation, he travelled with his family to the United States where he spent a year as a visiting professor at the Institute for Fluid Dynamics and Applied Mathematics at the University of Maryland at College Park. He was given a permanent appointment as a professor at the University of Maryland in the following year and he held this position until 1995. He was then appointed Professor of Aerospace Engineering and Engineering Mechanics, Professor of Mathematics, and appointed to the Robert Trull Chair in Engineering at the University of Texas at Austin. …
After coming to the United States, Babuska became the world-leading expert in finite element analysis.””
(“Guinevere and Lancelot – a metaphor of comedy or tragedy, without Shakespeare but with shocking ends to wonderful lives (Part 2)”, February 28, 2013, Feng Gao’s Posts – Rites of Spring)
Just like Carl de Boor being “the worldwide leader and authority in the theory and applications of spline functions”, quoted earlier, Ivo Babuska was “the world-leading expert in finite element analysis”, or at least in my understanding a leading expert of great depth in both the mathematics and the applications of finite elements. My interest in a potential extension of my Ph.D. research direction to the finite elements had led to my wide reading of literature on that subject, including publications by prominent numerical analysts such as, in addition to Babuska: Babuska’s former Maryland colleague, Werner Rheinboldt of the University of Pittsburgh; Babuska’s collaborator, Olgierd Zienkiewicz of the University College of Swansea in Wales who – like Babuska going to the University of Texas at Austin in 1995 – became UT Austin’s Joe C. Walter Chair of Engineering in 1989; Richard Varga of Kent State University; and Gilbert Strang of MIT.
(“The Finite Element Method—Linear and Nonlinear Applications”, by Gilbert Strang, 1974, Proceedings of the International Congress of Mathematicians, Vancouver; “Celebration of a Wide-ranging Community at Kent State”, by Daniel B. Szyld, July 23, 1999, Society for Industrial and Applied Mathematics; “OBITUARY: OLGIERD C. ZIENKIEWICZ (18 May 1921–2 January 2009)”, September 1, 2009, International Journal for Numerical Methods in Engineering; and, “Prof. Dr. Werner Rheinboldt: Honorary Professor at TUM since 2007”, Technische Universität München)
Note that finite element analysis was also the field of Berkeley professor Keith Miller who, as discussed earlier, denied my classmate Robert Rainsberger the chance to do Ph.D. study in it.
Babuska’s accomplishments have given him recognition beyond mathematics and engineering, as I noted:
“Ivo Babuska is one such fine example, an applied mathematician originally from Prague, capital of the Czech Republic, someone so accomplished that his birthday has been hailed as among:
“Prague’s “top 11 historical events” between 1197 and 1966 a.d. compiled by Mlada Fronta Dnes, the Czech Republic’s largest newspaper”.”
(February 28, 2013, Feng Gao’s Posts – Rites of Spring)
So was the distinction Zienkiewicz received in 1989 as he became UT Austin’s Joe C. Walter Chair of Engineering, when he also became the UNESCO Chair of Numerical Methods in Engineering at Universitat Politecnica de Catalunya in Barcelona, Spain – the first UNESCO chair in the world, hence an honor also for the field of numerical analysis:
“After retirement as Head of Civil Engineering at Swansea in 1987, Olek spent two months each year at the International Center for Numerical Methods in Engineering (CIMNE) at Universitat Politécnica de Catalunya (UPC) in Barcelona, Spain. In 1989 Olek was appointed as the UNESCO Chair of Numerical Methods in Engineering at UPC. This was the very first UNESCO chair in the world and arose from interactions with Geoff Holister who was working at UNESCO developing support to technology and engineering. The idea of such a position arose from an idea in the book “Small World” by David Lodge. In the book professors of English imagine a UNESCO Chair that will allow them to retire into a world of continuous travel with no lecture obligations at an extravagant salary – mostly things Olek already had achieved!”
(“Some Recollections of O.C. Zienkiewicz”, by R.L. Taylor, in “IACM Expressions”, Number 25, July 2009, Bulletin for The International Association for Computational Mechanics)
In 1987 at College Park, Maryland, Babuska was a professor at both the math department and at the institute headed by Smale’s peer Jim Yorke. With adaptive finite elements and computable a posteriori error estimates among his expertise, Babuska showed considerable interest in my computable average error estimates for numerical integration and their close links to spline functions in approximation theory.
After the computer science department’s decision not to offer me a job, Babuska forwarded my file to his peer, Prof. Thomas Seidman at Maryland’s Baltimore County campus, who on behalf of the math department there offered me a 2-year visiting assistant professorship.
As a foreign student, my U.S. study visa would expire after my Ph.D. graduation or another 18 months of postdoctoral research, unless a job led to a work visa. The visiting position would not include that; so after some thoughts I decided to stay in the Ph.D. program for one more year, and thanked Prof. Seidman for his help.
At this point in the early summer of 1987, Babuska agreed to forward my paper based on my upcoming Ph.D. thesis to a leading numerical analysis journal, of which he was an editorial board member, in Vienna, Austria. He also advised that for the next year 1988 I should focus on applying to Canadian universities. During that phone conversation, Babuska said something that made a lasting impression, something like, “It is possible. I believe everything is possible”.
Acting on the advice of Babuska and also that of Lenore Blum, whom I respected as a mentor and for whose Mills College math class I had once substituted for a week, in my last year at Berkeley I spent most of my study time on computer science, which had been my undergraduate major.
The fact that using my Ph.D. research work under a mathematician, whose current interest was in numerical computation but who was not a numerical analyst, I was able to become a computer science faculty candidate at three very good U.S. universities certainly boosted my confidence.
As discussed, my Ph.D. research was in the average analysis of numerical computation algorithms, a subject brought to my attention by Smale, and my focus on computable error estimates was inspired by Smale’s α-theory. In my Smalefest paper, after crediting Smale’s inspiration as quoted earlier I further elaborated on my rationale:
“Most numerical approximation methods simply do no have guaranteed and yet computable error bounds under a weak differentiability assumption; whereas a strong differentiability assumption is one way to obtain computable error estimates, estimates applicable under a weak differentiability assumption are also important, for this assumption usually captures the generality of a method and is the starting point of many algorithms in practice; most practical algorithms, thus, use computable but not guaranteed error estimates; they are heuristics that may be incorrect some of the time but prove to be generally useful in practice.”
(Feng Gao, in Morris W. Hirsch, Jerrold E. Marsden and Michael Shub, eds., 1993, Springer-Verlag)
As quoted, my goal was to use average analysis to bridge mathematical analysis and practical computable error estimates.
In 1987, Smale was turning in a different direction, a much more mathematical one.
In his 1981 and 1985 papers cited earlier, Smale had extensively used mathematics related to the Bieberbach conjecture, a major math problem since the 1910s, first solved by Louis de Branges in 1985, who like Smale became a plenary speaker at the 1986 International Congress of Mathematicians at Berkeley.
(1987, Berkeley, California, American Mathematical Society)
So in his 1987 graduate course, Smale spent much time developing some mathematics he hoped might lead to an alternate proof of the conjecture, i.e., by this time de Branges’s theorem; I followed it with considerable interest.
In contrast to his 1985 computable error estimates for his modified Newton’s method-type algorithm finding zeros of complex polynomials, namely his α-theory, in 1986-1988 Smale spent much time presenting another theory he and Mike Shub, in relation to the work of Curtis McMullen, developed regarding algorithms that would not need computable error estimates at all: when an algorithm is run in endless, “purely iterative” cycles it would be “generally convergent”, i.e., approach a solution pretty much every run.
In his 1985 paper, Smale had conjectured that for the class of complex polynomials with a fixed degree – one of the mathematically nicest classes of functions – no purely iterative algorithm is generally convergent.
(Steve Smale, October 1985, Volume 13, Number 2, Bulletin of the American Mathematical Society)
In his Harvard math Ph.D. thesis and a 1988 paper, Curtis McMullen proved Smale’s negative conjecture. On the positive side, Smale and Shub had shown in a 1986 paper that if – in addition to the standard arithmetic of addition, subtraction, multiplication and division – the operation of complex conjugation is also used, then there are purely iterative algorithms that are generally convergent.
In his paper contributed to the 1990 Smalefest conference, Mike Shub summarised it:
“… Newton’s method is an example of a purely iterative algorithm for solving polynomial equations. … A purely iterative algorithm is generally convergent if for almost all (f, x) iterating the algorithm on x, the iterates converge to a root of f. Smale [1986] conjectures that there are no purely iterative generally convergent algorithms for general d. McMullen [1988] proved this for d ≥ 4 and produced a generally convergent iterative algorithm for d = 3. For d = 2, Newton’s method is generally convergent. Doyle and McMullen [1979] have gone on to add to this examining d = 5 in terms of a Galois theory of purely iterative algorithms. In contrast, Steve and I showed in [Shub-Smale, 1986b] that if complex conjugation is allowed, then there are generally convergent purely iterative algorithms even for systems of n complex polynomials of fixed degree in n variables.”
