A Beautiful Mind (9 page)

From the start, Nash dazzled his mathematics professors; one of them called him “a young Gauss.”
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He took courses in tensor calculus — the mathematical tool used by Einstein to formulate the general theory of relativity — and relativity from Synge.
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Synge was impressed with Nash’s originality and his appetite for difficult problems.
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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.
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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.”
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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.
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He behaved oddly, playing a single chord on the piano over and over,
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leaving an ice cream cone melting on top of his castoff clothing in the lounge,
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walking on his roommate’s sleeping body to turn off a light,
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pouting when he lost a game of bridge.
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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.”
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Nash roomed with Weinberger for a term, but the two clashed constantly — Nash once pushed Weinberger around to end an argument
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— and Nash moved into a private room at the end of the hall. “He was extremely lonely,” recalled Siegel.
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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.
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“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.”
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•  •  •

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.
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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.”
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“Once the statement was made,” George Siegel said, “it stuck. John took a lot.”
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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.
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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.”
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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.
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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.
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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.
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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.
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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.”
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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.
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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.
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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.
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“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.”
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“He always had good examples and counterexamples,” another student recalled.
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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.”
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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.”
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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.”
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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.”
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“Diophantine equations were his love,” recalled Siegel. “None of us knew anything about them, but he was working on them then.”
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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.
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Nash himself does not recall. He did, however, take a course in international trade, his one and only formal course in economics, before graduating.
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It was in this course that Nash first began to mull over one of the basic insights that eventually led to his Nobel Prize.
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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,
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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.
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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.”
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