A Beautiful Mind Page 7

  Nash had competed as a freshman and a sophomore. On his second try, he’d managed to get into the top ten, but not the top five. He’d been cocky this time, too. In 1946 a mathematician named Moskovitz tutored the Carnegie Tech team using problems from past exams. Nash was able to solve problems that Moskovitz and the others could not solve. It was a tremendous blow to Nash that George Hinman ranked in the top ten in the 1946 competition and Nash didn’t.38

  Another nineteen-year-old might have shrugged off the disappointment, especially a boy who had been plucked out of a chemical engineering program, welcomed with open arms by the school’s mathematicians, and told that he had a brilliant future in mathematics. But for a teenager who had endured a lifetime of rejection by peers, the warm praise of such professors as Richard Duffin and J. L. Synge was too little, too late. Nash craved a more universal form of recognition, recognition based on what he regarded as an objective standard, uncolored by emotion or personal ties. “He always wanted to know where he stood,” said Harold Kuhn recently. “It was always important to be in the club.”39 Decades later, after he had acquired a worldwide reputation in pure mathematics and had won a Nobel Prize in economics, Nash hinted in his Nobel autobiography that the Putnam still rankled and implied that the failure played a pivotal role in his graduate career.40 Today, Nash still tends to identify mathematicians by saying, “Oh, So and So, he won the Putnam three times.”

  In the fall of 1947, Richard Duffin stood at the board silent and frowning.41 He was intimately familiar with Hilbert spaces, but he had prepared his lecture too hastily, had wandered down a cul de sac in the course of his proof, and was hopelessly stuck. It happened all the time.

  The five students in the advanced graduate class were getting restive. Weinberger, who was Austrian by birth, was often able to explain the fine points of von Neumann’s book Mathematische Grundlagen der Quantenmechanik, which Duffin was using as a text. But Weinberger was frowning too. After a few moments, everybody turned toward the gawky undergraduate who was squirming in his seat. “Okay, John, you go to the board,” said Duffin. “See if you can get me out of trouble.” Nash leaped up and strode to the board.42

  “He was infinitely more sophisticated than the rest of us,” said Bott. “He understood the difficult points naturally. When Duffin got stuck, Nash could back him up. The rest of us didn’t understand the techniques you needed in this new medium.”43 “He always had good examples and counterexamples,” another student recalled.44

  Afterward, Nash hung around. “I could talk to Nash,” Duffin recalled shortly before his death in 1995. “After class one day he started talking about Brouwer’s fixed point theorem. He proved it indirectly using the principle of contradiction. That’s when you show that if something’s not there, something dreadful will happen. Don’t know if Nash had ever heard of Brouwer.”45

  Nash took Duffin’s course in his third and final year at Carnegie. At nineteen, Nash already had the style of a mature mathematician. Duffin recalled, “He tried to reduce things to something tangible. He tried to relate things to what he knew about. He tried to get a feel for things before he actually tried them. He tried to do little problems with some numbers in them. That’s how Ramanujan, who claimed he got his results from spirits, figured things out. Poincaré said he thought of a great theorem getting off a bus.”46

  Nash liked very general problems. He wasn’t all that good at solving cute little puzzles. “He was a much more dreamy person,” said Bott. “He’d think a long time. Sometimes you could see him thinking. Others would be sitting there with their nose in a book.”47 Weinberger recalled that “Nash knew a lot more than anybody else there. He was working on things we couldn’t understand. He had a tremendous body of knowledge. He knew number theory like mad.”48 “Diophantine equations were his love,” recalled Siegel. “None of us knew anything about them, but he was working on them then.”49

  It is obvious from these anecdotes that many of Nash’s lifelong interests as a mathematician — number theory, Diophantine equations, quantum mechanics, relativity — already fascinated him in his late teens. Memories differ on whether Nash learned about the theory of games at Carnegie.50 Nash himself does not recall. He did, however, take a course in international trade, his one and only formal course in economics, before graduating.51 It was in this course that Nash first began to mull over one of the basic insights that eventually led to his Nobel Prize.52

  By the spring of 1948 — in what would have been his junior year at Carnegie — Nash had been accepted by Harvard, Princeton, Chicago, and Michigan,53 the four top graduate mathematics programs in the country. Getting into one of these was virtually a prerequisite for eventually landing a good academic appointment.

