June 1945–June 1948
In those days very few people became mathematicians. It was like becoming a concert pianist. — RAOUL BOTT, 1995
NASH WENT TO PITTSBURGH to become a chemical engineer, but his growing interest was in mathematics. It was not long before he abandoned the laboratory and slide rule for Möbius knots and Diophantine equations.1
With its smelters, power plants, polluted rivers, and ubiquitous slag heaps, Pittsburgh was a city of violent strikes and frequent floods.2 So dense was the sulfurous haze that engulfed its downtown that travelers arriving by rail often mistook morning for midnight. The Carnegie Institute of Technology, perched halfway up Squirrel Hill, hardly escaped the inferno. The ivory-colored brick of its buildings — designed, or so students said, to serve as factories should Andrew Carnegie’s school fail — were glazed yellow black. Its walkways were gritty with soot particles the size of pebbles. Its students were forced, before a lecture was half over, to brush the cinders from their lecture notes. Even at high noon in midsummer, one could stare directly at the sun without blinking.
In that era, Carnegie was shunned by the local ruling elite, which sent its children east to Harvard and Princeton. Richard Cyert, who joined the Carnegie faculty after the war and would later become its president, recalled, “When I came this place was really very backward.”3 The engineering school, with its two thousand or so students, still resembled the trade school for sons and daughters of electricians and bricklayers that it had been at the turn of the century.
But like so many other colleges right after the war, Carnegie was changing. Robert Doherty, its president, had seized the opportunities created by wartime research to turn the engineering school into a real university. He parlayed defense contracts and the prospect of ballooning enrollments into a big push to recruit brilliant young researchers in math, physics, and economics. “The theoretical sciences were being pushed very hard,” recalled Richard Duffin, a mathematician. “Doherty was trying to take CT into the big time.”4
Corporate giants like Westinghouse, whose headquarters were in Pittsburgh, supplied generous scholarships to lure talented young people to Carnegie. Among the scholarship recipients who entered Carnegie in 1945 were talented youngsters like Andy Warhol, the artist, as well as a group of young men who would eventually, like Nash, shun engineering for science and mathematics.5
• • •
Nash arrived by train in June 1945; gasoline rationing made car travel impractical.6 Carnegie Tech was still operating in wartime mode: classes went year-round, most campus activities remained canceled, and most of the fraternity houses were still shut. Within a year the campus would be inundated with veterans and classes would be jammed with these older students. But that June, two months before the war finally ended, it was mostly freshmen and sophomores who were on campus. The scholarship students were housed together in Welch Hall and took most of their classes together — small ones taught by hand-picked instructors, some of whom were first-rate. Nash took his first physics course from Immanuel Estermann, for example, a top-flight physicist who had done much of the experimental work that had netted Otto Stern, a German émigré, the 1943 Nobel Prize for physics.7
Nash’s engineering aspirations did not survive his first semester, killed off by an unhappy experience in mechanical drawing: “I reacted negatively to the regimentation,” he later wrote.8 But chemistry, his newly chosen major, proved no better suited to his temperament or interests. He worked briefly as a lab assistant for one of his teachers but got into trouble for breaking equipment.9 He was so bored at his summer job at the Westinghouse Lab that he spent most of his two months there making and polishing a brass egg in the lab’s machine shop.10 The final blow was a C in physical chemistry, which he got after a running dispute with the professor over the lack of rigor of the mathematics in the course. David Lide recalled, “He refused to do the problems the way the professor expected.”11 Of chemistry in general Nash would complain: “It was not a matter of how well one could think . . . but of how well one could handle a pipette and perform titration in the laboratory.”12
• • •
Even as he struggled in the laboratory, Nash was already discovering a brilliant group of newcomers to Carnegie. By his sophomore year, Doherty’s program of upgrading the theoretical sciences had brought to Carnegie John Synge, nephew of the Irish playwright John Millington Synge, who became head of the mathematics department. Despite his startling appearance — Synge wore a black patch over one eye and a filter that protruded from one of his nostrils — he was a man of great charm who attracted younger scholars like Richard Duffin, Raoul Bott, and Alexander Weinstein, a European émigré whom Einstein had once invited to become a collaborator.13 When Albert Tucker, a Princeton topologist who did pathbreaking work in operations research, came to Carnegie to lecture that year, he was so impressed with the depth of mathematical talent at Carnegie that he confessed that he felt as if he were “bringing coals to Newcastle.”14
From the start, Nash dazzled his mathematics professors; one of them called him “a young Gauss.”15 He took courses in tensor calculus — the mathematical tool used by Einstein to formulate the general theory of relativity — and relativity from Synge.16 Synge was impressed with Nash’s originality and his appetite for difficult problems.17 He and others began urging Nash to major in mathematics and to consider an academic career. Nash’s doubts that one could make a living as a mathematician took some time to overcome. But by the middle of his second year he was concentrating almost exclusively on mathematics. The Westinghouse scholarship administrators were unhappy with Nash’s switch to mathematics, but by the time they learned of it, it was a fait accompli.18
College is a time when many ugly ducklings discover that they are swans, not just intellectually but socially. Most of the boys in Welch Hall — precocious but immature — found common interests, kindred spirits, and a measure of acceptance painfully lacking in high school. Hans Weinberger recalled, “We were all nerds back in our high schools and here we were able to talk to one another.”19
