A Beautiful Mind

by Sylvia Nasar

  The editors of the Annals of Mathematics hardly knew what to make of Nash’s manuscript when it landed on their desks at the end of October 1954. It hardly had the look of a mathematics paper. It was as thick as a book, printed by hand rather than typed, and chaotic. It made use of concepts and terminology more familiar to engineers than to mathematicians. So they sent it to a mathematician at Brown University, Herbert Federer, an Austrian-born refugee from Nazism and a pioneer in surface area theory, who, although only thirty-four, already had a reputation for high standards, superb taste, and an unusual willingness to tackle difficult manuscripts.36

  Mathematics is often described, quite rightly, as the most solitary of endeavors. But when a serious mathematician announces that he has found the solution to an important problem, at least one other serious mathematician, and sometimes several, as a matter of longstanding tradition that goes back hundreds of years, will set aside his own work for weeks and months at a time, as one former collaborator of Federer’s put it, “to make a go of it and straighten everything out.”37 Nash’s manuscript presented Federer with a sensationally complicated puzzle and he attacked the task with relish.

  The collaboration between author and referee took months. A large correspondence, many telephone conversations, and numerous drafts ensued. Nash did not submit the revised version of the paper until nearly the end of the following summer. His acknowledgment to Federer was, by Nash’s standards, effusive: “I am profoundly indebted to H. Federer, to whom may be traced most of the improvement over the first chaotic formulation of this work.”38

  Armand Borel, who was a visiting professor at Chicago when Nash gave a lecture on his embedding theorem, remembers the audience’s shocked reaction. “Nobody believed his proof at first,” he recalled in 1995. “People were very skeptical. It looked like a [beguiling] idea. But when there’s no technique, you are skeptical. You dream about a vision. Usually you’re missing something. People did not challenge him publicly, but they talked privately.”39 (Characteristically, Nash’s report to his parents merely said “talks went well.”)40

  Gian-Carlo Rota, professor of mathematics and philosophy at MIT, confirmed Borel’s account. “One of the great experts on the subject told me that if one of his graduate students had proposed such an outlandish idea he’d throw him out of his office.”41

  The result was so unexpected, and Nash’s methods so novel, that even the experts had tremendous difficulty understanding what he had done. Nash used to leave drafts lying around the MIT common room.42 A former MIT graduate student recalls a long and confused discussion between Ambrose, Singer, and Masatake Kuranishi (a mathematician at Columbia University who later applied Nash’s result) in which each one tried to explain Nash’s result to the other, without much success.43

  Jack Schwartz recalled:

  Nash’s solution was not just novel, but very mysterious, a mysterious set of weird inequalities that all came together. In my explication of it I sort of looked at what happened and could generalize and give an abstract form and realize it was applicable to situations other than the specific one he treated. But I didn’t quite get to the bottom of it either.44

  Later, Heinz Hopf, professor of mathematics in Zurich and a past president of the International Mathematical Union, “a great man with a small build, friendly, radiating a warm glow, who knew everything about differential geometry,” gave a talk on Nash’s embedding theorem in New York.45 Usually Hopf’s lectures were models of crystalline clarity. Moser, who was in the audience, recalled: “So we thought, ‘NOW we’ll understand what Nash did.’ He was naturally skeptical. He would have been an important validator of Nash’s work. But as the lecture went on, my God, Hopf was befuddled himself. He couldn’t convey a complete picture. He was completely overwhelmed.”46

  Several years later, Jürgen Moser tried to get Nash to explain how he had overcome the difficulties that Levinson had originally pointed out. “I did not learn so much from him. When he talked, he was vague, hand waving, ‘You have to control this. You have to watch out for that.’ You couldn’t follow him. But his written paper was complete and correct.”47 Federer not only edited Nash’s paper to make it more accessible, but also was the first to convince the mathematical community that Nash’s theorem was indeed correct.