(“On the work of Steve Smale on the theory of computation”, by Michael Shub, in Morris W. Hirsch, Jerrold E. Marsden and Michael Shub, eds., 1993, Springer-Verlag)
I recall that the positive result when complex conjugation is permitted was presented by Smale in his graduate course; McMullen’s proof of Smale’s conjecture was presented by Smale at a department colloquium talk, but it came late as I was about to graduate and preoccupied with studying computer science. My lack of time and lack of specialization in the algebraic topology and Galois theory-related topics meant that I did not acquire a full technical understanding of it.
But I remember thinking that there was a Chris Mullin and now came a Curtis McMullen: Oakland NBA basketball team Golden State Warriors’ biggest star player was Chris Mullin, a former U.S. Olympic Dream Team gold medalist from St. John’s University in Queens, New York, while Curtis McMullen’s Ph.D. adviser Dennis Sullivan was the Einstein Chair of Science at Queens College of the City University of New York.
(“MAYOR GIULIANI HONORS FOUR NEW YORKERS FOR EXCELLENCE IN SCIENCE AND TECHNOLOGY”, February 24, 1998, New York City Mayor’s Press Office; and, “Chris Mullin Set for Appearance at Citi Field on Wednesday”, September 2, 2015, St. John’s University)
Subsequently in the 1990s McMullen became a UC Berkeley professor, but in 1997 returned to his alma mater Harvard before he was awarded the Fields Medal at the 1998 ICM, mainly for his research in chaos theory – Smale had been a founder of that field – and in that same year 1997 Mullin left the Warriors for the Indiana Pacers.
(September 2, 2015, St. John’s University; and, “1998 Fields Medalist Curtis T. McMullen”, American Mathematical Society)
McMullen was no doubt very bright. But the results in this direction by him, Smale and Shub also illustrated that, even for computational issues, focusing on a more pure-mathematics direction can lead to more advanced mathematical achievements.
More generally in 1987-1988, Smale and his collaborators took a more pure-mathematics direction by moving from analysis of algorithms to complexity theory.
There was an interesting title discrepancy for Smale’s plenary address at the 1986 ICM at Berkeley: the title was “Algorithms for Solving Equations” as in the ICM proceedings, but “Complexity aspects of numerical analysis” according to an 1987 book on the history of ICMs, quoting The New York Times, both cited earlier.
The The New York Times’ report in August 1986 quoted Smale on the difference between algorithm and complexity:
“… At the International Congress of Mathematicians this month in Berkeley, Calif., signs of the computer were everywhere. The opening plenary speaker, Stephen Smale of the University of California at Berkeley – a pure mathematician with a record of bringing fellow mathematicians into new areas – focused on the developing theory of complexity, which addresses questions of what sorts of problems can and cannot be solved on computers.
The problem-solving abilities of computers, Dr. Smale said, have created a challenge that is philosophical, logical and mathematical. “This subject is now likely to change mathematics itself,” he said. “Algorithms become an object of study, not just a means of solving problems.””
(“MATHEMATICIANS FINALLY LOG ON”, by James Gleick, August 24, 1988, The New York Times)
A computer algorithm is a means of solving problems, and so practical considerations would have to be important. Complexity is about what sorts of problems can or cannot be solved on computers, and so it may involve more fundamental mathematics about the problems and the algorithms – but understandably, studying if something “can” be done does not necessarily require all the practicalities of doing it.
Besides its dismissive title, “Mathematicians finally log on”, similar to the UC Berkeley numerical analysts’ attitudes I have described, the The New York Times article referred to Smale as a “pure mathematician with a record of bringing fellow mathematicians into new areas” – obviously, if they just got into the computer how could what they did be “applied”?
When first entering the numerical analysis field, Smale’s 1981 paper was titled, “The fundamental theorem of algebra and complexity theory”, concerned with fundamental mathematics and complexity theory. A few years later, his October 1985 paper’s title was “On the efficiency of algorithms of analysis”, concerning algorithms, and so more practically oriented. Now in 1986 his plenary address at the world’s leading gathering of mathematicians had both an “algorithm” title – for the printed proceedings – and a “complexity” title – for the actual talk at the congress.
More modestly on my part, in 1986 I derived computable average error estimates for a type of error estimation in numerical integration, and presented them for the first time in around May at an MSRI seminar – fulfilling a seminar-presentation requirement for the Ph.D. degree. That was also when my adviser first learned of the details of what would become my Ph.D. thesis.
But Smale was, after all, more of a “pure mathematician”: in 1987-1988 he was returning, along with his collaborators Lenore Blum and Michael Shub, to a complexity focus; they embarked on an ambitious project to develop an algebra-oriented, comprehensive complexity theory that would rival, and even encompass, the existent complexity theories in computer science.
Recall as in Part 3 that Lenore’s husband Manuel Blum had been a pioneer in complexity theory and for his achievements would be the 1995 winner of the A. M. Turing Award, computer science’s highest honor. Thus Lenore’s summary of their work was succinct, informative and telling:
“In 1989, Mike Shub, Steve Smale and I introduced a theory of computation and complexity over an arbitrary ring or field R [BSS89]. If R is Z2 = ({0, 1}, +, ⋅), the classical computer science theory is recovered. If R is the field of real numbers, Newton’s algorithm, the paradigm algorithm of numerical analysis, fits naturally into our model of computation.
Complexity classes P, NP and the fundamental question “Does P = NP?” can be formulated naturally over an arbitrary ring R. The answer to the fundamental question depends in general on the complexity of deciding feasibility of polynomial systems over R. When R is Z2, this becomes the classical satisfiability problem of Cook- Levin [Cook71, Levin73]. When R is the field of complex numbers, the answer depends on the complexity of Hilbert’s Nullstellensatz.
The notion of reduction between problems (e.g. between traveling salesman and satisfiability) has been a powerful tool in classical complexity theory. But now, in addition, the transfer of complexity results from one domain to another becomes a real possibility. …”
(“Computing over the Reals: Where Turing Meets Newton”, by Lenore Blum, October 2004, Volume 51, Number 9, Notices of the American Mathematical Society)
As Lenore put it in 2004, their theory cut across classical complexity theory of computer science, Newton’s method in numerical analysis, and the complexity aspect of classical mathematics – David Hilbert’s algebraic geometry a century earlier.
Lenore also pointed out that when certain “reduction” relationship between two things is established, a rich body of significant mathematical results in one can be transferrable to the other.
By the time of 2004, Lenore was the Distinguished Career Professor of Computer Science at Carnegie Mellon University, where Manuel and their son Avrim were also computer science professors:
“Professor Mom takes the office on one side of him, Professor Dad takes an office on the other. Son is caught up in parents’ well-meaning meddling both at work and at home. Hilarity ensues.
Think “Everybody Loves Avrim.”
…
The recruitment of Manuel and Lenore Blum, once happily ensconced in Berkeley, Calif., to the Carnegie Mellon computer science school two years ago was considered a coup, capping almost 20 years of effort.
…
A measure of their impact came last month, when Carnegie Mellon garnered a $24 million share of the National Science Foundation’s $156 million Information Technology Research program. Of the 14 Carnegie Mellon projects to receive funding, the largest was a $5.5 million award for Aladdin, which includes Manuel, Lenore and Avrim Blum among its investigators.”
(“Dad, mom join son to form a potent computer science team at CMU”, by Byron Spice, October 21, 2001, Pittsburgh Post-Gazette)
Such a happy family finale would be incomplete without a story about the humbler beginnings:
“The romance began in Caracas, Venezuela, where Manuel and Lenore grew up.
Manuel’s parents had fled Europe ahead of the Holocaust and, unable to get into the United States, settled in Caracas.
His father, a jeweler and expert watchmaker, came from the town of Chernovtsy, then part of Romania, but in a border region that often changed hands (it is now part of Ukraine). The joke was that the people of Chernovtsy spoke the language of whoever won the last war. Manuel grew up in Caracas speaking German.
…
“I thought if I could only understand how the brain works, I could be smarter,” he said. It set him on a course that would lead him to the field of computer science. But when he left Caracas for the United States in the mid-1950s to attend Massachusetts Institute of Technology, no such field existed. So he pursued his interest in the electrical activity of the brain by studying electrical engineering, then switched to neurobiology.
Lenore didn’t reach Caracas until she was 9, moving with her family from New York City in the 1950s. Unfamiliar with Spanish and initially unhappy in school, she persuaded her parents to let her take a year off. When she returned to school, her class was being taught long division. She found it fascinating, beginning her lifelong love of mathematics.
…
Following the advice of a high school teachers, she decided to study architecture, not mathematics, in college. Unable to gain admission to MIT, where Manuel was a graduate student, Lenore headed for the Carnegie Institute of Technology.
But after her first year at Carnegie Tech, she realized that math remained her true interest. She switched majors and ended up in an experimental mathematics class taught by Alan Perlis, a pioneer who would establish the computer science department at Carnegie Tech and, later, at Yale University.
