A Beautiful Mind

by Sylvia Nasar

  Nash started singling out individuals. One was a senior named Al Vasquez, who had never taken a course from Nash and was something of a protégé of Paul Cohen’s. “I’d see him in the common room. He’d say something. It wasn’t a conversation. More like a monologue. He gave me preprints of his articles and asked me strange questions about them.”4

  But none of this was especially alarming or suggested outright illness, just another stage in the evolution of Nash’s eccentricity. His conversation, as Raoul Bott put it, had “always mixed mathematics and myth.”5 His conversational style had always been a bit odd. He never seemed to know when to speak up or shut up or take part in ordinary give and take. Emma Duchane recalled in 1997 that Nash always, from their earliest acquaintance, which dated back to Nash and Alicia’s courtship, told interminable stories with mysterious, off-key punch lines.6

  In his game-theory course, Nash behaved like his usual self, according to students who were in the class.7 On the first day, he said to the class, “The question occurs to me: Why are you here?,” a remark that caused one student to drop the course. Later, he gave a midterm without announcing it in advance. He also paced a great deal and he sometimes fell into reveries in the middle of lecturing or answering a student’s question. Just before Thanksgiving, Nash had invited his TA from the game theory course, Ramesh Gangolli, and Alberto Galmarino, a student from the course whom he was helping to choose a dissertation topic, to accompany him on a walk.8 As they walked over the Harvard Bridge on the Charles River late one afternoon, Nash embarked on a lengthy monologue that was difficult to follow for the two, who had just come to the United States. It concerned threats to world peace and calls for world government. Nash seemed to be confiding in the two young men, hinting that he had been asked to play some extraordinary role. Gangolli recalled that he and Galmarino were quite disturbed and that they wondered briefly if they should inform Martin that something was not quite right. Awed as they were by Nash, and new as they were to America — and so reluctant to form any judgments — they decided to say nothing.

  Also around that time, Atle Selberg, one of the masters of analytic number theory, gave a talk in Cambridge. Nash, who was in the audience, seemed to think that Selberg knew some secret that he was holding back. Selberg recalled, “He asked some questions I thought were in a sense, to my way of thinking, somewhat inappropriate to the subject. He seemed to see something quite different than what I had intended… . [His] questions were formulated as if I had some hidden, not fully disclosed, agenda that he wanted to discover. The lecture was about the rigidity of several locally symmetric spaces. He asked some questions that seemed to imply I had a hidden, secret motive. He suspected it had something to do with the Riemann Hypothesis, which of course it did not. I was rather taken aback. This was something that had nothing to do whatsoever [with the Riemann Hypothesis].”9

  After the New Year’s party, people around the department started talking about Nash. Classes resumed January 4. A week or ten days later, Nash asked Galmarino to teach a couple of his classes. He was going away, he said. Galmarino, who was flattered by Nash’s confidence in him, readily agreed. Nash showed up at Rota’s apartment on Sacramento Street on his way out of town. Then he disappeared. 10

  Cohen disappeared at around the same time. After a few days, the scuttlebutt among the graduate students was that Nash and Cohen had run away together.11 As it happens Cohen had gone to visit his sister. He was terribly upset when he returned to hear what the others had been saying about him and Nash. Nash, meanwhile, had driven south, ultimately to Roanoke, but perhaps also to Washington, D.C.

  A couple of weeks later Nash slouched into the common room. Nobody bothered to stop talking. Nash was holding a copy of The New York Times. Without addressing anyone in particular, he walked up to Hartley Rogers and some others and pointed to the story on the upper left-hand corner of the Times front page, the off-lede, as Times staffers call it.12 Nash said that abstract powers from outer space, or perhaps it was foreign governments, were communicating with him through The New York Times. The messages, which were meant only for him, were encrypted and required close analysis. Others couldn’t decode the messages. He was being allowed to share the secrets of the world. Rogers and the others looked at each other. Was he joking?