  Harvard was his first choice.54 Nash told everyone that he believed that Harvard had the best mathematics faculty. Harvard’s cachet and social status appealed to him. As a university, Harvard had a national reputation, while Chicago and Princeton, with its largely European faculty, did not. Harvard was, to his mind, simply number one, and the prospect of becoming a Harvard man seemed terribly attractive.

  The trouble was that Harvard was offering slightly less money than Princeton. Certain that Harvard’s comparative stinginess was the consequence of his less-than-stellar performance in the Putnam competition, Nash decided that Harvard didn’t really want him. He responded to the rebuff by refusing to go there. Fifty years later, in his Nobel autobiography Harvard’s lukewarm attitude toward him seems still to have stung: “I had been offered fellowships to enter as a graduate student at either Harvard or Princeton. But the Princeton fellowship was somewhat more generous since I had not actually won the Putnam competition.”55

  Princeton was eager. From the 1930s onward, Princeton had a far stronger department and was snaring the lion’s share of the best graduate students.56 Princeton was, as a matter of fact, more selective than Harvard at that point, admitting ten handpicked candidates each year, as cfpposed to Harvard’s twenty-five or so. The Princeton faculty didn’t care a hoot about the Putnam, or about tests of any kind, or grades. They paid attention exclusively to the opinions of mathematicians whose views they respected. And once Princeton decided it wanted someone, it pursued him with vigor.

  Duffin and Synge were pushing Princeton hard. Princeton was full of purists — topologists, algebraists, number theorists — and Duffin especially regarded Nash as someone obviously suited, by interest and temperament, for a career in the most abstract mathematics. “I thought he would be a completely pure mathematician,” Duffin recalled. “Princeton was first in topology. That’s why I wanted to send him to Princeton.”57 The only thing Nash really knew about Princeton was that Albert Einstein and John von Neumann were there, along with a bunch of other European émigrés. But the polyglot Princeton mathematical milieu — foreign, Jewish, left-leaning — still seemed to him a distinctly inferior alternative.

  Sensing Nash’s hesitation, Solomon Lefschetz, the chairman of the Princeton department, had already written to him urging him to choose Princeton.58 He finally dangled a John S. Kennedy Fellowship.59 The one-year fellowship was the most prestigious the department had to offer, requiring little or no teaching and guaranteeing a room in Princeton’s residential college for graduate students. It was a sign of how much Princeton was panting for Nash. The $1,150 fellowship covered the $450 tuition and was more than ample for the $200 room rent for a year and $14 a week in dining fees, as well as living expenses.60

  For Nash, that clinched the decision.61 The difference in the awards could not have been huge in any practical sense. But, then, as so many times later in Nash’s life, a relatively trivial amount of money loomed in his decision. It seems clear that Nash calculated Princeton’s more generous fellowship as a measure of how Princeton valued him. A personal appeal from Lefschetz, with a flattering reference to his relative youth, also proved decisive. Lefschetz’s phrase “We like to catch promising men when they are young and open-minded” struck a chord.62

&nbs
p; Something else weighed on Nash’s mind that last spring at Carnegie. As graduation drew closer, he became more and more worried about being drafted.63 He thought that the United States might go to war again and was afraid that he might wind up in the infantry. That the army was still shrinking three years after the end of World War II and that the draft had, for all intents and purposes, ground to a standstill, did not make Nash feel safe. The newspapers — of which he was a regular reader — were full of signs, in particular the Russian blockade of Berlin and the subsequent American-British airlift that spring, that the Cold War was heating up. He hated any thought that his personal future might be hostage to forces outside his control and he was obsessed with ways to defend himself against any possible threats to his own autonomy or plans.

  So Nash was palpably relieved when Lefschetz offered to help him obtain a summer job with a Navy research project. The project in White Oak, Maryland, was being run by Clifford Ambrose Truesdell, a former student of Lefschetz.64 Nash wrote to Lefschetz at the beginning of April:

  Should there come a war involving the US I think I should be more useful, and better off, working on some research project than going, say into the infantry. Working on government sponsored research this summer would pave the way toward the more desirable eventuality.65

  Though Nash did not display outward signs of distress, the disappointments and anxieties of the spring cast a shadow over the summer between his graduation from Carnegie and his arrival at Princeton.

