A Beautiful Mind

by Sylvia Nasar

  There were other signs that Nash felt, at that particular juncture, a growing pressure to prove himself — as well as a newfound taste for taking risks. Nash had always been obsessed with money, even trivial amounts. Nash had made friends with Samuelson, Solow, and a number of other young economists at MIT. Samuelson recalled in 1996 that Nash told him about a bank with no checking charges at all. “Do they give you stamped, self-addressed envelopes too?” Samuelson shot back. Nash, who didn’t get the joke, immediately replied: “No. Do you know a bank that gives you stamped self-addressed envelopes?”34 Privately, Samuelson thought it was all a bit pathological. Norman Levinson, who complained to Samuelson about Nash’s parsimony, apparently once told him “to cut out his cheese-paring ways.” Levinson said: “One extra theorem will earn you more than all that stuff.” (Not everyone thought it was weird. Nash was able to convince Martin and a few others in the math department to switch their accounts to the Peoples National Bank of Rocky Mount, Virginia, which charged no fees on checking accounts!)35

  That summer Nash’s somewhat compulsive attitude toward money blossomed into an obsession with the stock and bond markets. Solow recalled: “It seemed he had a notion that there might be a secret to the market, not a conspiracy, but a theorem — something that if you could only figure it out, would let you beat the market. He would look at the financial pages and ask, Why is this happening? Why is that happening?’ as if there had to be a reason for a stock to go up or down.”36 Martin, the chairman of the mathematics department, also recalled that “Nash liked to chat about the stock market. He had the idea you could get rich.”37 Nash had some notion of arbitraging July 1999 bonds against September 1999 as well as various ideas about over-the-counter stocks.38 Solow was aghast to learn that Nash was investing his mother’s savings. “I was horrified,” he recalled. “That’s something else,” said Samuelson. “It’s vanity. It’s like claiming you can control the tides. It’s a feeling that you can outwit nature. It’s not uncommon among mathematicians. It’s not just about money. It’s me against the world. A lot of traders, start that way. It’s about proving yourself.”

  In late July, against this backdrop of grand designs, the Nashes, who had not yet gone on a proper honeymoon, left Cambridge for Europe. They sailed from New York on the lie de France.39 Their ultimate destination was Edinburgh, where the World Congress of Mathematics was to take place in the second week of August. Nash was giving a lecture on nonlinear theory. Many colleagues from MIT and Princeton would be there, and Nash was able to pay for his trip partly out of Sloan funds.

  But first they went to Paris. There, having calculated that importing a used car from Europe was a bargain, Nash purchased an olive-green Mercedes 180 diesel. He and Alicia then drove south over the Pyrenees to Spain, back to Italy, and up to Belgium. The trip was a success. “We were young,” Alicia recalls. “It was fun.”40 Another of his plans was to buy Alicia the diamond that he had promised her. Antwerp was the center of the world diamond market, and Nash had the idea that it would be advantageous to buy a stone directly from a wholesaler.41 Eli Stein’s father had been a diamond merchant there before the war and that is what may have given Nash the idea in the first place. If Nash had hoped for a bargain, he was disappointed; the yellow stone that he purchased was no cheaper than it would have been in the States, he recalled in 1996. From Belgium, they drove to the North Sea, crossed over into Sweden, and visited Lund and Stockholm before crossing back to England.

  They rendezvoused with Felix and Eva Browder in London and drove to Scotland with them. The men ignored the women, who sat together in the backseat gossiping (at that time, Eva recalled, “Nash wouldn’t talk to women”).42 On the second, rainy day of the drive, Felix managed to dent the Mercedes, prompting Nash to repeat incessantly for the rest of the trip that “this car has been Browderized.”43

  There were, as Alicia later said, “lots of famous people around.”44 Nash seemed very much his usual self. He pouted a bit when Milnor gave his invited half-hour lecture, a great honor. He got into a loud argument with Olga Ladyshenskaya from the University of St. Petersburg, an expert on a priori estimates of parabolic equations and the leading female mathematician of her generation. Nash was picking her brains and she, somewhat paranoid, reacted rather violently.45 The Nashes held a party in their hotel room. Nash raised eyebrows by complaining at great length that Alicia took too long to get dressed and that she was always late.46 But he showed no emotion when, as he and Alicia sat in the balcony with the Browders, Moore, Milnor, and others, the Fields prizes were awarded.