  Emma Duchane recalled driving with Nash and Alicia. She recalled that “he kept shifting from station to station. We thought he was just being pesky. But he thought that they were broadcasting messages to him. The things he did were mad, but we didn’t really know it.”13

  Nash gave one of his graduate students an expired license, writing the student’s nickname — St. Louis — over his own. He called it an “intergalactic driver’s license.” He mentioned that he was a member of a committee and that he was putting the student in charge of Asia. The student recalled, “He seemed to be joking around.”14 His manner took on a certain furtiveness. Another student, an undergraduate, recalled, “I have this impression of him darting about. I’d walk into a stairwell and he’d disappear as if he’d been lurking there.”15

  Nash showed up at the apartment of John and Karin Tate one evening. Everybody was horsing around and finally they settled down to play a game of bridge. Nash’s partner was Karin Tate. His bidding was bizarre. At one point he bid six hearts when, as it turned out, he held no hearts at all. Karin asked him, “Are you crazy?” Nash responded quite calmly, explaining that he somehow had expected her to read his bids. “He expected me to understand. He genuinely thought I could understand. I thought he was pulling my leg, but it became obvious that he wasn’t. I thought he was doing some sort of experiment.”16 Some people continued to think Nash was engaged in some elaborate private joke. There was a lot of discussion about it.

  Nash’s recollections of those weeks focus on a feeling of mental exhaustion and depletion, recurring and increasingly pervasive images, and a growing sense of revelation regarding a secret world that others around him were not privy to. He began, he recalled in 1996, to notice men in red neckties around the MIT campus. The men seemed to be signaling to him. “I got the impression that other people at MIT were wearing red neckties so I would notice them. As I became more and more delusional, not only persons at MIT but people in Boston wearing red neckties [would seem significant to me].”17 At some point, Nash concluded that the men in red ties were part of a definite pattern. “Also [there was some relation to] a crypto-communist party,” he said in 1996.

  Things started happening fast. Alicia Nash later compared Nash’s disintegration to that of a man who is conversing quite normally at a dinner party, suddenly starts arguing loudly, and finally has an all-out temper tantrum.18

  He told Cohen: “People are talking about me. You’ve heard them. Tell me what they’re saying.” Cohen recalled: “It had a nasty edge. I told him I didn’t know what he was talking about, that I hadn’t heard anything.”19

  Nash was still working on the Riemann problem. Once Nash accused Cohen of rifling through his trash can. Was he trying to steal Nash’s ideas about Riemann? Again, it sounded like a bit of an over-the-top joke, but it upset Cohen sufficiently so that he repeated the incident to a student.20

  In mid-February, Harold Kuhn, who was on a Fulbright in London with Estelle and his children, spent a few days in Paris where he visited a French mathematician, Claude Berge. Berge showed Kuhn a letter from Nash, written in four colors of ink, complaining that his career was being ruined by aliens from outer space.21

  Possibly, the event that triggered Nash’s strange letter to Berge was the announcement of the winner of the 1959 Bôcher Prize, Louis Nirenberg, the Courant professor who had suggested the partial differential equation problem to Nash. Paul Cohen later recalled that Nash’s reaction was furious. He told Cohen that he deserved the prize and that the fact that an older mathematician had won it was merely a sign that these things were “political.”22

  Nash also approached Neuwirth about his work. “He said he was giving this lecture on the Riemann Hyp
othesis,” Neuwirth recalled. “But when he started talking it was gibberish. Probability is everything!!! I knew that was crazy. I mentioned it to Newman, who brushed it off.”23

  On yet another occasion, Nash wandered into Moser’s office, unannounced as always. Moser, always affable, suppressed a feeling of irritation and waved him in. Nash stood at the blackboard. He drew a set that resembled a large, wavy baked potato. He drew a couple of other smaller shapes to the right. Then he fixed a long gaze on Moser. “This,” he said, pointing to the potato, “is the universe.” Moser nodded. Moser was at that time engaged in trying to apply Nash’s implicit function theorem to certain problems in celestial mechanics. “This is the government,” Nash said, in the same tone that used to say, “This is an elliptic equation.” “This is heaven. And this is hell.”24

