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HeimowitzNovember 7, 2007:

Lessons learned at Princeton: Reflections of a failed mathematician

Copyright Carl L. Heimowitz ’64

When I was 8, my father gave me the best advice of my life: “Son, if you are smart enough, there is no one in the world you cannot learn from.” Although this has proved true ever since, it was not until I arrived at Princeton that I learned its equally important corollary: “But it may be something quite different from what you expected.”

When someone hears that I studied mathematics at Princeton in the ’60’s, often as not they’ll ask if it really was like the movie, A Beautiful Mind – about John Nash *50, a schizophrenic Princeton mathematician who went on to win a Nobel Prize. I tell them that if anything, the film was understated – portraying Princeton as an academic gentleman’s club with members reading their papers and passing out pens as party favors, blithely coexisting with the occasional madman in their midst.

Over the years, other movies have been made about mathematicians at major universities – among them, IQ, Proof, and Good Will Hunting, each of which dealt with the duality of scholarship and unworldliness.

Scientists observe, historians interpret, philosophers try to relate their musings to the human condition. Mathematicians have no such pretext. Their constructs are artificial, arbitrary, and exist solely within the confines of their collective consciousness. To express these imaginings, they create new vocabularies. Without their intercession, these worlds do not exist.

Our accepted worldview is never more than some physicist’s current ideal. We have yet to manufacture a perfectly flat surface. Why, then, should mathematicians bother to be bound by “flatness,” when it is every bit as abstract? Think about how often we have had to relearn science, from particles and planets to what foods are good or bad. At its most practical, mathematics prepares us for worlds as yet unrecognized. “Reality” is vastly overrated.

The film that best captures the essence of my math department is National Lampoon’s Animal House – a zoo inhabited by brilliant misfits continually being marginalized, indeed alienated, by the mainstream while obliviously creating their own space. Both the movie and Princeton’s real-life department – in vastly different ways – evoke a primal search for excellence and fellowship in an environment that matters only to the protagonists – driven by a lemming-like force to follow their own stars even (or, perhaps, especially) at the expense of “fitting in.”

How ever did I end up in such a place? A review of my college transcript probably would reveal that I was the poorest student in the department. Although I knew by sophomore year that I was in way over my head, I persisted. Why? First was the advice of a teacher at Horace Mann, Robert A. McCardell ’49, that I should try to study in college those subjects that I most likely would never thereafter learn on my own. He was right. Although in recent years I have read Gibbon, William James, Faulkner, Audubon, Welty, Churchill, Tocqueville, Madison, and Parkman, I have not cracked a math book since leaving graduate school.

No small part was the allure of the elite. Then, as now, Princeton’s math department was a shining beacon to the world; I was determined to see how close to that flame I could circle. As it became harder, adolescent machismo took over, and I learned the tenacity of the six-hour marathon runner. I would never win, but dammit, I could prove I had the stamina to finish.

What I most fondly remember about those years of failure were the people – alternately crazy and great. Cloistered, yet doing work that changed the world – just look at Nash.

I never met John Nash. During my years at Princeton, he was at either MIT or the state hospital at Trenton. I was, nevertheless, well exposed to his brethren. To a smart-ass Jewish kid from the Bronx, Princeton’s math department was absolute refutation of any prejudice that the Gentiles aren’t all that smart.

Back then, the University was, and I hope still is, about excellence. In later life, as even the most gifted of us find Boyle’s or Gresham’s Law fading, our lasting education comes more from what we have learned of process over product and – most importantly – about people over theorems.

Here then are some stories about people who mattered far more than Fourier Transforms. They are certainly not limited to mathematicians or even to Princeton, quite rather about greatness and the quirkiness that so oft attends it.

I have at least one classmate who can prove he is sane because it says so on his discharge papers from the previously mentioned Trenton State Hospital.

Mathematicians work concurrently within multiple levels of consciousness, like so many windows in a computer, but, sadly, not so navigable – closer to a dream not quite remembered. In this case, my unfortunate classmate had been investigating a problem for years and ultimately was convinced that somewhere deep inside he had solved it but lacked the coherence to articulate his knowledge. As they carried him away, he reportedly repeated as his mantra, “I am supposed to become a teacher, yet I cannot teach myself what I have learned.” To this day, I cannot tell whether the trauma was caused more by his perceived inability to learn or to teach.

When it came to teaching, the math department was seldom conflicted. Our entire faculty seemed to know everything, and few but the most gifted students ever strayed beyond required courses. Pedagogy and showmanship were left quite readily on the back burner. Nobody ever took a higher-level math coursc because of the eloquence of the professor.

We lived in our own world. Our library was separate from Firestone. Decades before Paul Orfalea founded Kinko’s with its 24/7 culture, Fine Library was accessible to department members at all hours – as so many of us kept the habits (and appearance) of nocturnal marsupials. Envious liberal arts majors joked that there were no stairs to our fourth-floor library, since a precondition for entering the department was that we could fly up there on our own.

