Prof. Shlomo Sternberg, mathematician

I write with sadness of the recent passing of one of my teachers, Professor and Rabbi Shlomo Z. Sternberg z"l, late of the Harvard University Department of Mathematics, at age 88 in Jerusalem, on 2024 August 23.

Born in 1936, he earned his Ph.D. from Johns Hopkins University in 1955 -- at the age of 19. He joined the Harvard faculty in 1959 (at age 23) as the George Putnam Professor of Pure and Applied Mathematics, an endowed chair he held for almost 60 years, until 2017. Thereafter until his death, he was Emeritus Professor at the Harvard Mathematics Department.

Prof. Sternberg was a world-renowned geometer, exploring many different areas of that field. Many of his interests, including differential geometry and symplectic geometry, are highly relevant to mathematical physics, ranging from classical mechanics to thermodynamics, optics, quantum mechanics, and general relativity. He was a prolific publisher of his lecture notes in many courses, including many books as Dover Originals, inexpensive paperback editions held in high regard by Amazon reviewers of math and science books.

In addition, he was the co-creator, along with the late Prof. Lynn Loomis, of Harvard's world-famous Math 55 advanced freshman math class, ca. 1960. The two also authored the textbook Advanced Calculus to accompany the class, first published in 1968 and still available in a revised edition. (Unfortunately, within a couple of years the course would be handed over to a series of junior faculty members who shifted to an arid, airless, abstract, almost 100% diagramless text from the French "Bourbaki" group -- it was this version of the course that terrorized and discouraged freshpersons during the 1970s, and gave it its diabolical reputation.)

Prof. Sternberg was also a Talmud scholar and ordained rabbi who covered his head with a jauntily-angled beret. He became briefly visible to the general public in 1997 when quoted by NY Times writer Frank Bruni in dismissing a bestseller of the day, The Bible Code, as junk (an opinion he also substantiated in mathematics and Biblical studies journals). Among Orthodox Jews, he's maybe best-known for establishing that swordfish is kosher, a conclusion he came to after deep study of not only religious law but also ichthyology.

I'm not at all the best person to be writing an obituary of Prof. Sternberg. I was without question one of his least talented students. I wasted the opportunity I was given in 1972 when I was placed into his section of Math 21a in my freshman year (with Math 21b taught by Raoul Bott, another delightful and even more world-famous mathematician). I spent the Fall term of freshman year settling down from the discombobulation of winding up at Harvard, and the Spring cutting math class to audit an historical linguistics class that met at the same time.

But I'm writing this now because, to my amazement, no one else seems to have taken notice of his death other than a contributor to his Wikipedia page and a small Jewish Studies subnetwork, H-Judaic, of the H-net Humanities and Social Sciences network, cited by Wikipedia. More than a month after his death, the Harvard Math Dept. still had his webpage open -- but not any news item or announcement about his passing. Nothing on LinkedIn. No obituary in the NY Times or Boston Globe. Nothing.

Could this be because he maintained a home in the Old City of Jerusalem since at least the 1970s? (I may be wrong about when he established his residence, but he was certainly visiting there regularly at that time, and it was there that he passed away.) In other words, could the Zionism of one of the world's leading mathematicians be the reason almost no one publicly mourns and honors his death in 2024? I hope there is a more innocent explanation. [See Update, below.]

Rather than speculating further about this, I conclude with some personal reminiscences of Prof. Sternberg. I hardly knew him well: I was a deliberately low-profile member of two of his courses while I was an undergrad, and I had only one or two brief interactions with him by email in the decades after I left Cambridge. But in all of those interactions, I remember his warmth and humor.

In the first few weeks of my freshman year, I was very disoriented by my transplantation from Nassau County, Long Island, where everything was relatively new, into the 17th and 18th Century world of Cambridge and Boston. I was without anchor until around the third week of Math 21a, when Prof. Sternberg wrote a sequence of numbers on the board, and then let out with a honking New York accent that warmed my heart, "I CLA-im that this sequence of numbers converges awfully damn fast." He then proceeded to write out on the board a precise mathematical definition of "a.d.f. convergence," along with a proof.