…”
(Byron Spice, October 21, 2001, Pittsburgh Post-Gazette)
So it had begun in Caracas, Venezuela, where Smale later began his one-year sabbatical in July 1984, and now it has been happiness ever after for the Blums. I note that from Central America, Manuel went to a U.S. school where John Nash happened to teach though in a different field, and Lenore to Nash’s undergraduate alma mater in a different field.
But regarding me, as in Part 1, by 1999 Lenore refused to help my academic job prospect, stating:
If you can program, you don’t need to be in the academia”.
(January 29, 2013, Feng Gao’s Posts – Rites of Spring)
Back in 1987-1988, my focus on auditing computer science graduate courses was more practically oriented, and did not include the complexity theory course taught by none other than Manuel Blum. Fortunately, the two algorithm courses taught by Richard Karp did provide a reasonable coverage of the basic framework and concepts of complexity. As mentioned earlier, I then taught the corresponding graduate courses at UBC in 1988-1992. At UBC, the computer science complexity theory courses were the prerogative of our boss Maria Klawe’s husband, prominent theoretical computer scientist Nick Pippenger.
By the early fall of 1987 I had also produced first results in computer science research, on the analysis of intrinsic communication costs in parallel computation for some numerical computation algorithms, and so had a second topic for seminar presentation from that point on.
With Lenore’s networking help and arrangement, in October 1987 I gave seminar presentations at CUNY Queens College where Mike Shub had taught for many years, at IBM Thomas J. Watson Research Center where Mike was a scientist for about 2 years now, and at the University of Toronto’s computer science department that then offered me a 2-year postdoctoral fellowship, in affiliation with both the theoretical computer science group and the numerical analysis group.
The Toronto postdoc offer was the second job offer for me, after Baltimore County’s earlier in 1987, but the first from a major center of academic research. Berkeley math and CS professor Beresford Parlett, whom I respected as a mentor like Lenore, had suggested, after listening to my presentation at his numerical analysis seminar, that I do 18 months of postdoctoral research at MSRI, whereby I told him my consideration concerning my visa problem.
In December 1987 or January 1988, at James Curry’s invitation I gave seminar presentations at Boulder’s math and CS departments, and met also with computational scientists at the university’s computing center and at the Colorado School of Mines.
My interest in quantum physics and divergence had not vanished, and so on my own initiative I visited the retired physicist, Professor Robert Richtmyer in his office, whose book cited earlier was a major reference when I explored quantum mechanics in 1984-1985. Not unlike Berkeley’s Eyvind Wichmann, Richtmyer did not give me any real lead on the physics; instead he pointed to a book on his desk, “Difference Methods for Initial-Value Problems”, and asked if I knew.
(Robert D. Richtmyer, Difference Methods for Initial-Value Problems, 1957, Interscience Publishers; and, “Difference Methods for Initial-Value Problems (Robert D. Richtmyer and K. W. Morton)”, by Burton Wendroff, July 1968, Volume 10, Number 3, SIAM Review)
I had noticed Richtmyer’s numerical analysis book in my past library literature searches but had not really studied it, and so answered that my Ph.D. work also involved the use of divided differences – for computable average error estimates.
So when UBC computer science department acting head, numerical analyst Uri Ascher mentioned in Part 3, brought me there for a formal interview around mid-February, he emphasized that he had heard about me from a recent trip of his to Boulder and from his contacts at Toronto. The other UBC numerical analyst, former computer science head Jim Varah cited in Part 3, arranged with David Kirkpatrick to secure funding for the fixed-term position offered to me by Uri.
While visiting UBC, I was also brought over by the University of Victoria’s computer science department for an unofficial interview there.
In around early May when I was formally interviewed by Simon Fraser University’s school of computing science, which had a strong theoretical computer science group but did not have any numerical analyst, among the professors attending my seminar presentation was Bob Russell, a numerical analyst at the mathematics department.
Chatting at the lectern after my talk, Bob pointed to a spot in my resume where my paper, based on my Ph.D. thesis and submitted through Babuska to a numerical analysis journal, was listed as “to appear”, and asked when it would appear. I replied that I had not heard from the journal after the submission. Bob said then it should not be described as “to appear”; I acknowledged he was right.
I was offered a tenure-track position, and was expected to open numerical analysis courses within the school of computing science. After returning to Berkeley, I phoned school director James Delgrande – previously cited in Part 3 – to apologize for the infraction in my resume, and he replied that they liked what they saw so it did not matter.
Fortunately, my paper was later accepted and was published in October 1989.
Like Babuska, Bob Russell’s expertise included the finite element method. He was often cited as R. D. Russell, including in a SIAM 45th-anniversary meeting session in July 1997 at Stanford, mentioned earlier, where presentations were given by Bob, Berkeley’s Keith Miller, Miller’s Ph.D. graduate and UVic graduate, LANL’s Andrew Kuprat, and my former fellow Berkeley math Ph.D. student Guojun Liao.
After my arrival in Vancouver, Bob, who had a University of New Mexico math Ph.D., told me he was the son of a LANL scientist – a physicist if I am not mistaken.
Locally in the Vancouver region, Bob had often co-authored papers with UBC’s Uri Ascher – as in Part 3 Uri had once been a scientist at the Army Mathematical Research Center at Wisconsin-Madison, the place Carl de Boor was.
So, all 3 Canadian job offers were in relation to both theoretical computer science and numerical analysis.
In Summer 1988 I got to be the teaching assistant for a 3rd-year numerical analysis course, after years of TA work for introductory calculus classes including under professors Bob Anderson, David Gale and Ken Ribert. The instructor was Nate Whitaker, Alexandre Chorin’s African-American Ph.D. student who had graduated and was doing postdoctoral research at Lawrence Berkeley National Laboratory as I recall, and getting ready to become a tenure-track assistant professor at the University of Massachusetts Amherst.
It was a last-minute practice for me, as my scheduled UBC teaching duty in Fall 1988 would include a graduate course on numerical linear algebra (matrix computation), the specialty of former department head Jim Varah who by this time was the director of CICSR, the university-level Centre for Integrated Computer Systems Research.
During that summer Prof. Beresford Parlett, Berkeley’s expert on numerical linear algebra, gave me a month’s “postdoc” support partly because I was writing a short research paper with him.
But when I went to Bernice Gangale who, assisted by Jeanne Coffee, handled administrative support for the center for pure and applied mathematics, to finalize the paperwork for the financial support, I was told that the center director, Alberto Grünbaum, said my work should be categorized as “postgraduate” and the job description “postgraduate researcher”.
It was only a month’s time so whatever the title, and I understood that it wasn’t a serious postdoctoral fellowship in duration, work or pay. But when I had just received a doctoral degree, wouldn’t “postdoctoral” make sense? My classmate friend Mei Kobayashi had worked for a year at Harvard after her 1981 Princeton bachelor’s degree, and that I knew was “postgraduate” work.
Clearly, to the critically demanding I was short of the postdoctoral research and visiting faculty experiences.
Months before the May graduation commencement, Smale told me that he had nominated me to the department for the Bernard Friedman Memorial Prize in Applied Mathematics for outstanding graduate student research.
I did not pin much hope on that, knowing the numerical analysts’ dismissiveness of Smale’s work and Grünbaum’s close relationship with them. As discussed, back in 1984 I did not bothered to apply to change my Ph.D. candidacy to my original declaration of “applied mathematics”, after it had been categorized as “mathematics”. Also, for the committee to approve my thesis, consisting of two professors in addition to the adviser, I sought the consents of Bob Anderson and Morris Hirsch, Smale’s long-time friend since the anti-war days cited in Part 2, rather than the numerical analysts.
The winner of the Bernard Friedman Prize that year was Yong-Geun Oh, a classmate from South Korea, with a Ph.D. thesis titled, “Nonlinear Schrodinger Equations with Potentials: Evolution, Existence, and Stability of Semi classical Bound States”. The title indicated relevance to quantum mechanics, while the type of issues studied were similar to what I had learned under Kato. I thought it must be close to Grünbaum’s interest, although Oh’s adviser was Prof. Alan Weinstein, a former Ph.D. student of Shiing-shen Chern’s, and Oh’s collaborators included Prof. Jerrold Marsden – later an editor, along with Hirsch and Shub, for the proceedings of the Smalefest conference cited earlier.
(“Stability of Semiclassical Bound States of Nonlinear Schrδdinger Equations with Potentials”, by Yong-Geun Oh, 1989, Volume 121, Number 1, Communications in Mathematical Physics; and, “Yong-Geun Oh”, Mathematics Genealogy Project)
It wasn’t the first time Smale recommended me for an honor, though every time not to be.
Back in 1986 I went to ask if he could nominate me for the Sloan doctoral dissertation fellowship, Smale responded that he had already nominated Joel Friedman. I said that I should have been considered if only because of my seniority as his student, but since he had decided it was okay with me. A day later Smale left a note in my mailbox to get me to his office; there he said that, for technical reasons only and not as a precedent, he would also nominate me. In the end neither received it, but Joel soon graduated in 1987 for the Princeton job.
