Table of contents
This somewhat atypical attitude culminated a short time later with my announcement to my parents that they could no longer have any dominion over me, could no longer tell me at all what to do, the corollary being that they would of course be absolved of any responsibility for my well-‐‑being and, by further implication, I would necessarily need to leave home. Adding salt to the wound I announced further that, though accepted to the U of Chicago, U of Wisconsin, and U of Rochester, I had no intention of attending university as there was nothing that I could not figure out myself and that I would be leaving for San Francisco, the nearest Norwegian Consulate being there, to become a whaler in the Southern Ocean ….. in the morning.
This I duly did, only to be brought up short by the courtly gentleman running the Norwegian Consulate, who after gravely listening to my overall plan, gently but firmly, no admonishment in his tone, intoned that I was about 100 years too late, that teen-‐‑age boys, no matter how wild the hair in their derriere, could not run off to sea …… anymore.
Although infrequent by this time my attention to the advice of others, I did mark his message and as an alternative, though with no particular goal, set up shop in San Francisco, food and shelter courtesy of Western Union where I acquitted myself well as a telegram messenger boy, albeit the only one with an English racer sporting but one brake, the front one, with which to handle the hills of San Francisco, this the ultimate determinant as to my fall attendance at the U of Rochester when upon careening down a hill I had to choose between a pedestrian or a taxi, the screeching smash into the back of the taxi breaking the bike’s frame in two …… with no bike, and after so many months San Francisco’s allure receding, I succumbed to the blandishments of undergraduate life, a decision I do regret …….. except for the fact that, as a result of that decision, I met ……. Stan Tennenbaum.
As I had had Ms Childre’s calculus class in high school, I was placed in Tony Hager’s advanced calculus, about 15 of us, Mon-‐‑Wed-‐‑Fri, 10:00am …… Tony was a nice guy, recent PhD who had just arrived as part of Leonard Gillman’s (very successful) efforts to build the mathematics department into a world class repository of mathematical talent, but a pretty meat and potatoes lecturer, inspiration not his strong point …… There was another calculus course, the introductory one, 200-‐‑300 students, in the roman amphitheatre Hoyt Hall meeting the same time Mon-‐‑Wed-‐‑Fri, 10:00am …. As I was living in a freshmen dorm, many of the students on my corridor were in this other course. It wasn’t long before the rumblings reached me, rage, fear, astonishment, confusion, anxiety, hysteria regarding this crazy professor, incomprehensible, out of control, bewildering, unfathomable ….. curiosity piqued, I skipped my class (never to appear there again) and sat myself in this one, center, close to the front ….. shortly he entered with his characteristic lithe, relaxed but purposeful walk, Stan Tennenbaum, the man who was to have (outside of my father) the greatest influence on my life, dwarfing all others, the most scintillating, charismatic, exciting, mesmerizing man I’ve ever personally known.
From the moment of his first words I was transfixed….. for here, far from the madman fulminating in the overwrought psyches of the attending students, was the clearest, most rational, most penetrating intelligence I had encountered, one who believed there was truth, there was reality, one whose unremitting goal was to seek such, any other goal mundane, nearly perverse by comparison. I immediately grasped the intellectual firmament on which he resided, the bedrock of assumptions that informed and underlay his speech and actions, the metaphysical vantage point on which he balanced. With no perceptible persuasion, I instantly became an acolyte, a true believer, a made man, trenchantly faithful, of diamond loyalty ….. he was the flame, I was a moth.
As I listened it became patently obvious why the students were panicked, little fawns in the headlights, stricken with anxiety. The majority of University of Rochester undergraduate fodder were upper middle class kids, ‘good’ kids, from the northeast, particularly the New York, New Jersey area. They were hard working, reasonably intelligent, coddled, bent on fulfilling mummy and daddy’s expectations that they get into med school, law school, or graduate school.
They had lock-‐‑stepped through elementary school, junior high, and high school, and were now about to do the same, with no particular enthusiasm, through university ….. again, they would be other-‐‑organized, told what to do, and with scant resistance would docilely fall in line. They had never queried the educational constructs that ordered their lives, indeed they had little queried societal constructs in general.
Almost uniformly they were without the faintest glimmer that they held, or should do, their lives in their own hands which is the precursor to such questioning, no recognition that they were, or could be, ‘the master of my fate… the captain of my soul’.
Had they taken any other calculus class, no calamity would have ensued. There would be classes, lectures, notes, homework, tests, exams, all would be clear, stale, dull …… but ordered …. and recognizable.
Unforeseen misfortune, they had stumbled into unknown territory, fraught with peril, they had entered Stan’s domain, the domain of a ‘true’ university, a housing, an enlarged carapace that attended and enveloped Stan wherever he went.