  Ted and Lucy Martin had been in Mexico on a winter vacation. When Martin returned, Levinson took him aside and told him that Nash was having a nervous breakdown. “Tell me about it,” said Martin, who said later that he “almost didn’t believe in these things.” Martin recalled, “Levinson said, ’He’s very paranoid. If you go down to his office, he won’t want you between him and the door.’ Sure enough, when I went down to his office that Sunday night, Nash edged himself over between me and the door.”25

  Strange letters began turning up in the department mail. Ruth Goodwin, the department secretary, would put them aside and show them to Martin.26 They were addressed to ambassadors of various countries. And they were from John Nash. Martin panicked. He tried to retrieve the letters, not all of which were addressed and most of which weren’t stamped, from mailboxes around the campus.

  What was in the letters? None have survived, but various people recalled hearing from Martin that Nash was forming a world government. There was a committee that consisted of Nash and various students and colleagues in the department. The letters were addressed to all the embassies in Washington, D.C. The letter said he was forming a world government. He wanted to talk to the ambassadors. Later he would talk to the heads of state.27

  Martin was in a most awkward position. The faculty, after some internal dissension, had just voted on Nash’s promotion, and it was now before the president of the university’. He dithered and delayed.

  Meanwhile, Adrian Albert, the chairman of the mathematics department at the University of Chicago, called Norman Levinson. What was Nash’s state of mind? he asked Levinson. Chicago had made an offer of a prestigious chair to Nash, Nash was scheduled to give a talk, and now he had received a very odd letter from Nash.28 It was a refusal of the Chicago offer. Nash had thanked Albert for his kind offer but said he would have to decline because he was scheduled to become Emperor of Antarctica. The letter, Browder recalled in 1996, also contained references to Ted Martin’s stealing Nash’s ideas. The affair came to the attention of MIT president Julius Stratton, who, upon seeing a copy of Nash’s letter, is supposed to have said, “This is a very sick man.”

  The spring term began February 9. Shortly after Washington’s birthday, Eugenio Calabi, who was a member that year at the Institute for Advanced Study in Princeton, gave a seminar at MIT. Undergraduates, even very bright ones, didn’t normally attend departmental seminars, but Al Vasquez, a senior, decided he would go. He put on a sport coat and tie for the occasion. Feeling rather self-conscious, he sat a few rows from the rear and hoped that he looked less conspicuous than he felt.

  He had noticed, as he sat down, that Nash was sitting in the row behind him. In the middle of Calabi’s lecture, Nash started speaking rather loudly, although he did not appear to be addressing Calabi. After a few moments, Vasquez realized that Nash was talking to him. “Vasquez, did you know that I’m on the cover of Life magazine?” Nash kept repeating until Vasquez turned around.29

  Nash told Vasquez that his photograph had been disguised to make it look as if it were Pope John the Twenty-third. Vasquez, he said, also had his picture on a Life cover and it too was disguised. How did he know that the photograph, apparently of the pope, was really of himself? Two ways, he explained. First because John wasn’t the pope’s given name but a name that he had chosen. Second, because twenty-three was Nash’s “favorite prime number.”

  Almost the strangest thing, Vasquez later recalled, was that Calabi kept on lecturing as if nothing untoward were happening, and the rest of the audience too ignored the interchange, although it must have been audible to everyone in the room.

  • • •

  Nash and Calabi knew each other from their graduate-school days at Princeton. Before Calabi had come up to Cambridge, Nash had telephoned him at his apartment on Einstein Drive and asked whether the Calabis could put him and Alicia up for a few days.30 He wanted to spend a few days at the institute consulting with Atle Selberg, the number theorist, and preparing a talk that he was scheduled to give at the upcoming regional math society meeting.

  Calabi and the Nashes went out to dinner after Calabi’s talk. Both Nashes seemed unusually nervous, Calabi recalled. “At one point, Nash made a wrong turn and Alicia began yelling hysterically. He was somewhat anxious.”

  The next day, the Nashes left for Princeton while Calabi stayed on in Cambridge. A day or two later, Calabi got a call from his wife, Giuliana, who said that Nash was behaving very strangely and would he come home?