Unlike me or Joel Friedman, but like David Witte, the Bernard Friedman Prize winner Yong-Geun Oh started his academic career with years of postdoctoral research and short-term teaching at top universities, including a postdoctoral year at MSRI, 2 years of instructorship at NYU’s Courant Institute and a year of membership at Princeton’s Institute for Advanced Study, before starting as an tenure-track assistant professor at Wisconsin-Madison – Witte could have settled on one there had not been for a higher ambition as discussed – where he became a full professor in 2001.
(Fall 1997, Department of Mathematics, University of Wisconsin; and, “Yong-Geun Oh: Brief Narrative Research Resume”, Center for Geometry and Physics, Institute for Basic Science, Pohang University of Science and Technology)
My choice of an immediate faculty job leaned toward an independent academic career but was a compromise: goal-oriented in choosing a fixed-term position at the academically stronger UBC partly because of the arrival of Klawe and Pippenger, as suggested by Karp, over a tenure-track one at SFU, yet with some disappointment that it wasn’t a scientifically more advanced route like at Canada’s academically leading University of Toronto.
The scientific prominence of the Berkeley professors I studied under over 6 years certainly reaffirmed and strengthened my sense of optimism in possibilities and potentials: Tosio Kato was a recent winner of the Wiener Prize in Applied Mathematics, Andrew Majda was in the process to take up a professorship at the prestigious Princeton University, and of course Steve Smale was a Fields Medalist; as mentioned earlier, among my first-year professors was also recent Steele Prize winner Gerhard Hochschild, besides Kato.
The award-winning prominence was more ground-breaking, as both Smale and Kato were the first Berkeley winners of the respective prizes, which were among the leading prizes of mathematics.
In the 1980s, the leading mathematical prizes awarded by the mathematical community were the Fields Medal of the International Mathematical Union, the Steele Prizes of the American Mathematical Society, and the Wiener Prize and Birkhoff Prize awarded jointly by AMS and the Society for Industrial and Applied Mathematics.
The International Mathematical Union, which organizes the International Congress of Mathematicians every 4 years with awarding of prizes, describes its current set of prizes as follows:
“… The Fields Medal recognizes outstanding mathematical achievement. The Rolf Nevanlinna Prize honors distinguished achievements in mathematical aspects of information science. The Carl Friedrich Gauss Prize is awarded for outstanding mathematical contributions that have found significant applications outside of mathematics. The Chern Medal is awarded to an individual whose accomplishments warrant the highest level of recognition for outstanding achievements in the field of mathematics.
The Fields Medal was first awarded in 1936, the Rolf Nevanlinna Prize in 1982, and the Carl Friedrich Gauss Prize in 2006. The Chern Medal was awarded for the first time in 2010.”
(“IMU Awards and Prizes”, International Mathematical Union)
As described, in 1936 the Fields Medal became the first and only IMU prize, until 1982 when the Rolf Nevanlinna Prize was added for mathematical aspects of information science; more recently the Gauss Prize was added in 2006 in relation to applying mathematics to other subjects, and the Chern Medal in 2010 as “the highest level of recognition” in mathematics – without the Fields Medal’s age requirement of not exceeding 40 in the year of the award.
The Field Medal was first established through the efforts of Canadian mathematician J. C. Fields, who had organized the 1924 ICM:
“At the 1924 International Congress of Mathematicians in Toronto, a resolution was adopted that at each ICM, two gold medals should be awarded to recognize outstanding mathematical achievement. Professor J. C. Fields, a Canadian mathematician who was Secretary of the 1924 Congress, later donated funds establishing the medals, which were named in his honor. In 1966 it was agreed that, in light of the great expansion of mathematical research, up to four medals could be awarded at each Congress.”
(“Fields Medal Details”, International Mathematical Union)
The IMU list of Fields Medal recipients shows that Stephen Smale, one of the four 1966 recipients, was the first for UC Berkeley. Per the IMU list, so was every of Smale’s co-recipients the first for his university: Paul Joseph Cohen of Stanford University, Michael Francis Atiyah of Oxford University and Alexander Grothendieck of the University of Paris; but as detailed in Part 2, Smale had stood out as a left-wing student activist during the McCarthy era of the 1950s at the University of Michigan, and then as a Berkeley anti-Vietnam War movement leader in 1965.
Tosio Kato enjoyed a similar status as Berkeley’s first with the Wiener Prize in Applied Mathematics.
According to SIAM, the Norbert Wiener Prize and the George David Birkhoff Prize are the only two “highest” prizes, awarded for:
“an outstanding contribution to applied mathematics in the highest and broadest sense”.
(“Prizes, Awards and Lectures Sponsored by SIAM”, Society for Industrial and Applied Mathematics)
Both prizes have been jointly awarded by SIAM and AMS.
The SIAM list of recipients shows the Wiener Prize was first awarded in 1970, and has been awarded every several years; its second winner, in 1975, was Peter Lax of New York University – Chorin’s former Ph.D. adviser mentioned earlier.
Kato and co-recipient Gerald Whitham were winners of the Wiener Prize’s third awarding, in 1980, and Kato was the first UC Berkeley recipient.
The other leading prize awarded by the mathematical community was the Leroy P. Steele Prizes. Per AMS’s descriptions, among its prizes the Steele Prizes have been the only ones for mathematics in general and open to all mathematicians, awarded for lifetime achievement, research, or exposition; other prizes are specialized ones, such as the Oswald Veblen Prize in Geometry that Smale had received in 1964 as in part 2, the Delbert Ray Fulkerson Prize “in the area of discrete mathematics”, and the Ruth Lyttle Satter Prize in Mathematics for “mathematics research by a woman in the previous six years”. Beginning in 1988 there has been a National Academy of Sciences Award in Mathematics .
(“Prizes and Awards”, American Mathematical Society)
My first-year graduate algebra professor Gerhard Hochschild was a Steele Prize winner in 1980 for his research, but unlike Kato and Smale, Hochschild was not the first UC Berkeley recipient of that prize.
The Steele Prizes was first awarded in 1970. The second winner, Phillip Griffiths of Princeton University in 1971 for a 1970 paper, had formerly been a UC Berkeley fellow and faculty member, 1962-67.
(“Phillip A. Griffiths: Curriculum Vitae”, School of Mathematics, Institute for Advanced Study)
The honor of the Steele Prizes’ first UC Berkeley recipient went to Professor Hans Lewy in 1979 for his research, one year before Hochschild.
Lewy’s award was like Smale’s, politically speaking. Lewy had been one of 3 tenured math professors among 29 Berkeley professors and 2 UCLA professors fired in the early 1950s in the McCarthy era due to their refusal to sign the University of California’s Loyalty Oath to declare that they were not and had never been Communists:
“Fear of communism was being developed and fanned for political purposes by a junior senator from Wisconsin, Joseph McCarthy, in the late 1940s. McCarthy eventually formed a committee that went to universities to question professors concerning their connection to the Communist Party. More widely known are the inquisitions of Hollywood actors, but it extended to all levels of public influence. McCarthy was spreading fear of educators as well.
Wanting to show proof of loyalty, Robert Gordon Sproul, then President of the University of California, proposed the Loyalty Oath which would have all professors declare they were not and never had been communists.
Some 29 tenured professors from UC Berkeley and two from UCLA (one of whom later became a UC President) refused to sign. They declared that political affiliation should not be required to be made public, and the Communist Party was a legal party in the US. It was a matter of principle.
The Regents of the time mandated that all professors had to sign, or be fired. In the Mathematics Department, three professors refused: John Kelley, Hans Lewy, and Pauline Sperry. Another professor, D.H. Lehmer, attempted to avoid signing by taking a leave of absence to take a federal job at UCLA as Director at the Institute for Numerical Analysis. However, he was told he needed to sign before he could go on the payroll. With five children to support, he eventually signed but with objection.