Sophomore year, I studied linear algebra with a professor who, while quite into middle age, was still regarded as the best tennis player at Princeton (no mean feat). Reportedly he had competed for the Davis Cup in the ’40’s. Clearly, focus on game and being able to shut out the audience are critical success factors both for athletes and mathematicians. I remember one class when, in the midst of a proof, a question was asked about an obscure variant. The professor stopped, started pacing, and with chalk and eraser still in hand walked out the door. Twenty minutes later, when the bell rang, he was still missing. A search party found him pacing the far end of the third floor of the Palmer Physical Laboratory. Upon re-entry, his parting words were: “Class dismissed. Proof Tuesday.”

Lesson learned: focus, focus, focus.

I have had professors lecture with one foot in a wastebasket for half an hour, or blush when talking about “osculating functions,” or fail to even notice a student kicking in a glass door when it was stuck.

Passion was expressed in many ways.

I remember Professor Albert Tucker *32 pausing mid-lecture, teary-eyed, as he recalled John von Neumann’s death, and how Tucker posthumously defended him in the brouhaha over the relative significance of early conjectures by Borel vis-à-vis an academic paternity suit over who sired game theory. Today one can find such displays of emotion only on Dr. Phil.

Professor Tucker was our department chair. Unlike other departments, where chairmanship was regarded with great envy as a source of power and prestige, it was our understanding that mathematicians serve only if promised limited tenure – lest it interfere with their true calling.

Sometimes passion and pragmatism would converge. My favorite professor at Princeton is Oskar Morgenstern, a man I never had a class with, met only once, and heard of directly only twice thereafter – but from each event learned a lesson.

Professor Morgenstern, who (with von Neumann) is generally acknowledged as the creator of game theory (Nash’s field as well), gave a course on the subject in the graduate economics department. Undergraduates were permitted to enroll in graduate courses with the permission of the instructor and a dean. To study with Morgenstern was as irresistible as a back-stage pass to Olympus. I was granted an appointment, and the meeting went exceptionally well. Morgenstern said that I already knew more math than any of his economics students, and that he looked forward to having me in his class. I said that I would like to prepare, and had bought his (and von Neumann’s) Theory of Games and Economic Behavior and hoped to get through it over the summer. “Don’t bother,” he snorted, “it’s just a fossil. Read Luce and Raiffa if you must; it’s much more current.”

Another life lesson in humility and pragmatism.

Clutching Professor Morgenstern’s signed approval, I strutted over to Nassau Hall, entered a second-floor office, and proclaimed to a youngish man, “Excuse me, I need a dean to sign this form.” Quite fatally the wrong thing to say to the newly-minted dean, who promptly denied my request. Sometime later, I ran into this same dean, who demanded to know what I had said to Professor Morgenstern to make him call to complain that professors – not deans – should decide whom they get to teach. I told the dean that I had been ashamed to tell Professor Morgenstern of my misfortune; did this mean that now I could take the course? “No,” said the dean, demonstrating that, even then, bureaucracy trumped academics.

Another life lesson learned.

Publishing, as well as mathematics, rewards brevity, requiring the omission of countless tales. Perhaps in this era of blogs, someone will create a space where others can tell their own stories. Those seeking a more scholarly history of the great men who made our department what it is should visit the mathematics department’s online “The Princeton Mathematics Community in the 1930s: An Oral History Project,” which is available at: http://infoshare1.princeton.edu/libraries/firestone/rbsc/finding_aids/mathoral/math.html

No greater tribute can be found to Albert Tucker and his colleagues.

In the pre-Internet era, it was impossible to keep up with work in progress in our chosen areas. All too often a doctoral candidate, picking up some obscure Russian journal, would learn that his thesis topic had been independently completed and published – rendering his own efforts moot. Some would end their lives by jumping from the Cleveland Tower. Others just seemed to expire from frustration.

The final story (perhaps apocryphal) was told by a friend and doctoral candidate at Columbia. It is of a colleague who, panicked by his overlong lack of progress, had come to such an end. At the memorial service, his adviser offered the following eulogy:

“I knew X for all too short a time, and then, purely as a student. It is only since this untimely passing that I have learned of his other dimensions. He was a loving son and devoted brother and quite involved in a number of non-academic activities.

“There is always a great sadness whenever we lose such a promising student -- under any circumstance. In X’s case it is especially unfortunate, for had he but considered the case where n=17….” END

Carl L. Heimowitz ’64 worked in the insurance and banking industries while a graduate student at N.Y.U. in operations research. He joined Harcourt Brace Jovanovich, becoming director of future publishing technologies, before leaving to become national director of technology for Arthur Young’s tax practice. In 1989 he co-founded Future Communications Corp. and with his business partner subsequently purchased Moseley Associates, a publishing consulting group.