A Beautiful Mind (58 page)

In late July, Alicia’s mother brought John Charles, a big, handsome two-year-old, to Princeton. Nash called the reunion “a big occasion for me since I haven’t seen our little boy all during 1961!”
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Then, at the beginning of August, Nash attended a mathematics conference in Colorado where he ran into a number of old acquaintances and went on a day-long excursion with Spencer, an enthusiastic mountaineer, to climb Pike’s Peak.
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Nash and Alicia were living together once more, but not especially happily. The turbulence of the two previous years had produced an accumulation of hurts and resentments, and the resulting coldness lingered and was exacerbated by new conflicts over money, childrearing, and other issues of daily living. None of this was made easier by the fact that Nash’s in-laws now lived with them. Carlos Larde’s health had deteriorated markedly, and he and his wife Alicia moved to Princeton that fall. The two couples shared a house at 137 Spruce Street.
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It was a great help that Mrs. Larde cared for Johnny while Alicia went to work, but living together created another layer of strain, especially for Alicia.

They tried to make the best of it. Nash attempted to care for his son, picking him up at nursery school and the like. They socialized with the Nelsons, the Milnors, and a few others. Once or twice, they drove up to Massachusetts to visit John and Odette Danskin, who had moved there the previous fall, and to see John Stier.
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The visits were rather fraught and Eleanor used to call John Danskin afterward to complain about Nash. On one visit, apparently, Nash had come with a bag of doughnuts. “Eleanor kept saying, ’How cheap!’ ” Odette recalled.
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In early October, Nash attended a most historic conference in Princeton.
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The conference, organized by Oskar Morgenstern, and attended by virtually the entire game-theory community, amounted to a celebration of cooperative theory. There
was little mention of noncooperative games or bargaining. But John Harsanyi, a Hungarian, Reinhard Selten, a German, and John Nash, dressed in odd mismatched clothing, mostly silent, were all there.
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This was the first time these three men had met, and they would not meet again until they traveled to Stockholm a quarter of a century later to accept Nobel Prizes. Harsanyi remembers asking one of the Princeton people why Nash said so little during the sessions. The answer, Harsanyi recalled, in a conversation in Jerusalem in 1995, was “He was afraid he would say something strange and humiliate himself.”
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Nash was able to work again, something he had not been able to do for nearly three years. He turned once more to the mathematical analysis of the motion of fluids and certain types of nonlinear partial differential equations that can be used as models for such flows. He finished his paper on fluid dynamics, begun while he was in Trenton State hospital.
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It was titled “Le Problème de Cauchy Pour Les Equations Differentielles d’une Fluide Générale”-and published in 1962 in a French mathematical journal.
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The paper, which Nash and others have described as “quite a respectable piece of work”
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and which the
Encyclopedic Dictionary of Mathematics
called “basic and noteworthy,” eventually inspired a good deal of subsequent work on the so-called “Cauchy problem for the general Navier-Stokes equations.” In the paper, Nash was able to prove the existence of unique regular solutions in local time.
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“After Nash’s hospitalization he came out and seemed OK,” Atle Selberg recalled. “It was good for him to be at the IAS. Not everybody on the Princeton faculty was very friendly. It’s true that he didn’t speak. He wrote everything on blackboards. He was perfectly articulate in writing. He gave a lecture on Navier-Stokes equations — which concern hydrodynamics and partial differential equations — something I don’t know much about. He seemed fairly normal for a while.”
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He was most at ease in one-on-one encounters where his sense of humor came to his aid. Gillian Richardson, who was on the staff of the institute’s computer center from 1959 to 1962, recalled eating lunch with Nash in the institute dining hall and Nash’s saying all sorts of dry, wry things about psychiatrists. One time he asked, “Do you know a good psychiatrist in Princeton?” — adding that his own psychiatrist “ ‘sat on a throne way above’ him, and he wondered if I knew one who didn’t share that peculiarity.”
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Nash showed up in French 105, the third-semester French course at the university, one day and asked Karl Uitti if he could audit it. He struck the French professor as “the typically dreamy and out-to-lunch mathematician.”
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Nash attended quite regularly and kept up with the work. He seemed less interested in picking up conversational “tourist French” than in acquiring “a sense of French structure,” Uitti recalled, adding, “He was quite pro-French. He liked the language and the people.”

Uitti and Nash became rather friendly and met outside class, and on a number of occasions with Alicia. At some point, Uitti asked Nash why he was learning French. Nash answered that he was writing a mathematical paper. “There was only one person in the world who would be able to understand it and that person was French. He wanted, therefore, to write the paper in French,” Uitti said. Uitti could not recall Nash’s intended audience; chances are it was either Leray, who was at the institute that year, or Grothendieck. After the paper was published, Nash gave it to another member of the Institute to read. The next time he saw the man, Nash asked him, “Did you detect the sexual overtones?”
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Uitti commented in 1997:

That was the time that de Gaulle was in power and strong pressure was being exerted on French scientists to deliver their papers in French. Nash always struck me as very well-bred, very courteous. I’m certain that there was in his mind a sense of respect for whomever he was writing the paper for. It was sweet of him and I liked him for it.
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Nash asked Jean-Pierre Cauvin to edit a draft of the paper.
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Cauvin, who was doing quite a bit of translation work at the time, recalled Nash’s telling him that “Paris was the center for this kind of mathematics.” Nash also turned to a French undergraduate, Hubert Goldschmidt, for help.
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Nash had not given up the idea of returning to France. He submitted the Cauchy paper to the
Bulletin de la Société Mathématique de France
on January 19. He was, Cauvin thought, more withdrawn and subdued than ever, and in retrospect it is clear that he was thinking a great deal about leaving Princeton. Very likely, he got in touch with Grothendieck at the Institut des Hautes Études Scientifiques. In April Oppenheimer wrote to Leon Motchane, director of the IHES, to ask Motchane to formally invite Nash to spend the first half of the academic year 1963 — 64 there.
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Oppenheimer also asked Leray, who was at the institute that year, to see if he could provide a grant from the Centre de la Recherches Nationale Scientifiques for the second half of the year.
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At the same time, he noted that Nash would have been welcome to continue at the Institute for a second year: “If [Nash] asked to stay here for the autumn, I think that my colleagues would probably accede; but that is not his choice.”