  Martin’s surprise proposal, in the early part of 1953, to offer Nash a permanent faculty position set off a storm of controversy among the eighteen-member mathematics faculty.48 Levinson and Wiener were among Nash’s strongest supporters. But others, like Warren Ambrose and George Whitehead, the distinguished topolo-gist, were opposed. Moore Instructorships weren’t meant to lead to tenure-track positions. More to the point, Nash had made plenty of enemies and few friends in his first year and a half. His disdainful manner toward his colleagues and his poor record as a teacher rubbed many the wrong way.

  Mostly, however, Nash’s opponents were of the opinion that he hadn’t proved he could produce. Whitehead recalled, “He talked big. Some of us were not sure he could live up to his claims.”49 Ambrose, not surprisingly, felt similarly. Even Nash’s champions could not have been completely certain. Flatto remembered one occasion on which Nash came to Levinson’s office to ask Levinson whether he’d read a draft of his embedding paper. Levinson said, “To tell you the truth I don’t have enough background in this area to pass judgment.”50

  When Nash finally succeeded, Ambrose did what a fine mathematician and sterling human being would do. His applause was as loud as or louder than anyone else’s. The bantering became friendlier and, among other things, Ambrose took to telling his musical friends that Nash’s whistling was the purest, most beautiful tone he had ever heard.51

  PART TWO

  Separate Lives

  21

  Singularity

  Nash was leading all these separate lives. Completely separate lives.

  — ARTHUR MATTUCK, 1997

  ALL THROUGH HIS CHILDHOOD, adolescence, and brilliant student career, Nash had seemed largely to live inside his own head, immune to the emotional forces that bind people together. His overriding interest was in patterns, not people, and his greatest need was making sense of the chaos within and without by employing, to the largest possible extent, the resources of his own powerful, fearless, fertile mind. His apparent lack of ordinary human needs was, if anything, a matter of pride and satisfaction to him, confirming his own uniqueness. He thought of himself as a rationalist, a free thinker, a sort of Spock of the starship Enterprise. But now, as he entered early adulthood, this unfettered persona was shown to be partly a fiction or at least partly superseded. In those first years at MIT, he discovered that he had some of the same wishes as others. The cerebral, playful, calculating, and episodic connections that had once sufficed no longer served. In five short years, between the ages of twenty-four and twenty-nine, Nash became emotionally involved with at least three other men. He acquired and then abandoned a secret mistress who bore his child. And he courted — or rather was courted by — a woman who became his wife.

  As these initial intimate connections multiplied and became ever-present elements in his consciousness, Nash’s formerly solitary but coherent existence became at once richer and more discontinuous, separate and parallel existences that reflected an emerging adult but a fragmented and contradictory self. The others on whom he now depended occupied different compartments of his life and often, for long periods, knew nothing of one another or of the nature of the others’ relation to Nash. Only Nash was in the know. His life resembled a play in which successive scenes are acted by only two characters. One character is in all of them while the second changes from scene to scene. The second character seems no longer to exist when he disappears from the boards.

  More than a decade later, when he was already ill, Nash himself provided a metaphor for his life during the MIT years, a metaphor that he couched in his first language, the language of mathematics: B squared -I- RTF = 0, a “very personal” equation Nash included in a 1968 postcard that beg
ins, “Dear Mattuck, Thinking that you will understand this concept better than most I wish to explain …” The equation represents a three-dimensional hyperspace, which has a singularity at the origin, in four-dimensional space. Nash is the singularity, the special point, and the other variables are people who affected him — in this instance, men with whom he had friendships or relationships.1

  Inevitably, the accretion of significant relationships with others brings with it demands for integration — the necessity of having to choose. Nash had little desire to choose one emotional connection over another. By not choosing, he could avoid, or at least minimize, both dependence and demands. To satisfy his own emotional needs for connectedness meant he inevitably made others look to him to satisfy theirs. Yet while he was preoccupied with the effect of others on him, he mostly ignored — indeed, seemed unable to grasp — his effect on others. He had in fact no more sense of “the Other” than does a very young child. He wished the others to be satisfied with his genius —“I thought I was such a great mathematician,” he was to say ruefully, looking back at this period — and, of course, to some extent they were satisfied. But when people inevitably wanted or needed more he found the strains unbearable.