  White Oak is a suburb of Washington, D.C. In the summer of 1948, it was a swampy, humid woodland full of raccoons, opossums, and snakes. The mathematicians at White Oak were a hodgepodge of Americans, some of whom had been working for the Navy since the middle of the war, and others, German prisoners of war. Nash found himself a room in downtown Washington, which he rented from a Washington, D. C., police officer. He rode to White Oak in a car pool every day with two of the Germans.66

  Nash had been looking forward to the summer. Lefschetz had promised that the work would be pure mathematics.67 Truesdell, quite a good mathematician, was a tolerant supervisor who encouraged the mathematicians in his group to pursue their own research. He essentially gave Nash carte blanche, issuing no instructions and merely saying that he hoped Nash would write something before he left at the end of the summer. But Nash seemed to have trouble working. He made no apparent progress on any of the problems he had mentioned vaguely to Truesdell at the start of the summer, and he never handed in a paper. At the end of the summer, he was forced to apologize to Truesdell for having wasted his time.68

  Nash spent most of his days, evidently, simply walking around rather aimlessly, lost in thought. Charlotte Truesdell, Truesdell’s wife and the project’s girl Friday, recalls that Nash seemed terribly young, “like a sixteen-year-old,” and almost never spoke to anyone. Once when she asked him what he was thinking, Nash asked whether she, Charlotte, didn’t think it would be a good joke if he put live snakes in the chairs of some of the mathematicians. “He didn’t do it,” she said, “but he thought about it a lot.”69

  3

  The Center of the Universe Princeton, Fall 1948

  … a quaint ceremonious village. — ALBERT EINSTEIN

  … the mathematical center of the universe. — HARALD BOHR

  NASH ARRIVED in Princeton, New Jersey, on Labor Day 1948, the opening day of Truman’s re-election campaign.1 He was twenty years old. He came by train, directly from Bluefield, via Washington, D.C., and Philadelphia, wearing a new suit and carrying unwieldy suitcases stuffed with bedding and clothes, letters and notes, and a few books. Impatient and eager now, he got off at Princeton Junction, a nondescript little middle-class enclave a few miles from Princeton proper, and hurried onto the Dinky, the small single-track train that shuttles back and forth to the university.

  What he saw was a genteel, prerevolutionary village surrounded by gently rolling woodlands, lazy streams, and a patchwork of cornfields.2 Settled by Quakers toward the end of the seventeenth century, Princeton was the site of a famous Washington victory over the British and, for a brief six-month interlude in 1783, the de facto capital of the new republic. With its college-Gothic buildings nestled among lordly trees, stone churches, and dignified old houses, the town looked every inch the wealthy, manicured exurb of New York and Philadelphia that, in fact, it was. Nassau Street, the town’s sleepy main drag, featured a row of “better” men’s clothing shops, a couple of taverns, a drugstore, and a bank. It had been paved before the war, but bicycles and pedestrians still accounted for most of the traffic. In This Side of Paradise, F. Scott Fitzgerald had described Princeton circa World War I as “the pleasantest country club in America.”3 Einstein called it “a quaint, ceremonious village” in the 1930s.4 Depression and wars had scarcely changed the place. May Veblen, the wife of a wealthy Princeton mathematician, Oswald Veblen, could still identify by name every single family, white and black, well-to-do and of modest means, in every single house in town.5 Newcomers invariably felt intimidated by its gentility. One mathematician from the West recalled, “I always felt like my fly was open.”6

  Even the university’s mathematics building conjured up images of exclusivity and wealth. “Fine Hall is, I believe, the most luxurious building ever devoted to mathematics,” one European émigré wrote enviously.7 It was a gabled, Neo-Gothic red brick and slate fortress, built in a style reminiscent of the College de France in Paris and Oxford University. Its cornerstone contains a lead box with copies of works by Princeton mathematicians and the tools of the trade — two pencils, one piece of chalk, and, of course, an eraser. Designed by Oswald Veblen, a nephew of the great sociologist Thorstein Veblen, it was meant to be a sanctuary that mathematicians would be “loath to leave.”8 The dim stone corridors that circled the structure were perfect for both solitary pacing and mathematical socializing. The nine “studies” — not offices!— for senior professors had carved paneling, hidden file cabinets, blackboards that opened like altars, oriental carpets, and massive, overstuffed furniture. In a gesture to the urgency of the rapidly advancing mathematical enterprise each office was equipped with a telephone and each lavatory with a reading light. Its well-stocked third-floor library, the richest collection of mathematical journals and books in the world, was open twenty-four hours a day. Mathematicians with a fondness for tennis (the courts were nearby) didn’t have to go home before returning to their offices — there was a locker room with showers. When its doors opened in 1921, an undergraduate poet called it “a country club for math, where you could take a bath.”

