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
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
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
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
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
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
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
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
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
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
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
– 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