When you entered Stan’s class, you entered the totality of his Cardinal Newman’s ‘Idea of a University’ scholastic world, as pristine and devoted to truth as the moment it found near realization in Hutchin’s University of Chicago. Make no mistake, upon entering Stan’s class, you have entered his ‘city on a hill’, no sop, caveat, obeisance, compromise with any other.
This notion of a university, of long historical development, was laden with assumptions quite natural to Stan, the air he breathed, but unknown to the unsuspecting students.
First, foremost, is the assumption that there is truth, it is knowable, the tool for its comprehension and discovery is the mind, the modus operandi for its amplification and elucidation is rationality.
A university is an entity, an institution, independent and unto itself with no obligations or commitments to any other outside itself that is composed of a collection of professors and students, the professors only distinguishable from the students by virtue of the fact that they know some things that the students don’t, their articulation one of transference of that knowledge from professor to student, all with a belief in, a commitment to, a pursuit of the truth regardless of subject matter or field of endeavor, all organization and practical considerations subject to the maximization and realization thereof.
Secondly, was the assumption that the students, as members of the university, were grown ups, independent of nature and thought, serious as to their ‘self actualization’, cognizant, and relishing, that they were in control of, managed, organized, directed their own lives, were in attendance because they had chosen to be so and wished to truly learn the subject, principally for its own sake but secondarily as it might relate to larger goals.
‘In loco parentis’, antithetical to this assumption, had no place here, was given short shrift, was left languishing outside the walls.
Thirdly, the professors, were completely independent entities beholden to no one with respect to their activities and pursuits and within the confines of a given class completely unshackled as to its content, organization, conduct, and pedagogical device.
Stan, the living embodiment of a member, professor of a ‘true university’ conducted his class accordingly. In its particulars, he frightened the bejesus out of the average U of R student ……. for me, for the first (and ultimately, the only) time, l was elated, dancing on air, I had found someone who understood, revered, and lived intellectual freedom, passionate pursuit of truth, a will and joy in choosing and forging his path, one for whom ‘university’ had real meaning and who ‘walked the walk’ to bring it to me, crystalline heaven established on stolid earth.
The air was always informal, but serious, intense. Dressed in elegant casual, slacks, open collar shirt, jacket, Brooks Brothers the favored brand since his University of Chicago days, Stan would start a lecture in a low-‐‑key fashion, introducing the topic for the day, unfailingly clear, his voice relaxed, measured, in complete command of the material, utterly confident, no hesitations, lapses, confusions, circumventions …. whether talking to 2 or 200 (as in the case of the calculus class), it was as if he were talking to you one on one, intimate, he completely aware of and engaging (if not captivating) you, involving you in a conversation, measuring, gauging your understanding and leading, the Socratic carrot dangled. Regardless the material, in this case beginning calculus, Stan was more interested (in a freshman class) in progressing your understanding of yourself with respect to learning, to knowing, to believing in your own mind, to becoming independent and confident in your own thought ….. far from the average professor, distancing himself from the student hoi polloi, delivering a one-‐‑ sided monologue of material more easily absorbed through the text book he mimicked, Stan at the outset engaged you, probing, questioning, challenging …..truly interested in your development, he was not your friend, he was your ‘profess’or …. For the student who had screwed up the courage to, with 200 sets of eyes upon him, respond to a question, there awaited not approval, appreciation but rather…. ‘really ??’………………………………………………………………………….. ’are
you sure ??’ ….. after a couple of iterations of such, the hapless student, unless of very hardy self-‐‑belief, would fade into questioning himself, but at least a lesson of a different sort was learned. Another variant of this was ‘how much are you willing to bet ?’, a different measure of how sure you were about whatever it was you were saying …… ever instructive this question prevailed over and over in every class I ever had with Stan, one of the most interesting episodes being when Stan asked Bonnie Gold in a number theory course whether she would bet her life on something she had just stated, upon which Bonnie in a fluster exploded with ‘I wouldn’t bet my life on anything !!’.
Though there was always a nominal topic to each of Stan’s lectures, say for example summation of certain infinite series, the excitement was in knowing in advance that you had no idea in which direction the ‘conversation’ would veer. Always speaking extemporaneously, never notes (please !!) but with consummate depth, erudition, and certain philosophical orientation, a lecture from Stan was always an adventure, hugely interesting, entertaining, with definite instructive point but unpredictable a priori ….. this of course is part of what was so frightening to that student (so many of them) that wanted to know where he was going and what was expected of him in getting there.
What you might (reasonably) ask does this have to do with inculcating calculus into the resistant heads of the undergraduates? And for that we look at the course as a whole, the constellation of elements working in concert ….. first there of course was a text, a beginners calculus by Serge Lang I think, by all accounts a good exposition though my subsequent impression was Stan was somewhat dismissive, somewhat distrustful of Lang (or at least Lang was of him), who was at the University of Chicago at the same time, perhaps because of his association with the Bourbaki, red rag to a bull anathema to Stan. Stan’s view and orientation, and one he was at great pains to discuss at length with the students in and out of class, was that if you truly wanted to learn the calculus (or anything else) you found the very best text you could find (for example, Courant’s ‘Differential and Integral Calculus’), you (slowly) worked through the theorems by (always) first attempting to prove them yourself, you (at the very least) ensured you (thoroughly) understood the theorems and their proofs, and coup de grace, you did all of the problems. Hey, presto !!