  33

  Schemes Fall 1958

  The growing consciousness is a danger and a disease.

  — FRIEDRICH NIETZSCHE

  THE NASHES WERE BACK in Cambridge and Nash was already teaching when Alicia discovered, half with joy, half with dismay, that she was pregnant. Alicia, who liked her job and her paycheck, would have preferred to wait a few years. It had been Nash’s wish that they start a family right away.1 He stopped short of saying that his desire for another child had been his motive for marrying, but he reminded Alicia often that the whole purpose of marriage, in his view, was to produce children.2 Now that his wish was to be realized, Nash was on the whole rather pleased, passing the great news on to Albert Tucker in a postscript to a letter in early October by referring to “a ‘new addition’ that we are expecting.”3

  He demanded that Alicia stop smoking. When she lit up at a math party he told her to put out her cigarette and made a scene after she refused.4 But otherwise, all seemed to be well. Nash was teaching a graduate course. The course number — M711, a sly reference to craps — was Nash’s idea and helped draw enough students to fill a small amphitheater.5 Nash’s first assignment also reflected his high spirits. He asked his students to invent a way to grade each other’s papers so that he, Nash, wouldn’t have to be bothered.

  Nash was at that moment preoccupied with his own future and feeling increasingly restless. Martin had assured him that he was coming up for tenure that winter.6 The promise of a decision mollified him somewhat: Nash wrote to Tucker that the situation at MIT had “reached a modus vivendi condition which is an improvement over early 1958. ”7

  But the sense that others were deciding his future oppressed him. And he was more convinced that he didn’t belong at MIT. “I do not feel this is a good long-term position for me,” he wrote to Tucker, saying that he was afraid of becoming isolated within the department like Wiener. “I would rather be one of a smaller number of more nearly equal colleagues.”8 His sister Martha recalled that “he had no intention of staying at MIT. He wanted to go to Harvard because of the prestige.”9

  Meanwhile, the University of Chicago was putting out feelers about Nash’s possible interest in moving there.10 Chicago had gone a long time without making any senior hires, even after Andre Weil had left for the Institute for Advanced Study. Now the math department had a new chairman, Adrian Albert, and some cash.11 Albert was looking at a young Harvard professor, John Thompson, who had done brilliant work in group theory,12 and also at Nash, who had a number of strong supporters in the department, including Shiingshen Chern.

  Nash felt the pressure from these decisions acutely and decided, in any case, that he wanted to get away the following year for a separate sabbatical. He wanted to spend the fall term of 1959 in Princeton at the Institute for Advanced Study and the spring term in Paris at its French equivalent, the Institut des Hautes Études Scientifiques, which, like the Institute, was dominated by mathematicians and theoretical physicists. Around the end of October, he began the process of applying for various grants, including those from the National Science Foundation, the Guggenheim Foundation, and the Fulbright program. He also applied to the Institute for a membership. He wrote: “This is part of the plan. The other part is to learn French.”13

  Albert Tucker was supportive. He wrote to the Fulbright program on October 8 that “Nash is eager to talk mathematics with others he thinks are up to snuff… . He is oft
en rather rough on those less able … but this is standard practice in France … Nash should do well with energetic give and take … benefit from relationship with Leray.”14 His letter of recommendation to the National Science Foundation called Nash “one of the most talented and original mathematicians in the US ... in his final year of a Sloan fellowship. One of two or three best men who ever got a Sloan.”15 His November 26 letter to the Guggenheim Foundation was couched in similarly laudatory terms.16

  What Nash planned to work on isn’t clear. He was at the time thinking about several different problems, including quantum theory and the Riemann Hypothesis. His desire to go to Paris may or may not have been motivated by Leray’s presence at the College de France. Gian-Carlo Rota recalled: “He was bragging that he had enough fellowships to survive three or four years.”17

  One particularly unpleasant episode occurred in the early fall. His investments had proved disastrous,18 to say the least, and he had to confess his failure to Virginia. He also had to promise to repay her. “I’ll forward my debt,” Nash was forced to write Virginia that fall. The amount wasn’t huge, but the whole thing was quite upsetting.19

  Everything, in short, seemed suddenly to be in flux — which may be why Nash found himself drawn to another young man. That summer a brilliant mathematician, six years Nash’s junior, turned up at MIT. By the mid-1960s, Paul Cohen would be famous for solving a logical puzzle posed by Godel — a result so stunning that The New York Times reported it20 — and would win both a Fields and a Bôcher.21 But in the fall of 1958, Cohen was a fiercely ambitious, enormously frustrated upstart.