…
Finally, in 1952-53 the California Supreme Court ruled the Loyalty Oath to be unconstitutional. …”
(“Loyalty Oath Controversy: Interview with Leon Henkin”, Fall 2000, Vol. VII, No. 1, Berkeley Mathematics Newsletter)
Lewy’s prior experience as a Jewish mathematician fleeing the rise of Nazism in Germany played a role in his resolve to refuse what he viewed as totalitarian tendency in the Loyalty Oath requirement:
“Hans Lewy was born on October 20, 1904 in Breslau, Germany (now Wroclaw, Poland)…
Göttingen, in 1922 when Hans Lewy matriculated, was among the premier mathematical establishments in the world. With Klein and Hilbert still in residence, as well as Runge, Prandtl, Landau, and Emmy Noether, Courant, of course, and many others {Reid, 1970} it radiated irresistible scientific excitement. …
Friedrichs also arrived in 1922 and their lifelong friendship took hold immediately. …
He completed his thesis in 1926 with Courant and became, together with Friedrichs, Courant’s Assistant and a Privatdozent. …
…
Lewy left Germany quite soon after Hitler assumed power in 1933. He went first to Italy and then to Paris where Hadamard had managed to obtain for him a year’s support. … In Paris, on the recommendation of Hadamard, he was offered a one to two year position at Brown, funded by the Duggan Foundation. In the fall of 1933, Lewy was in Providence. …
On the invitation of G.C. Evans, Lewy went to Berkeley in 1935. Courant, visiting Berkeley in 1932, had spoken enthusiastically of Lewy’s work on that occasion. Courant himself was, in fact, offered a position at Berkeley. …
With the outbreak of the war, Lewy took flying lessons and obtained a solo license in the hope of offering his services, but was soon called to Aberdeen Proving Grounds as part of the University of California contingent. He also worked half-time with the Office of Naval Research in New York. Here he became interested in water waves and the Dock problem, resuming his collaboration with Friedrichs…
…
During the Loyalty Oath controversy in the state of California, Lewy was part of the group dismissed for refusal to sign the oath. Having seen Fascism at fist hand in Italy, and watched its rise in Germany, he was wary of cooperating with any totalitarian tendencies in his new country. … He was on the faculty at Harvard in the fall of 1952 and then at Stanford in 1952 and 1953. … In the settlement of this dispute by the courts, the professors were reinstated and Lewy returned to Berkeley. …”
(“Hans Lewy: A Brief Biographical Sketch”, by D. Kinderlehrer, in David Kinderlehrer ed., Hans Lewy Selecta, Volume 1, 2002, Birkhäuser)
Lewy’s stand against McCarthyism led not only to his firing by UC but also the German consul general’s refusal to extend his passport:
“A new exhibition at UC Berkeley’s Magnes Collection of Jewish Art and Life tells the stories of more than 70 scholars, writers and artists — many of them Jewish, related to Jews or political dissidents — who escaped the rise of Nazism and fascism in Europe in the 1930s and ‘40s and brought their talents and dreams with them to UC Berkeley.
…
During an opening reception, University of California President Janet Napolitano praised the exhibition’s remarkable story and called the collaboration “a priceless learning opportunity.”
…
… The exhibit features, for example, war-rations books and anonymous hate mail sent to musicologist Alfred Einstein. Visitors can also see a German consult general’s rejection of a request to extend a passport, in response to math professor Hans Lewy’s three-year suspension when he refused to sign the campus Loyalty Oath. Family photos and a 1985 certificate, awarding Austria’s Medal of Honor to Max Knight, are also on view.”
(“Intellectual migration from fascist Europe to Berkeley”, by Kathleen Maclay, February 4, 2014, University of California)
So it was fitting, that a Jewish mathematician with a math Ph.D. from the world renowned University of Göttingen under the mathematical patriarch Richard Courant, having escaped Nazi Germany and participated in U.S. military research during World War II, took a stand against McCarthyism and later in 1979 became the first Berkeley winner of American Mathematical Society’s top general prize – in line with Steve Smale’s honor as Berkeley’s first Fields Medal winner in 1966.
As in Part 2, Courant, founder of NYU’s Courant Institute, and another mathematical patriarch, Oswald Veblen of Princeton’s Institute for Advanced Study, were once featured with the young mathematician John Nash in a Fortune magazine article in the summer of 1958 – only months before Nash’s miserable attempt to start a world peace movement at MIT that would end with Nash’s psychiatric committal.
As quoted above, in the early 1930s UC Berkeley had tried to recruit Courant, who did not move there but recommended his student Hans Lewy enthusiastically. Lewy was only one of many young mathematicians who had worked under Courant at Göttingen, in a manner that later drew criticisms about Courant:
“As a Privatdozent, whose meager fees were paid by his students, usually few in number, Lewy jokingly reported in 1928 a “lucrative” semester: “Now when people ask why I went into mathematics I can answer, ‘For the money!’”
In addition to teaching, he served with Friedrichs as one of Courant’s many assistants. Although in the future Courant was often to be criticized for exploiting such younger men, Lewy always considered the time he spent as assistant exceedingly valuable.”
(“Hans Lewy, 1904-1988”, by Constance Reid, in David Kinderlehrer ed., Volume 1, 2002, Birkhäuser)
It was scientific prestige, but meager pay, to be a Privatdozent and Prof. Richard Courant’s assistant at the University of Göttingen.
Lewy’s specialty was in partial differential equations, the field in which I studied under Tosio Kato and my officemate Steve Pomerantz received his Ph.D. under Murray Protter, and related to the field my classmate Robert Rainsberger received his Ph.D. under Heinz Cordes as earlier.
After his passing in 1988, Lewy’s colleagues and peers Protter and Kato, along with colleagues John Kelley and Derrick Lehmer who had in 1950 shared his opposition to McCarthyism, wrote about his important contributions:
“Professor Lewy was known as a person of integrity and strong moral principles. In 1950, he refused to sign a special loyalty oath imposed on the faculty by the University of California’s Board of Regents; for this reason he and a number of other professors were fired. They were later vindicated and reinstated when the courts determined that taking the oath would have violated their civil rights.
Hans Lewy was one of the great mathematicians of the twentieth century; he showed unparalleled originality in his work, which was characterized by the unexpected. In 1957 he started the mathematical world by exhibiting a simple partial differential equation which has no solution at all, thus changing the thinking of the experts in the field.
In another of his best known works, written in 1928 with Courant and Friedrichs, he developed criteria for determining conditions which guarantee the stability of numerical solutions of certain classes of differential equations. This work turned out to be crucial later for the use of high speed computers in solving such equations; thousands of research articles have been written on numerical solutions of differential equations based on his pioneering work.
While still in Göttingen, he published a series of fundamental papers on partial differential equations and the calculus of variations. He solved completely the initial value problem for general nonlinear hyperbolic equations in two independent variables. … He proved the well-posedness of the initial value problem for wave equations in what is now called Sobolev spaces two decades before these spaces became a common tool for specialists. …”
(“Hans Lewy, Mathematics: Berkeley: 1904-1988 Professor Emeritus”, by M. Protter, J.L. Kelley, T. Kato and D.H. Lehmer, 1988, University of California)
While studying under Kato I regularly, and later from time to time, attended the weekly seminar on partial differential equations and became familiar with this group of professors who were quite senior, and very genial and affable.
Quite a few times I mentioned Hans’s research to my roommate Kezheng. Sometimes when Kezheng menitoned the name “Hans” I wasn’t sure which one he was referring to, because I also knew another, Kezheng’s auto insurance agent who became my agent: soon after my arrival at Berkeley, Kezheng taught me driving and added my name as a driver to the Farmers Insurance auto policy for his old Ford, and his agent Hans was a very friendly man.
In the summer of 1983 with Kezheng and I the drivers, we and several Chinese visiting scholars took a tour of Western U.S., sightseeing at places like Salt Lake City, Yellowstone, Grand Canyon, and Death Valley where our rental car had a flat tire as in my February 2013 blog post.
(February 28, 2013, Feng Gao’s Posts – Rites of Spring)
One of those visiting scholars, Zhujia Lu (陸柱家), by the early 2000s when I visited Beijing was the director of scientific research at the Academy of Mathematics and Systems Science in the Chinese Academy of Sciences.
Another of the visiting scholars, Zeke Wang (王則柯), had just finished a visiting scholarship at Princeton where he did research with Prof. Harold Kuhn on a topic inspired by Smale’s work on finding zeros of complex polynomials. I hadn’t chosen Smale as my Ph.D. adviser at that point but Kuhn – the same last name as the philosopher Thomas Kuhn, once a Princeton professor also – was well-known for the mathematical work he had done with another Princeton professor, Albert Tucker – as in Part 2 John Nash’s Ph.D. adviser.
(“On the cost of computing roots of polynomials”, by Harold W. Kuhn, Zeke Wang and Senlin Xu, February 1984, Volume 28, Issue 2, Mathematical Programming; and, “Karush–Kuhn–Tucker conditions”, Wikipedia)
At the time I did not know about Tucker’s former Ph.D. student John Nash, but my father was a former graduate student of Zeke’s father, SYSU Chinese literature Professor Wang Qi (王起), mentioned in my Chinese blog posts in February and June 2011. At Berkeley was when I met Zeke, as he had gone to study and then teach at Peking University since the 1960s, and was only recently moving to Sun Yat-sen University – known in China as Zhongshan University for Sun Yat-sen’s more common name, Sun Zhongshan.
(November 22, 2010, Feng Gao’s Blog – Reflections on Events of Interest; “忆往昔，学历史智慧（三）——文革“破旧立新”开始的记忆”, February 20, 2011, and, “忆往昔，学历史智慧（四）——青少年时代的部分文化熏陶”, June 22, 2011, 高峰的博客 – A refreshed feeling)
Though the Farmers Insurance agent Hans was of a considerably larger build and a more authoritative personality, than Hans Lewy, their friendliness reminded me of the old-time farmers, or perhaps in the case of Lewy as described by mathematical biographer Constance Reid, a gardener:
“The Lewy’s had one son, Michael, who is now also a mathematician.