  On one occasion, Nash had walked into another apartment, used the bathroom, and walked out again. All the apartments on Einstein Drive looked virtually identical from the outside and mistakes were commonplace, but even afterward Nash didn’t seem to be aware that he had been in the wrong apartment.

  On the afternoon of February 28, Nash was even more agitated. Calabi had just returned. “He was acting much more nervous than usual. Very agitated. At the moment of leaving, he was misplacing notes, running back and forth between the car and the house. Alicia was trying to calm him down.” Calabi watched, full of misgivings. Speaking of Nash’s mathematical investigation, he said, “I knew in that area that problem was not going to yield to a flash of inspiration.”31

  Nash’s consultations with Selberg apparently came to naught. Selberg had merely been irritated by Nash’s persistence, as he later recalled, and told Nash, in even harsher terms, that the probabilistic approach he was pursuing had been tried before and had already been demonstrated to be fruitless.32

  One can only imagine the fear and confusion that Nash felt that afternoon as he stood before the 250 or so mathematicians who came to his lecture, sponsored by the American Mathematical Society, in a Columbia University auditorium.33

  Harold N. Shapiro, a professor at the Courant Institute and a number theorist who had known Nash since the summer they spent together at RAND in 1952, introduced Nash.

  There was in fact an air of tremendous expectation in the hall. Regional AMS meetings were essentially job meetings. The audience consisted both of job seekers and established mathematicians, among them many who knew Nash and his work intimately. “Here was a great young mathematician with a proven ability for tackling the most difficult problems about to announce what he felt was a likely solution to the deepest problem in all of mathematics,” recalled Shapiro. “I remember hearing that he was interested in prime numbers. Everybody’s reaction was that if Nash turns to number theory, number theorists better watch out. There was a buzz.”34

  Peter Lax, a professor at the Courant Institute, described it as “a very strange adventure.”

  Lipman Bers reminded me, as we were listening to Nash’s talk, that Heifetz gave his first concert at Carnegie (accompanied by the pianist Godowski). An older violinist, turning to the musician seated next to him, said, “It’s very hot in here.” “Not for the pianist,” came the answer. It must have been hot in there, but only for the number theorists in the audience. It was work in progress. I couldn’t judge it. Mathematicians don’t usually present unfinished work.35

  At first, it seemed like just another one of Nash’s cryptic, disorganized performances, more free association than exposition. But halfway
through, something happened. Donald Newman recalled in 1996:

  One word didn’t fit in with the other. I was at Yeshiva. Rademacher, who had worked on the Riemann Hypothesis, was present. In fact, he wrote a brilliant paper on How Not to Solve the Riemann Hypothesis. It was Nash’s first downfall. Everybody knew something was wrong. He didn’t get stuck. It was his chatter. The math was just lunacy. What does this have to do with the Riemann Hypothesis? Some people didn’t catch it. People go to these meetings and sit through lectures. Then they go out in the hall, buttonhole other people, and try to figure out what they just heard. Nash’s talk wasn’t good or bad. It was horrible.36

  Cathleen Morawetz, who had enjoyed joking around with Nash at Courant two years earlier, ran into Nash in the stairwell after the talk: “He was laughed out of the auditorium,” she recalled. “I felt terrible. I said something nice to him, but I was disturbed. He seemed very depressed.” (Later Cathleen used the phrase “heaping scorn on him” to describe the audience reaction.)37

  Nash had been invited to give a talk at Yale as well on his way back to Cambridge. It was his second talk at Yale that year, but he couldn’t find his way there. He kept calling Felix Browder, then teaching at Yale, and telling him that he couldn’t understand how to get off the Merritt Parkway.

  Nash talked about the Riemann Hypothesis just as he had at Columbia. Again, it was a disastrous performance, as recalled by Browder, who contrasted his performance with the earlier one. “The preceding year there was no hint of trouble. That is when he finished the parabolic equations proof. [In fact] he completed the proof during a talk. I [had] asked him if he wanted to come and give another talk at Yale. It wasn’t coherent. I thought something was wrong.”38