  22

  A Special Friendship Santa Monica, Summer 1952

  Away from contact with a few special sorts of individuals I am lost, lost completely in the wilderness… so, so, so, it’s been a hard life in many ways.

  — JOHN FORBES NASH, JR., 1965

  AFTER JOHN NASH LOST EVERYTHING — family, career, the ability to think about mathematics — he confided in a letter to his sister Martha that only three individuals in his life had ever brought him any real happiness: three “special sorts of individuals” with whom he had formed “special friendships.”1

  Had Martha seen the Beatles’ film A Hard Days Night? “They seem very colorful and amusing,” he wrote. “Of course they are much younger like the sort of person I’ve mentioned… . I feel often as if I were similar to the girls that love the Beatles so wildly since they seem so attractive and amusing to me.”2

  Nash’s first loves were one-sided and unrequited. “Nash was always forming intense friendships with men that had a romantic quality,” Donald Newman observed in 1996. “He was very adolescent, always with the boys.”3 Some were inclined to see Nash’s infatuations’ as “experiments,” or simple expressions of his immaturity — a view that he may well have held himself. “He played around with it because he liked to play around. He was very experimental, very try-outish,” said Newman in 1996. “Mostly he just kissed.”4

  Newman, who liked to joke about his past and future female conquests,5 had firsthand knowledge because Nash was, for a time, infatuated with him — with predictable results. “He used to talk about how Donald looked all the time,” Mrs. Newman said in 1996.6 Newman recalled: “He tried fiddling around with me. I was driving my car when he came on to me.” D.J. and Nash were cruising around in Newman’s white Thunderbird when Nash kissed him on the mouth. DJ . just laughed it off.7

  Nash’s first experience of mutual attraction — “special friendships,” as he called them — occurred in Santa Monica.8 It was the very end of the summer of 1952, after Milnor had moved out and Martha had flown back home. The encounter must have been fleeting, coming in the last days of August, just before he was due to leave for Boston, and very furtive. But it was nonetheless decisive because for the first time he found not rejection but reciprocity. Thus it was the first real step out of his extreme emotional isolation and the world of relationships that were purely imaginary, a first taste of intimacy, not entirely happy, no doubt, but suggestive of hitherto unsuspected satisfactions.

  The only traces of Nash’s friendship with Ervin Thorson that remain are his description of him as a “special” friend in his 1965 letter and a series of elliptical references to “T” in letters in the late 1960s.9 Few if any of Nash’s acquaintances met him; Martha recalled a friend of Nash’s who once spent the night on the couch of their Georgina Avenue apartment, but not his name.10

  Thorson, who died in 1992, was thirty years old in 1952.11 He was a native Californian of Scandinavian extraction. Nash described him to Martha as an aerospace engineer, but he may in fact have been an applied mathematician. He had been a meteorologist in the Army Air Corps during the war. Afterward, he earned a master’s degree in mathematics at UCLA and went to Douglas Aircraft in 1951, just a few years after Douglas had spun off its R&D division to form the RAND Corporation.12 At that time, Douglas was mapping the future of interplanetary travel for the Pentagon, and Thorson, who eventually led a research team, was very likely involved in these efforts.13 His great passion, conceived twenty years before the United States launched Viking, was the dream of exploring Mars, his sister Nelda Troutman recalled in 1997.

  Thorson was, his sister said, “very high strung, not a social person at all, very bright, knew a lot, very very academic.”14 Nash could easily have met him — given the close ties between Douglas and RAND, which was also heavily involved in studies of space exploration — at a talk or seminar, or perhaps even at one of the parties that John Williams, the head of RAND’s mathematics department, gave.