Nash did not suggest that Alicia go with him to France, and this time Alicia did not try to dissuade him. Nor did she offer to go. It was clear that, by some mutual and unspoken agreement, the marriage was over and they were going to go their separate ways.

That winter, Nash spent more and more time in the Fine Hall common room, usually showing up at teatime and staying until evening. “He wore baggy, rumpled
clothes,” Stefan Burr, then a graduate student, recalled. “He didn’t seem at all aggressive. In some ways his manner was not that different from a lot of mathematicians’.”
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For a while, Burr and Nash were playing endless games of Hex. The board in Fine had been drawn years before on heavy cardboard and was so worn that the lines had constantly to be redrawn with a ballpoint pen.

He was beginning to seem less well again. Borel recalled, “He was not quite right. He seemed to me very diminished. His mathematics was not at the same level. I found him odd, unpredictable, nonsensical. It was very painful. The secretaries were afraid of him. He was someone to avoid. You never knew what he would do or say.”
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One time the Borels had Alicia and Nash over for tea. “We served tea and cookies,” said Borel. “Nash went into the kitchen. I followed him. What do you want?’ I asked. Well, I’d like some salt and pepper.’ ”
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Gaby Borel added: “After he put salt and pepper in his tea, he complained that the tea tasted awful.”
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During the spring, his state of mind had become more angry and restless, and he was beginning again to harp on his old obsessions. He decided, rather suddenly, to travel to the West Coast, where he saw, among others, Al Vasquez, who had graduated from MIT and was now a graduate student at Berkeley, Lloyd Shapley, and Al Tucker’s former wife, Alice Beckenback, and her new husband. Vasquez recalled:

I just walked into the common room [at Berkeley] and he was there. He was as surprised to see me as I was to see him. He didn’t announce his visits in advance. I had no idea where he was staying. But he was around for more than just a day or two. He hadn’t been looking for me. I had the impression that he’d been in Europe, the East Coast, and that he was traveling around. He talked a lot. He quite explicitly talked about [insulin] shock therapy. He described shock therapy as extremely painful. He also said he was taken back from Europe on a ship and in chains. Slavery was a word he used a lot. He was very bitter about his experiences.

He was pretty disoriented. He wasn’t able to talk about anything else but his obsessions. I was put off. It was odd. I never did understand why he talked to me. He knew me. He wasn’t really trying to communicate. He wanted to talk elusively. [Yet] it wasn’t gibberish. It was even clever at times, full of puns and allusions.
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Shapley, to whom Nash had written a great many letters, also found Nash’s appearance in Santa Monica distressing. “He thought of me as a close friend. One had to put up with it. He would send me postcards in colored inks. It was very sad. They were scribbled with math and numerology, as if he were not expecting a reply. I was much on his mind. He had decayed in a very spectacular way,” Shapley recalled in 1994. “He was groping.”
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Shapley remembered Nash telling him, “I
have this problem. I think I can straighten it out if I can figure out which members of the Math Society did this to me.” He didn’t stay long, Shapley said, adding:

It was a bit frightening. We had two young children. What was clear was that there was no way to talk to him or even follow what he was saying. He’d switch from topic to topic. It’s very hard to be a good mathematician if you can’t hold a thought in your mind.’
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In June, Nash left for Europe. He was due to attend a conference in Paris in the last week in June and the World Mathematical Congress in Stockholm in^ early August. He went to London first, where he stayed at the Hotel Russell in Bloomsbury, which he described as “very grand.”
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He got himself a private postal box and was once again writing letters, some on toilet paper, in green ink, in French. He was also sending drawings, including one of a prostrate figure pierced with arrows. One, postmarked June 14, contained a scrap of paper with the following written on it in green ink: 2 + 5 + 20 + 8 + 12 + 15 + 18 + 15 + 13 = 78.

The conference at the College de France in Paris was a small and intimate affair, very much dominated by Leray, who was very excited at that time about nonlinear hyperbolic equations. Ed Nelson, who had become quite friendly with Nash over the academic year, recalled Leray’s saying that it was a scandal that there were no global existence theorems. “The feeling he conveyed,” Nelson said, “was that we had better get to work, or the world might come to an end at any moment.”
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Most of the speakers gave their talk’s in English. Lars Hormander, who was also there, recalled that “1962 was very different from earlier visits.”
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But Nash insisted on giving his lecture in what he called his “pidgin French.”
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He did not speak extemporaneously but read from his notes in his very soft voice and with his very strong American accent. Hormander recalled: “Nash’s paper was respectable mathematically. It was a surprise to all of us [that he could have produced it at all]. For us it was like seeing somebody rise from the grave.”
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His behavior, however, was decidedly odd, Hormander later said:

Malgrange, the official conference organizer, had a dinner for the participants. At the table, Nash exchanged his plate with the person next to him. Then he traded yet again until he was satisfied that his food wasn’t poisoned. Everybody was very aware of his bizarre behavior but nobody said a word.

Malgrange had bought a nice big jar of caviar which was being passed around. When the jar came to Nash, he tipped the entire thing upside down onto his plate. Everybody was very well-behaved and said nothing.
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