Once he became a family man and a householder, Lewy discovered the joys of home repair, woodwork and gardening. He took pride in the fact that, unlike professors he had known in his youth, he could – and would – do things with his hands. … Because of his propensity for seeing both sides of a question, he could not make life and death decisions even for plants and left undisturbed “volunteers” that other gardeners would have eradicated. …
He was often joyously unrestrained and enthusiastic. …
…
The most dramatic event of his more than fifty years at Berkeley occurred during the McCarthy era when the Regents of the University decided that members of the faculty should sign a loyalty oath … Lewy recognized the threat to academic freedom and refused to sign… He was not, however, doctrinaire on the subject and counseled others, especially younger colleagues, that they must look at their weapons before they decided to fight. He himself was well armed, having resolved when he had had to leave Göttingen that he would save a year’s salary as soon as possible in case he ever had to leave another job. … he was one of the few who managed to remain on friendly terms with those who had different views. Ultimately the California Supreme Court declared the oath unconstitutional and ordered the University to reinstate the non-signers with back pay and privileges. …”
(Constance Reid, in David Kinderlehrer ed., Volume 1, 2002, Birkhäuser)
That sounds like Hans the professor I knew, joyful, intellectual, hardworking, principled yet flexible, and willing to counsel others with his wisdom – except that back at Göttingen his meager income as a Privatdozent and Courant’s assistant probably wouldn’t have let him save much.
I wonder if and what Lewy may have “counselled” the young John Nash in 1957, when Nash seriously questioned quantum mechanics and had an argument with the physicist Robert Oppenheimer at the IAS in Princeton – according to Sylvia Nasar’s book, A Beautiful Mind, Lewy might be among the persons Nash had discussions with:
“Nash left the Institute for Advanced Study on a fractious note. In early July he apparently had a serious argument with Oppenheimer about quantum theory – serious enough, at any rate, to warrant a lengthy letter of apology from Nash to Oppenheimer written around July 10, 1957… After calling his own behavior unjustified, Nash nonetheless immediately justified it by calling “most physicists (also some mathematicians who have studied Quantum Theory) . . . quite too dogmatic in their attitudes,” complaining of their tendency to treat “anyone with any sort of questioning attitude or a belief in “hidden parameters” . . . as stupid or at best a quite ignorant person.”
…
“I embarked on [a project] to revise quantum theory,”, Nash said in his 1996 Madrid lecture. “It was not a priori absurd for a non-physicist. Einstein had criticized the indeterminacy of the quantum mechanics of Heisenberg.”
He apparently had devoted what little time he spent at the Institute for Advanced Study that year talking with physicists and mathematicians about quantum theory. Whose brains he was picking is not clear. Freeman Dyson, Hans Lewy, and Abraham Pais were in residence at least one of the terms. …
It was this attempt that Nash would blame, decades later in a lecture to psychiatrists, for triggering his mental illness – calling his attempt to resolve the contradictions in quantum theory, on which he embarked in the summer of 1957, “possibly overreaching and psychologically destabilizing.””
(Sylvia Nasar, 1998, Simon & Schuster)
You see, according to Nash, “most physicists” believed quite dogmatically that quantum mechanics as the theory of particle physics did not need other “hidden parameters”; “some mathematicians” like John von Neumann then catered to these physicists’ worldview by making efforts to prove that no “hidden parameters” exist – a claim I had serious doubts about as discussed earlier.
As in Part 2, while formally at the Institute for Advanced Study in the academic year 1956-1957, Nash spent most of his time at NYU Courant Institute instead; his looking into quantum theory was mentioned in the 1958 Fortune article mentioned earlier, along with his stock-market prediction hobby:
“He is now an associate professor at M.I.T. and is looking into quantum theory. He also applies mathematics to one of his hobbies: stock-market predictions.”
(“This 1958 Fortune article introduced the world to John Nash and his math”, by Stephen Gandel, May 30, 2015, Fortune)
Perhaps I should have brought my questions about the mathematics of quantum physics to Prof. Kato and his Berkeley peers in partial differential equations: their mathematics was close to physics and Kato himself had a physics Ph.D.
Or perhaps lucky that I didn’t. As Nash later insinuated in 1997, quoted earlier from Nasar’s book, even without getting into politics like he did in 1958 – and I did in 1992-1993 – that kind of scientific ambition could already be a ground for mental-health concern!
In Nash’s mind maybe, but not in mine.
But the professors who taught me, or whom I got to know, in my first year at Berkeley were overwhelmingly older seniors. While the computer science professors I audited graduate courses with in 1987-1988, namely Jitendra Malik, Alvin Despain, David Messerschmitt, John Ousterhout, and Richard Karp, are all living today, my first-year graduate math course professors – except the younger Polish visiting professor I have not re-identified – namely William Bade, Gerhard Hochschild, Abraham Seidenberg, and Tosio Kato, have all passed away.
The first to go, at an intriguing time from my vantage point, was Seidenberg, on May 3, 1988, only weeks short of his 72nd birthday on June 2, in Milan, Italy:
“The distinguished mathematician and historian of mathematics Abraham Seidenberg, who taught at Berkeley for 42 years, died in Milan, Italy, on May 3, 1988. He had been born in Washington, D.C., on June 2, 1916 and received his B.A. degree at the University of Maryland in 1937 and his Ph.D. at Johns Hopkins in 1943 before joining the Department of Mathematics at Berkeley as Instructor in 1945. He became Professor in 1958 and Professor, Emeritus in 1987. His career included a Guggenheim Fellowship, Visiting Professorships at Harvard and at the University of Milan, and numerous invited addresses, including several series of lectures at the University of Milan, the National University of Mexico, and at the Accademia Nazionale dei Lincei in Rome. At the time of his death, he was in the midst of another series of lectures at the University of Milan.”
(“Abraham Seidenberg, Mathematics: Berkeley: 1916-1988 Professor Emeritus”, by M. A. Rosenlicht, G. P. Hochschild and P. Lieber, 1989, University of California)
May 3, 1988, only days before my graduation commencement in mid-May.
This wasn’t the first such timing for me. As in Part 2, 10 years earlier in February 1978 when I entered Sun Yat-sen University mathematics department as a freshman, around that time Professor Lifu Jiang ( 姜立夫) passed away, who was the most senior professor at SYSU and a former teacher of Berkeley MSRI founding director Shiing-shen Chern.
Jiang was in a sense the founder of modern mathematics in China, as the founding director of the Institute of Mathematics at Academia Sinica – today’s Chinese Academy of Sciences – in the 1940s, but with Chern soon in actual charge:
“… The Institute had been in preparation since 1942 in wartime Kunming, but all its members had full-time jobs at universities, and sometimes even abroad. The director Chiang Li-fu (Jiang Lifu 姜立夫) left China for the USA in May 1946, and actual leadership passed into the hands of S.S. Chern, then a professor at Tsinghua University, who had become a leading expert on differential geometry during his studies in Hamburg and Paris in the mid-1930s. S.S. Chern had spent the years 1943-5 at the Institute for Advanced Studies in Princeton and arrived back in Shanghai in April 1946. He turned the Preparatory Office into a kind of graduate school …”
(Jiri Hudecek, Reviving Ancient Chinese Mathematics: Mathematics, History and Politics in the Work of Wu Wen-Tsun, 2014, Routledge)
Prof. Jiang lived to 87 years of age, passing on February 3, 1978:
“Lifu Jiang, original name Jiang Jiangzuo (born July 4, 1890, Zhejiang—died February 3, 1978, Guangzhou), mathematician, educator, founder of Department of Mathematics of Nankai University, and once was the director of Institute of Mathematics at the Academia Sinica.”
(“Lifu Jiang”, November 10, 2015, School of Mathematical Sciences, Nankai University)
That was the 3rd day of the month in which I became a mathematics freshman, when Jiang died. Then 10 years later, on the 3rd day of the month of my mathematics Ph.D. graduation, Seidenberg died.
Quite an eerie coincidence, given that I was the only member of the SYSU and UC Berkeley mathematics departments at those respective times.
Maybe it wasn’t a coincidence, or it was a more serious one, as Jiang had been a University of California graduate:
“Jiang graduated from University of California with a B.S. degree in 1915. In 1919, Jiang received a doctor of sciences degree from Harvard University.”
(November 10, 2015, School of Mathematical Sciences, Nankai University)
Was that Berkeley, math? In 1915 Berkeley was still the only UC campus, when what would later become UCLA was still a part of San Jose State University.
(“University of California”, Wikipedia)
Jiang’s original name was Jiang Jiangzuo (姜蔣佐); according to Chinese media sources his undergraduate education was at Berkeley, and his English name was Chan-Chan Tsoo as in his Harvard doctoral thesis.