  Cohen, who had grown up poor in New York, had been on the math team at Stuyvesant High School, and had just earned his Ph.D. at the University of Chicago.22 But his thesis had not been well received and as a consequence he had been unhappily marooned at the University of Rochester. Desperate to get away, he had begged his old friend from Stuyvesant, Eli Stein, to help him get an instructorship at MIT.23 This Stein had managed to do, and Cohen had come to Cambridge as soon as classes ended at Rochester.

  Big, slightly feline in his movements, his eyes burning with fiery intensity under a high dome of a forehead, Cohen was self-obsessed, suspicious, aggressive, and charming by turns. He spoke several languages. He played the piano. His ambitions were seemingly unlimited and he spoke, from one moment to the next, of becoming a physicist, a composer, even a novelist. Stein, who became a close friend of Cohen’s, said: “What drives Cohen is that he’s going to be better than any other guy. He’s going to solve the big problems. He looks down on mathematicians who do mathematics for the sake of making incremental improvements in the field.”24

  He was as fast as Newman, ambitious as Nash, arrogant as the two put together, and he very quickly fell in with the other two. Cohen was competitive — “wildly competitive,” as one fellow instructor put it. “He was good at tearing people down,” Adriano Garsia recalled in 1995.25 They challenged each other with problems. “Well, Nash what kind of garbage are you working on now?” Cohen would say. “What wrong theorems did you prove today? Okay … you want a real problem? I’ll give you a problem!” They ragged the chess players mercilessly. As Garsia recalls, “They were always eager to show how much better they were at whatever game it was that other people were playing. They engaged in horseplay … playing tunes on beer bottles.” D.J. and Paul typically got the better of Nash, but not always. Cohen was the more articulate. But occasionally Nash could shut them up. “He could say an enormous amount in three words,” said Garsia.

  They delighted in ganging up on a graduate student struggling with a dissertation, dissecting a problem that some poor guy had been working on for two years and springing their own solution on him. They liked to argue that theirs was more powerful, but in fact they abjured elegance for brute force. “They wanted to solve it any way at all,” said Garsia.

  Nash “cultivated” Cohen, according to the latter. It was “unusual,” Cohen recalled. “Maybe I liked him because he liked me. He’d ask me to lunch. He was not a friend of mine, though. I don’t know that he had any friends.”26 Still, Cohen was intrigued. He used to go to dinner with the Nashes, speaking Spanish to Alicia, wondering how Nash had won this beautiful girl, and aware that Alicia was somehow “concerned” about Nash’s paying so much attention to Cohen.

  Nash never made any advances or ever said anything personal to Cohen. But he dropped hints. He’d say things like “So and So was a homosexual,” Cohen recalled. Or he’d say a word and ask Cohen if he knew what it meant. If Cohen said no, Nash would come back with “Oh, you don’t know what so and so means.” People around the department were soon gossiping that Nash was in love with Cohen.27

  Cohen was flattered, even fascinated, by Nash’s interest, but he took special delight in rubbing Nash’s face in the disparity between the grandiose claims and reality. He was critical, to the point of viciousness, of Nash’s hubris. Later, Cohen would say, “Mathematically I didn’t interact with him. I didn’t feel I could talk to him about mathematics.”

  But they did talk a good deal about Nash’s ideas on the Riemann Hypothesis. “Nash thought he could work on any problem he wanted,” said Cohen in a tone of mild outrage. “He wrote a letter to Ingham, and he passed it around. I shot it down. What he was trying to do, you couldn’t do. I would have been very unsympathetic to Nash’s notion. The Riemann Hypothesis can’t be solved as stated. He came by with this letter. But any expert would have said these ideas are naive. What I admired is the enormous self-confidence to even conjecture. If he’s right, this guy’s intuition is in the stratosphere. But it turned out to be just another wrong idea.”