The following year, I jumped at the chance to take Social Science 167, a first-time and never-again course jointly taught by Prof. Sternberg and Harvard Law School celebrity Alan Dershowitz. Entitled "Probabilistic Inference in Legal Systems," it was a comparison of the use of probability in both the Talmudic and the U.S. legal systems. Prof. Sternberg was to teach us the math and also about relevant Talmudic examples, and Dershowitz about the US legal system. Prof. Dershowitz came out far, far worse for the contrast.

The most memorable lecture was about the use of probability in food and wine-related cases almost 2,000 years ago. It was well established law that if a child was found outside the gates of a city where a majority of residents were non-Jews, based on probabilities it was assumed the child, too, was not Jewish, and therefore could be fed any sort of food. But if the city had a majority of Jewish residents, by the same reasoning the child could only be fed kosher food. Another case, though, involved a break-in at a Jewish home, where the thief had evidently taken some swigs directly from a wine skin filled with kosher wine. The law was that if a non-Jew drank directly from the skin (like drinking directly from the bottle, in our terms), the wine was no longer kosher. This city had a majority non-Jewish population, so, on the analogy of the abandoned child cases, it seemed certain that the wine was no longer viable for religious purposes. But in this case, Prof. Sternberg said with a twinkle, the rabbis on the court judging the matter happened to know that the majority of thieves in the town were Jewish -- so the wine was OK.

In college, I'd also been a rather lousy student of physics, which on paper had been my concentration (major). In fact during my upperclass years and for a couple of years beyond them, I wanted absolutely nothing to do with STEM subjects at all. But this slowly reversed starting in my late 20s, so that by the time I turned age 50, I decided that I was of an age when I should finally learn something about general relativity (Einstein's theory of gravity), a topic I'd neglected in my youth. This is a very geometric theory, and I wrote to Prof. Sternberg about whether his lecture notes on the subject might be too advanced for someone with my background. He very graciously wrote back to me right away, and we had a brief correspondence. During our exchange of emails, I confessed that despite being lackluster in math, for almost 25 years I'd been continually buying math textbooks on various 1st-year grad student-level topics, even though I could never make it more than a page or two past Chapter 1 in any of them. I found my lack of progress frustrating. "You know," he wrote back, "you can learn a lot of math from reading Chapter 1 of a lot of textbooks." I never felt silly about indulging my curiosity after that.

[UPDATE: After I sent an email to the Harvard Math Department in late September, asking why they hadn't bothered to honor someone who had been a distinguished department member for over 60 years, they did post a brief, 3-paragraph announcement on Oct 02. It quotes another faculty member, Senior Lecturer Paul Bamberg, a Math 55 student from the 1960s (and my prof for Physics 151 - Classical Mechanics, one of the most beautiful courses of any type that I have ever taken) as saying that Prof. Sternberg "was the most brilliant person I ever met." Given that Dr Bamberg has been a member of both the Physics and Math Departments at Harvard, and is himself a gifted teacher, that's saying a lot (particularly since the Physics Department back then boasted the likes of theoreticians Julian Schwinger, Steven Weinberg, Shelly Glashow, and Sidney Coleman, 3 out of 4 of whom got Nobel Prizes). At the same time the Math Department took down Prof. Sternberg's page on the Department site -- but also with it, unfortunately, links to free PDFs of his many books and sets of lecture notes that he had, with characteristic generosity, made available during the later decades of his career. To honor his memory, these should be reinstated. UPDATE bis: Links to a few of them have been restored and are available here: https://people.math.harvard.edu/~shlomo/]

Bill Gates, a year or so behind me, was another student on whom Prof. Sternberg made a lasting impression: https://www.gatesnotes.com/How-Not-to-be-Wrong, though I don't know if they stayed in touch after the former's truncated stay at Harvard.

I hope someone who knew Prof. Sternberg well will soon write a proper tribute to this teacher and human being. May his memory be a blessing.