(“数学家姜立夫”, August 13, 2002, Xinuanet)
Now I can find “Chan Chan Tsoo” in the UC official record, published in 1916 by the University of California Press, Berkeley. Chan, i.e., Jiang, was the only obvious Asian on the graduation honor roll of December 20, 1915:
“Of the 165 who received the bachelor’s degree on December 20, 1915, twenty-six received “Honors” as follows: Anatomy, Alverda Elva Reische; Astronomy, Charles Donald Shane; Drawing, Elva Britomarte Spencer; English, Samuel Francis Batdorf, Sidney Coe Howard, Isabelle Elizabeth de Meyer, Neil Louise Long; French, Belle Elliott Bickford; German, Jennie Schwab; Hygiene, Florence Harriett Cadman; Latin, Mildred Goyette; Mathematics, Maryly Ida Krusi, Chan Chan Tsoo; Philosophy, Ruth Eloise Beckwith, Ada Rebecca Bray Fike; Physical Education, Frederick Warren Cozens; Zoology, Ebba Olga Hilda Braese, Pirie Davidson, Dorothy Sherman Rogers, Katherine Badeau Rogers, Frances Ansley Torrey; College of Mining, Omar Allen Cavins; College of Agriculture, Laurence Wood Fowler, Amram Khazanoff, William E. Gilfillan, Edith Henrietta Phillips.”
(“GRADUATED WITH HONORS”, 1916, Page 272, The University of California Chronicle An Official Record, Volume XVIII, University of California Press, Berkeley)
It looked like in those Zoology days the only subjects the university students were good at were English and Agriculture!
And maybe a little Mathematics and Philosophy?
Jiang was a professor at SYSU since 1952:
“… Jiang helped found and was the director of Institute of Mathematics at the Academia Sinica. Jiang founded department of Mathematics at Lingnan University in 1949, he taught there and Zhongshan University in 1952.”
(November 10, 2015, School of Mathematical Sciences, Nankai University)
1952 was when the private Christian Lingnan University was taken over by Sun Yat-sen (Zhongshan) University, on the decision of the Chinese Communist government as noted in my November 2010 blog post.
(November 22, 2010, Feng Gao’s Blog – Reflections on Events of Interest)
While Abraham Seidenberg at UC Berkeley might not be as prominent as Lifu Jiang at Sun Yat-sen University, he was a brilliant research mathematician:
“Seidenberg’s writings, as were his lectures, are noted for their meticulous clarity of expression. His publications in pure mathematics include some very influential work in commutative algebra, notably his joint paper with I.S. Cohen that greatly simplified the existing proofs of the so-called going-up and going-down theorems of ideal theory… His papers on differential algebra include several on … the so-called Lefschetz-Seidenberg principle of differential algebra, an analog of the Lefschetz principle for algebraic geometry, which says, very roughly, that algebraic geometry of characteristic zero is the same as algebraic geometry over the field of complex numbers. Another famous result is the Tarski-Seidenberg theorem, to the effect that there is a decision procedure for algebra over the real number field and for elementary geometry, first proved by Tarski using complicated logical machinery, then restated more simply by Seidenberg and given a much simpler mathematical proof.
…
Among Seidenberg’s publications are a large number of articles on the mathematics of primitive peoples and on the history of mathematics, in particular on ancient mathematics. Most of these articles are in support of his thesis that both arithmetic and geometry have their origins in ritual. His sources are the anthropological literature and Egyptian, Babylonian, Greek, Indian and Chinese documents. Although this work was a center of some controversy, in large part because of the general aversion among anthropologists to diffusion theories of culture, important aspects of it have received striking vindication. …”
(M. A. Rosenlicht, G. P. Hochschild and P. Lieber, 1989, University of California)
No doubt Seidenberg’s English was better than his peers’, and he could help improve what they did if he figured out what they were doing.
The Berkeley math professors were among the top researchers in their fields, even ones like Seidenberg who have not been awarded major prizes. I remember Professor Shoshichi Kobayashi, on the occasion of a dinner at his home at the invitation of Mei, telling me that the department’s hiring criteria required the successful candidate to be within the top 3 or 5 in his or her research field.
There is another way to look at Seidenberg’s brilliance and generosity. Born in the United States Capital and educated in Maryland of that region, Seidenberg grew to love Italy, especially Milan, spending a significant amount of his time there lecturing on mathematics, as told in the UC article on his death.
Even though Berkeley’s Seidenberg live a life some 15 years shorter than SYSU’s Lifu Jiang, his wife Ebe Cagli Seidenberg, an Italian Jewish writer whom he had met at Johns Hopkins University in Baltimore, Maryland, later moved to Rome and lived to 87 – the same age as Jiang.
(“Ebe Cagli Seidenberg”, Institute of Modern Languages Research, School of Advanced Study, University of London; and, “Abraham Seidenberg”, School of Mathematics and Statistics, University of St Andrews, Scotland)
Like Zeke Wang mentioned earlier, son of my father’s former graduate adviser Prof. Wang Qi, Prof. Lifu Jiang’s son Boju Jiang (姜伯駒), more senior than Zeke, studied and then taught mathematics at Peking University since the 1950s, and Zeke later became a student of his and then a colleague. Like his contemporary Peking University professor Gongqing Zhang, mentioned earlier, Prof. Boju Jiang spent time as a visiting scholar at UC Berkeley during my time there.
Shortly before my graduation, my Berkeley biophysics Ph.D. student friend Dar, mentioned earlier, suggested that I buy a car and bring it to Canada, for the reasons that a new immigrant’s belongings were free of customs duties and consumer cars were about 30% cheaper in the U.S.
Dar suggested, further, that I consider the Milano sedan, made by the Italian auto maker Fiat under the Alfa Romeo brand, a car his professor had liked very much during a recent European sabbatical – in Italy if I remember right – and brought two back.
Milano, that is Milan in Italian, no?
Dar knew more than I did about many things, not just quantum physics. In a December 2009 blog post I recalled about a Berkeley girl student I had had some infatuations with, and what Dar might have found out:
“And speaking of the Justine Bateman-lookalike student I had come across often at Berkeley in the 1980s, I returned to Berkeley in the summer of 1990 for a research stay when I was already teaching at UBC in Vancouver, and one evening a Berkeley old-time friend “Dar” who was also from Guangzhou, and I went to a Telegraph Avenue pub for a drink, and “Shawna” was sitting right there with a boy friend.
“Dar” has since finished his post-doctoral work at the Salk Institute in San Diego and at Stanford, and now works in Houston, Texas.”
(““Nairobi to Shenzhen”, and on to Guangzhou (Part 2)”, December 15, 2009, Feng Gao’s Blog – Reflections on Events of Interest)
There was no “Alfa Romeo and Juliet” in the plans of some, was there? Now in 2015 there is “Juliet and Alfa Romeo”, finally, but made in Slovenia and not – Ivo Babuska’s – Czech Republic.
(“FNE at Slovenian Film Festival in Portoroz: Juliet and Alfa Romeo”, by Damijan Vinter, September 14, 2015, Film New Europe)
In any case, the Milano model was recent and well equipped and Dar said it did not sell well in North America and so a buyer might get a good deal. Indeed, visiting a few dealerships, including one in San Jose with Dar, I found that the existing 1987 stock was selling slowly – at around $18,000 and equipped like a luxury car costing $10,000 more, but Alfa Romeo’s quality and maintenance costs were not reassuring.
In the end, the one I bought for Canada was a slightly used one costing around $15,000. The most appealing feature for me was the anti-lock braking system, ABS, available only in high-end cars at that point, something that was to be very useful in snowy climates, such as in Canada.
But I did not expect that the ABS was to become one of the faultiest parts of my car, as I recalled in my January 2013 blog post:
“… my previous car in Vancouver and Honolulu, an Alfa Romeo Milano sedan, had an elusive, borderline malfunctioning anti-lock braking system.”
(January 29, 2013, Feng Gao’s Posts – Rites of Spring)
I arrived in Vancouver on August 24, 1988, unaware that it happened to be an anniversary of the most powerful domestic terror bombing in the United States up to that point, that had occurred in 1970 targeting none other than the Army Mathematics Research Center at Wisconsin-Madison – the place my undergraduate adviser had highly recommended for my graduate study.
I wrote about it in my March 2011 blog post, that the Army math research center headed by the mathematician J. Barkley Rosser was the target but the physics department bore the losses, and that one of the killers, Leo Frederick Burt, then escaped to Canada and was never caught:
“When I applied for graduate study in the United States Professor Li seriously recommended the U. S. Army Mathematics Research Center at the University of Wisconsin, Madison …
Little did I know that the Army Math Research Center had been a target of deadly violence, by anti-Vietnam War students in the 1970 “Sterling Hall bombing”: led by the mathematician J. Barkley Rosser the Center survived the most powerful domestic bombing prior to the 1995 Oklahoma City bombing but much of the Physic department’s laboratories were destroyed and a talented postdoc researcher, Robert Fassnacht, was killed; one of the perpetrators, university rowing athlete Leo Frederick Burt, escaped to Canada and remains one of America’s Most Wanted to this day.