  A year later, after he had been hospitalized, some blamed disappointed love and the intense rivalry with a younger man for Nash’s breakdown.28 Ironically, Cohen’s career wound up mirroring Nash’s. After his great success, he turned to the Riemann Hypothesis and physics. He did publish, but rarely and never anything that rivaled the work he did before age thirty. “Nothing was worthy of his notice,” said a mathematician who knew him at MIT. “He sat in glorious isolation.”29

  34

  The Emperor of Antarctica

  There is a kindling. A slow fire burning.

  —JOSEPH BRENNER, psychiatrist, Cambridge, Massachusetts, 1997

  SOMEONE WAS CALLING, “It’s time to play charades. It’s time to play charades.”1 A crowd of costumed guests filled the entire ground floor of the Mosers’ small frame house in Needham. Outside, snow had been falling for hours. Inside, the atmosphere was thick with smoke, liquor, jazz. Everyone was talking, laughing a little louder than usual, heads close together, waving cigarettes, posing for the camera, still a bit self-conscious but already loosening up in the carnival-like atmosphere. The Mosers were dressed as pirate and Indian squaw. Karin Tate, Artin’s musician daughter, was dressed as a black cat. Her husband, John, the algebraist, came as the Vector Space Man, wearing a metal cap with bobbing antennae and arrows all over his chest. Gian-Carlo Rota looked as elegant as ever in his monk’s tunic, his dark-haired wife, Teresa, dashing in her Spanish bolero and slim black pants.

  Richy Emery, the Mosers’ son, watched through the dining-room window as a big dark car pulled into the driveway and a virtually naked man got out. There was a pounding on the kitchen door and Richy ran to open it. As Nash came striding into the room, followed by Alicia, heads turned, eyebrows shot up, and conversation suddenly quieted. Alicia was laughing excitedly and Nash wore a smirky smile as they surveyed the astonished guests. He was barefoot and entirely naked except for a diaper and a sash, which was draped across his powerful chest, that had the numerals 1959 written on it. Having stolen the show, Nash grinned and bowed, waved a baby bottle full of milk at the assembled company, which was laughing loudly at this point — and then sauntered into the living room to join in the game of charades.

  Jürgen and Gertrude were just dividing the guests into two teams. Nash was on one team, Richy on the other. When it was Richy’s turn,
Nash walked over to him and whispered in his ear the name of the character that he was supposed to act out. Richy was delighted. He adored Nash, who was much younger and more animated than most of Jürgen’s math friends. Richy’s pantomime initially mystified everyone. Finally a woman, the best player in the room, read his eleven-year-old mind: The Critique of Pure R£ason! Richy looked over at Nash, who shrugged his shoulders and gave him a big grin.

  Between that New Year’s Eve, December 31, 1958, and the last day in February, as his fellow mathematicians and friends looked on in puzzlement, Nash would undergo a strange and horrible metamorphosis. But on New Year’s Eve, he was, by all accounts, simply his flamboyant, eccentric, and slightly off-key self, playful and mischievous. Alicia was in high spirits as well. The idea for Nash’s costume had been hers.2 She was the one who sewed it, draped his sash, and choreographed the entrance a moment past midnight. There is no hint of unease or premonition in the photograph of Nash sprawling somewhat drunkenly, with a laughing, gleeful Alicia on his lap, her arm on his shoulder. Most of the evening, though, it was Nash who was curled up in Alicia’s lap. Some of the other partygoers found it extremely bizarre, “really gruesome,” “disturbing.”

  Nash had already crossed some invisible threshold. The feverish activity and the fierce competition with Cohen and Newman in the common room, so noticeable in the early fall, had already slowed. He seemed a trifle more withdrawn, a little spacier. A graduate student who had just come into Nash’s orbit recalled his not being able to keep up with Cohen and Newman. Paul Cohen recalled in 1996 that that fall Nash would make little jokes, little offhand remarks about world affairs, interesting license numbers, and the like. They were funny — Nash was always very bright and very witty — but they showed that something was not all right. “I’d think, ‘That’s going a little too far,’” Cohen said.3