Nash was not so lucky. While his professors singled him out as a potential star, his new peers found him weird and socially inept. “He was a country boy, unsophisticated even by our standards,” recalled Robert Siegel, a physics major, who remembered that Nash had never attended a symphony performance before.20 He behaved oddly, playing a single chord on the piano over and over,21 leaving an ice cream cone melting on top of his castoff clothing in the lounge,22 walking on his roommate’s sleeping body to turn off a light,23 pouting when he lost a game of bridge.24
Nash was rarely invited to go to concerts or restaurants with the group. Paul Zweifel, an avid bridge player, taught Nash how to play bridge, but Nash’s pouting and inattention to the details of the game made him a poor partner. “He wanted to talk about the theoretical aspects.”25 Nash roomed with Weinberger for a term, but the two clashed constantly — Nash once pushed Weinberger around to end an argument26 — and Nash moved into a private room at the end of the hall. “He was extremely lonely,” recalled Siegel.27
Later in life, as his accomplishments multiplied, his peers would be more apt to be forgiving. But at Carnegie, where he was thrust together with other adolescents around the clock, he became a target. He was not so much bullied — the other boys were afraid of his strength and temper — as ostracized and relentlessly teased. That he was envied for his size and his brains only fueled the teasing. “He was the butt of people’s jokes because he was different,” recalled George Hinman, a physics student.28 “Here was a guy who was socially underdeveloped and acting much younger. You do what you can to make his life miserable,” Zweifel admitted. “We tormented poor John. We were very unkind. We were obnoxious. We sensed he had a mental problem.”29
• • •
That first summer, Nash, Paul Zweifel, and a third boy spent an afternoon exploring the subterranean maze of steam tunnels under Carnegie. In the dark, Nash suddenly turned to the others and blurted out, “Gee, if we got trapped down here we’d have to turn homo.” Zweifel, who was fifteen, found the remark pretty odd. But during Thanksgiving break, in the deserted dormitory, Nash climbed into Zweifel’s bed when the latter was sleeping and made a pass at him.30
Away from home, living in close proximity with other adolescents, Nash discovered that he was attracted to other boys. He spoke and acted in ways that seemed natural to him only to find himself exposed to his peers’ contempt. Zweifel and other boys in the dormitory started calling Nash “Homo” and “Nash-Mo.”31 “Once the statement was made,” George Siegel said, “it stuck. John took a lot.”32 No doubt, he found the label hurtful and humiliating, but his anger is all that anyone witnessed.
The boys made him the butt of various pranks. One time, Weinberger and a couple of others used a footlocker as a battering ram to break down Nash’s door.33 Another time, Zweifel and a few others, knowing of Nash’s extreme aversion to cigarette smoke, rigged up a contraption that smoked an entire pack of cigarettes and collected the smoke. “A bunch of us crowded around John’s door and blew the smoke under it,” Zweifel recalled. “Almost instantaneously, his room filled up with cigarette smoke.”34 Nash exploded in rage. “He came roaring out of his room, picked up Jack [Wachtman], and threw him down on the bed,” said Zweifel. “He ripped off Wachtman’s shirt and bit him in the back. Then he ran out of the room.”
At other times, Nash defended himself the only way he knew how. He wasn’t practiced in invective, sarcasm, or ridicule, so he went for childish displays of contempt. “ ‘You stupid fool,’ he’d say,” Siegel recalled. “He was openly contemptuous of people who he didn’t think were up to his level intellectually. He showed that contempt for all of us: ‘You’re an ignoramus.’ ” After a year or so, after he had acquired a reputation for being a genius, he began to hold court in Skibo Hall, the student center.35 Like the fairground magician with his swords, he would sit in a chair and challenge other students to throw problems at him to solve. A. lot of students came to him with their homework. He was a star — but an outcast too.
• • •
Nash stared glumly at the announcement tacked to the bulletin board outside the math department office in Administration Hall, which looked, even on the sunniest of days, like the inside of the Lincoln Tunnel. He stood in front of the board for a long time. He hadn’t made it into the top five.36
Nash’s fantasy of instant glory crumbled. The William Lowell Putnam Mathematical Competition was a prestigious national tournament for undergraduates, sponsored by an old-money Boston family known mostly for its Harvard presidents and deans.37 Today the contest attracts upward of two thousand participants. In March 1947, it was a decade old and drew about 120. But even then, it was the first chance to establish one’s rank in the world of mathematics as well as to seize the limelight.
Then, as now, contestants were given a dozen problems and half an hour each to solve them. The problems were famously difficult. In any given year, the median score out of 120 possible points was zero. That meant that at least half the contestants weren’t able to obtain so much as partial credit for even a single problem, and this in spite of the fact that most contestants had been chosen by their departments to compete. To have a prayer of winning — placing in the top five — a young mathematician had to be super-fast or especially ingenious. The prizes involved a nominal amount of money, twenty to forty dollars for each of the top ten contestants, and two hundred to four hundred dollars for each of the top five school teams, but winners became instant mini-celebrities in the mathematics world and were virtually assured a spot in a top graduate program. Different graduate programs pay more or less attention to the Putnam, but at Harvard it is, and always has been, a very, very big deal. That year Harvard pledged a fifteen-hundred-dollar scholarship to one of the winners.
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. Wein berger, 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 opposed 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
• • •
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