  Princeton in 1948 was to mathematicians what Paris once was to painters and novelists, Vienna to psychoanalysts and architects, and ancient Athens to philosophers and playwrights. Harald Bohr, brother of Niels Bohr, the physicist, had declared it “the mathematical center of the universe” in 1936.9 When the deans of mathematics held their first worldwide meeting after World War II, it was in Princeton.10 Fine Hall housed the world’s most competitive, up-to-the-minute mathematics department. Next door — connected, in fact — was the nation’s leading physics department, whose members, including Eugene Wigner, had driven off to Illinois, California, and New Mexico during the war, lugging bits of laboratory equipment, to help build the atomic bomb.11 A mile or so away, on what had been Olden Farm, was the Institute for Advanced Study, the modern equivalent of Plato’s Academy, where Einstein, Gödel, Oppenheimer, and von Neumann scribbled on their blackboards and held their learned discourses.12 Visitors and students from the four corners of the world streamed to this polyglot mathematical oasis, fifty miles south of New York. What was proposed in a Princeton seminar one week was sure to be debated in Paris and Berkeley the week after, and in Moscow and Tokyo the week after that.

  “It is difficult to learn anything about America in Princeton,” wrote Einstein’s assistant Leopold Infeld in his memoirs, “much more so than to learn about England in Cambridge. In Fine Hall English is spoken with so many different accents that the resultant mixture is
termed Fine Hall English… . The air is full of mathematical ideas and formulae. You have only to stretch out your hand, close it quickly and you feel that you have caught mathematical air and that a few formulae are stuck to your palm. If one wants to see a famous mathematician one does not need to go to him; it is enough to sit quietly in Princeton, and sooner or later he must come to Fine Hall.”13

  Princeton’s unique position in the world of mathematics had been achieved practically overnight, barely a dozen years earlier.14 The university predated the Republic by a good twenty years. It started out as the College of New Jersey in 1746, founded by Presbyterians. It didn’t become Princeton until 1896 and wasn’t headed by a layman until 1903 when Woodrow Wilson became its president. Even then, however, Princeton was a university in name only —“a poor place,” “an overgrown prep school,” particularly when it came to the sciences.15 In this regard, Princeton merely resembled the rest of the nation, which “admired Yankee ingenuity but saw little use for pure mathematics,” as one historian put it. Whereas Europe had three dozen chaired professors who did little except create new mathematics, America had none. Young Americans had to travel to Europe to get training beyond the B.A. The typical American mathematician taught fifteen to twenty hours a week of what amounted to high school mathematics to undergraduates, struggling along on a negligible salary and with very little incentive or opportunity to do research. Forced to drill conic sections into the heads of bored undergraduates, the Princeton professor of mathematics was perhaps not as well off as his forebears of the seventeenth century who practiced law (Fermat), ministered to royalty (Descartes), or occupied professorships with negligible teaching duties (Newton). When Solomon Lefschetz arrived at Princeton in 1924, “There were only seven men there engaged in mathematical research,” Lefschetz recalled. “In the beginning we had no quarters. Everyone worked at home.”16 Princeton’s physicists were in the same boat, still living in the age of Thomas Edison and Alexander Graham Bell, preoccupied with measuring electricity and supervising endless freshman lab sections.17 Henry Norris Russell, a distinguished astronomer by the 1920s, fell afoul of the Princeton administration for spending too much time on his own research at the expense of undergraduate teaching. In its disdain for scientific research, Princeton was not very different from Yale or Harvard. Yale refused for seven years to pay a salary to the physicist Willard Gibbs, already famous in Europe, on the grounds that his studies were “irrelevant.”18