Again this assumed the student sported the attributes of a member of a ‘true’ university, Stan’s real point to his lectures, to do what he could in developing such.
Next there were graduate assistants around, always available to check the problems (not assigned, Stan was not going to hold their hands to that extent) any student (not trusting his native wit) cared to do, the graduate assistants also deployed to grade exams….
Further, forget office hours, Stan’s door was always open, he ever ready to talk to a student, untold hours spent with his undergraduates in contrast to the can’t be bothered professors. His office was always full, he fully engaged with each student, again probing for, exposing the real problem the student was having, nearly always not of mathematical nature, but rather psychological.
With all of these elements, Stan’s how to lectures and the supporting structure, the student with a modicum of initiative had the wherewithal to get a good grounding in the calculus …. yet still the hysteria persisted.
In part this was caused by the anxiety as to how they would be measured, their grades, how would they get that A to get into medical school, an issue fundamentally irrelevant to Stan and one for which he little patience. Historically, ancient universities, collections of people seriously interested in knowledge, simply offered a set of exams which, when passed, gave a measure of acknowledgment, the baccalaureate. Over time this simplicity degraded into the complexity of more and more exams for smaller and smaller increments, ultimately finding nearly obscene expression in American universities, multiple tests in a given course, a scale A-‐‑F, all mere impediments to one seriously intent on real learning.
Stan’s solution in this morass, not at all to placate the students but rather the inevitable implication of his attempt to function as if in a true university, was to give two very straightforward exams, mid-‐‑term and final, and a grade for the course of either A or B, no failures, course attendance irrelevant ….. additionally a student would get an A for showing any initiative whatever in any form, say for example a notebook of problem solving, this carried out in the extreme when one of the basketball players who could in truth not tell a derivative from an integral got an A for a really good showing on the basketball court.
This ‘gift’ to the basketball player was in part due to Stan’s reverence for sports and sports figures, not as unrelated to academic pursuit as it might first appear, the two antithetical in the minds of most people ….. for Stan achievement on the playing field was indistinguishable to achievement on the mental playing field. Both required courage, stamina, practice, really hard work, staying power, commitment, tenacity, and development, building up from level to level. A finely executed football play held the same beauty and joy as the discovery of a simple proof, particularly if it featured a smaller player succeeding through wit and guile against a larger opposition. Stan’s lectures were littered with analogies to sport, the mind a muscle requiring practice and exercise like any other. He himself had played football until damaging his back, not surprising in one who occasionally played without a helmet in order as he said ‘to impress a girl’….. diving too, indeed it may be in that practice that he did his back in what with his creative efforts to do complicated tandem dives with a friend …… practice and working really hard were never to be underestimated, developing critical discipline as well as building capability, both obtaining when he was forced in high school to do really hard plane geometry problems, which he believed essential to his ultimate capacity to doggedly, determinedly tackle very difficult advanced mathematics. That persistence, resolve, and determination are essential to achievement is particularly evident given that but 3% of highly talented people reach their potential due to the general lack of such. Stan’s regard for sports figures carried on throughout his life, one story the day he recognized a great college football player on the street, spent the afternoon with him watching his old films, the athlete undone that he was remembered.
Stan’s interest and thought regarding the relationship of mental and physical activities was part of his deep interest in achieving successful results in mathematics, solving problems ….. in his lectures he spent much time with this, often posing a problem, and then with pointed questions, lamping the way, the wide awake student fixedly engaged, through to solution …..
Acutely aware of mathematicians who had thought on this art, he had high regard for and pointed us to George Polya’s two volume set, ‘Mathematics and Plausible Reasoning’, Hilbert and Cohn-‐‑Vossen’s ‘Geometry and the Imagination’, Courant and Robbins’ ‘What is Mathematics?’.
In this first calculus course, the majority of the students, purblind and mystified, resigned themselves to this trial, one but to be weathered, an early cross to bear, but ultimately to be put behind them in their beeline to law school (or whatever) ……. farmer Stan had opened the barnyard gates and beckoned to the verdant open fields beyond but, startled and leery, they remained transfixed, encephalitic lethargica to the end. There were a few however that listened closely, that opened their minds, that began tentative steps into those fields beyond the gates. Stan always said he could identify those for whom this would happen at the start of any semester, just by looking into their eyes. For myself, I forthwith skipped Tony’s class altogether and could be found Mon-‐‑Wed-‐‑Fri, 10:00AM, in Hoyt Hall, 1st row, centre.