  If Thorson, who never married, was a homosexual, his surviving sister did not know it.15 With his family, at any rate, he was unusually closemouthed, not just about his work, which was highly classified, but about all aspects of his personal life.16 Given the mounting pressure to root out homosexuals in the defense industry during the McCarthy era, Thorson would have had to practice great discretion in any case; his career at Douglas was to last for another fifteen years.17 When he abruptly resigned from Douglas in 1968, he apparently did so at the age of forty-seven because he feared dying. Several of his colleagues had recently died of heart attacks and Thorson, who had some sort of mild heart condition, decided he couldn’t cope with the stress and overwork anymore. He moved back to his hometown of Pomona and became a virtual recluse except for an active involvement in the Lutheran church, living with his parents for the next twenty-five years until his death.

  Whether Nash and Thorson saw each other again when Nash returned to Santa Monica for a third summer two years later or on one of his trips to Santa Monica during his illness in the early and mid-1960s is not known. But Nash continued to think of Thorson and to refer to him obliquely until at least 1968.

  23

  Eleanor

  These mathematicians are very exclusive. They occupy a very high terrain, from which they look down on everyone else. That makes their relationships with women quite problematic.

  — ZIPPORAH LEVINSON, 1995

  NASH WAS BACK in Boston in his old quarters by Labor Day. Number 407 Beacon Street was an imposing brick row house built before the turn of the century facing the Charles.1 Its current owner, Mrs. Austin Grant, was the widow of a Back Bay physician. She liked to point out her home’s opulent features to her lodgers, such as the carriage room where its original owners once waited for their horsedrawn carriages to be brought around. And she often bemoaned the neighborhood’s decline. “Don’t leave your bags on the street while you come in; they might not be there when you come out again,” she said to Nash the day he moved in.

  Nash occupied one of the front bedrooms, a large, comfortably furnished room with a fireplace. Lindsay Russell, a young engineer who had recently graduated from MIT, lived next door. Mrs. Grant regularly took Russell aside to remark on Nash’s idiosyncrasies. Nash acquired a huge set of barbells and began lifting weights. When Nash made the dining-room chandelier, which hung directly below his bedroom, vibrate with his exertions, Mrs. Grant would say, “What does he think this is? A gymnasium?” Nash’s mail also received comment, particularly the postcards from his mother expressing the hope, as Russell recalled, that “in addition to the pursuit of mathematics and other intellectual pursuits, he would make friends and engage in social activities.”

  With one single exception, however, Nash never had any visitors. Russell remembers once
waking up in the middle of the night. There was a sound coming from Nash’s room. It was a giggle. The giggle of a woman.

  The pretty, dark-haired nurse who admitted Nash to the hospital on the second Thursday in September was named Eleanor.2 He was due to have some varicose veins removed3 and seemed awfully nervous — and young, more like a student than a professor.4 Eleanor knew his doctor to be a notorious incompetent.5 And a drunk. She was curious how an MIT professor had wound up with a quack like that. Nash told her that he’d chosen the doctor at random by closing his eyes and running his fingers down the list’ of physicians in the lobby. She felt, she recalled, rather protective of him.

  Nash was on the ward for only a couple of days. Eleanor thought he was cute and sort of sweet, but when he left, she hardly expected to see him again. Somehow or other, they bumped into each other on the street not long afterward. It was a Saturday afternoon and Eleanor was on her way to meet a friend to buy herself a good winter coat. “I didn’t chase him. He chased me. He kept pestering me,” Eleanor recalled. “I wound up going shopping with him.”6

  They walked over to Jay’s Department Store together. Nash followed her up to the coat department, which was on the second floor. He kept staring at her, not saying much, waiting for her to choose a coat. She started to enjoy herself. “John was very attractive,” Eleanor recalled, laughing. “When I saw him, I thought he was something special.” She began pointing to the ones she wanted to try on, and with elaborate courtesy he held out each coat for her to slip into. She thought she liked a purple one best. Nash started clowning around. He pretended he was her tailor, flung himself on his knees before her, loudly made believe he was measuring her coat for alterations — and generally made a fool of himself. Embarrassed, Eleanor blushed, protested, and tried to hush him up. “Get up quick!” she whispered. Secretly, however, she was quite thrilled.