…
I arrived in Vancouver on August 24, 1988 – unaware that coincidentally it was an anniversary date of the 1970 Sterling Hall Bombing in Madison.”
(March 29, 2011, Feng Gao’s Blog – Reflections on Events of Interest)
Actually, I didn’t just arrive in Vancouver but drove across the U.S.-Canada border. The date of my arrival wasn’t exactly my choice, as the tentative date range was agreed upon with UBC computer science acting head Uri Ascher – he happened to have previously worked at the Wisconsin-Madison army math research center – in consideration of the Fall 1988 semester schedule and the time needed for my housing search, while Uri arranged in advance for my temporary stay at the Faculty Club. My car was then shipped from Berkeley to Seattle and I booked a San Francisco-Seattle flight for a day when my car would be available for the 140-mile drive to Vancouver.
What I didn’t know was not only it being an anniversary of a past U.S. army math research center bombing but also, on the eve of my crossing into Canada, the death of Hans Lewy:
“He died on August 23, 1988 in Berkeley. He and Helen had recently returned from a trip to Europe where he delivered his last paper, [73], in honor of Ennio De Giorgi.”
(D. Kinderlehrer, in David Kinderlehrer ed., Volume 1, 2002, Birkhäuser)
Jesus Christ, a second Berkeley math professor death with an Italian factor in the summer of 1988 – this one a leading mathematical prize winner, and related to the Italian mathematician Ennio De Giorgi.
Recall as in Part 2, De Giorgi was the Italian mathematician in Pisa who had proved a theorem before John Nash did in the 1950s, and still Nash’s credit for it contributed to his receiving the Abel Prize in May 2015, and unfortunately to the deaths of him and his wife in a taxi accident returning from the Oslo ceremony!
In Part 2 I have wondered about the metaphor of “vampire”, as opposed to “guardian angel”, over the circumstances of the deaths, that the Nash couple had a limo service prescheduled for 5 hours later and Lisa Macbride, daughter of Nash’s Abel Prize co-recipient Louis Nirenberg, suggested they take a taxi, and the taxi driver turned out to be named Girgis.
As for Hans Lewy, he may have been suffering from cancer, according to his The New York Times obituary at the time:
“Hans Lewy, a professor emeritus of mathematics at the University of California at Berkeley, died of leukemia Aug. 23 in Berkeley, where he lived. He was 83 years old.”
(“Dr. Hans Lewy, 83, Mathematics Profesor”, September 2, 1988, The New York Times)
At least it hadn’t been an auto accident. But Lewy’s cancer was not the direct cause of death – his Italian trip was, as later told by his friends such as his former Ph.D. student David Kinderlehrer, quoted earlier, and the mathematical biographer Constance Reid here:
“Lewy became emeritus in 1972, but he did not stop doing mathematics. Even in the summer of his death he gave a talk at a meeting in Cortona, Italy, on new work that involved attacking the Carathéodory conjecture from a different, variational angle. He had hoped to finish off the problem, but the complete solution was not to be granted to him. While in Europe, following a strenuous schedule in order to see as many as possible of his European friends, he caught a cold that developed into pleurisy. On his return to Berkeley he was hospitalized, fatally ill. He died on August 23, 1988, two months before his eighty-fourth birthday.”
(Constance Reid, in David Kinderlehrer ed., 2002, Birkhäuser)
It was only a cold, that then turned into pleurisy – two deaths in 4 months due to visiting Italy, one might have to wonder about the condition of public hygiene there.
Hans Lewy had a lifelong love of Italy since 1929:
“In 1929, again on Courant’s recommendation, Lewy obtained a year’s fellowship from the Rockefeller Foundation. He spent the first semester in Rome – the beginning of a lifelong love affair with Italy, to which he was to return on countless occasions – and the second semester in Paris. …”
(Constance Reid, in David Kinderlehrer ed., 2002, Birkhäuser)
For over two decades, Hans did collaborative research at the University of Pisa where De Giorgi was:
“In 1964-1965 Lewy accepted an invitation from the Scuola Normale Superiore and the University of Pisa. During that time, Pisa was achieving stature as a vigorous world center with Andreotti, De Giorgi, and Stampacchia among its leaders. Here, Lewy helped create the emerging area of variational inequalities with Stampacchia. Their work was fundamental to the growth of the subject, introducing new types of free boundary problems. He published in this area through the 1980s. In 1969-1970, he returned to Rome on the invitation of the Accademia dei Lincei. He was elected a Foreign Member in 1972. He also retired in 1972, continuing his research with undiminished vitality.”
(D. Kinderlehrer, in David Kinderlehrer ed., 2002, Birkhäuser)
Hans Lewy’s relationship with China can also be traced back a long time. In 1947 when Hans married his wife Helen Crosby, they spent 3 months of their around-the-world honeymoon in China, including teaching mathematics there:
“ In 1947 he and Helen Crosby, an artist, writer, and translator, were married. Their honeymoon included a trip around the world, beginning with a return to Europe. Also included was a two month stay in Chengtu, Szechuan (Chengdu, Sichuan) where Lewy gave a course on water waves and a third month visiting other institutions in China. Still under Nationalist rule, China was rarely visited by westerners in those years.”
(D. Kinderlehrer, in David Kinderlehrer ed., 2002, Birkhäuser)
Hans became fond of the Chinese, calling them “the Italians of the Orient”:
“Lewy became very fond of the Chinese people, whom he liked to describe as “the Italians of the Orient”.”
(Constance Reid, in David Kinderlehrer ed., 2002, Birkhäuser)
Perhaps his “guardian angel” was no longer present – when he died only weeks short of his 84th birthday of October 20 – for the talented Hans Lewy, who spoke multiple languages fluently and “actively studied Chinese up to the time of his death”:
“Lewy was the first son and second child of Max and Greta (Rösel) Lewy. His father was a merchant who dealt in accessories for women’s millinery, and his mother before her marriage had been a teacher of German in an expatriate enclave in Hungary. Her interest and ability in languages were inherited by her son. In addition to a thorough grounding in Greek and Latin, which he had received in his Gymnasium days, he was so fluent in French and Italian that he was frequently mistaken for a native on the streets of Paris and Rome. He could converse in Russian, once delivering a lecture in that language, and he actively studied Chinese up to the time of his death. …”
(Constance Reid, in David Kinderlehrer ed., 2002, Birkhäuser)
In his youth, Hans could have chosen to become a professional musician, as his wife Helen reminisced:
“The combination of mathematics and music, while not uncommon, especially in the Europe of Hans Lewy’s time, was, in his case, serious enough to force him to make, in his teens, a difficult career choice. He played the violin, the viola and the piano with mastery, and, at times in his life also the clarinet and the cello. He composed many string quartets—which unfortunately were lost,—and at least one string trio …
…
His parents would not permit the unusual skills of their son to be exploited, until, under pressure from his teacher, they agreed when he was 16 to allow him to perform in public, for one time only: the concert took place in Bautzen in July, 1920. …
…
Actually the teenager was allowed another performance before the public; it took place also in Bautzen, in October of the same year. This time he was soloist for Mozart’s D-sharp violin concerto. The reviews were, to say the least, enthusiastic. Here are excerpts…:
Bautzner Tageblatt: “… Mozart’s splendid work was interpreted with classic poise and superior precision, and the youthful violinist received rich applause that came from the heart.”
The Bautzner Nachrichten review hailed him as a “Virtuoso” and “Wunderkind with true Mozartian charm” and predicted for him a great future as a musician.
…
His father favored mathematics; his mother was not sure; and he, of course, wanted both.
In the end mathematics won, and he soon left home for his studies in Göttingen. There he played with the city orchestra …”
(“The Music in Hans Lewy’s Life”, by Helen Lewy, in David Kinderlehrer ed., 2002, Birkhäuser)
In August 1988 when I drove into Canada, the other Hans I had known, i.e., Kezheng’s Farmers Insurance agent, was no longer my auto insurance agent. By 1984 I no longer shared Kezheng’s old Ford but had jointly bought a used Datsun with a Chinese visiting scholar studying law, also by the family name Lu (陸), who later became an international trade lawyer in Beijing; establishing a good driving record then allowed me to switch to a State Farm Insurance policy with a cheaper rate.
The Ford had an auto transmission, but the Datsun and the Alfa Romeo were stick-shift cars. I had learned to drive the stick-shift in 1983-1984, taught by a musician friend, a Chinese orchestra conductor and composer who had come to UC Berkeley as a visiting music scholar, earned a San Francisco State University master’s degree, become a successful music teacher, worked as the music director for a North Berkeley Christian church, and excelled as an organizer for Bay Area community music events, including a Chinese music concert at San Francisco’s Davies Symphony Hall which she conducted. She also co-signed my auto loan for the Milano.
When this talented female musician died of cancer in 1991, she was only 48.
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