A Beautiful Mind (44 page)

When they were with other people, Nash talked to the mathematicians, Alicia to the wives or Emma. Yet her attention was always focused on Nash: what he was saying, how he looked, how others reacted to him. He too, seemed always aware of her, even when he appeared to be ignoring her. That he wasn’t especially nice to her, or generous, mattered less than that he was interesting and made things happen.

Their friends accepted Nash’s new status as a married man with more or less good grace. Some found Alicia “ambitious, strong-willed,” others quite the opposite. Rogers recalled in 1996 that “Alicia subordinated herself to John. She wasn’t there to compete with him. She was totally dedicated to his support.”
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Some of their acquaintances found their relationship oddly cool, but others came away with the impression that marriage suited Nash well and that Alicia was having a good effect on him. “Somehow, he was relating a little better,” Rogers recalled. Zipporah Levinson agreed: “John was awkward. Alicia made him behave.”
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Photographs of Alicia taken in those months show a radiant young woman. It was, as Alicia would say many years later, “a very nice time of my life.”
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Nash continued to work on the problem he had solved the previous year at Courant. There were some small gaps in the proof, and the paper Nash had begun to write, laying out a full account of what he had done, was in very rough shape.
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“It was,” a colleague said in 1996, “as if he were a composer and could hear the music, but he didn’t know how to write it down or exactly how to orchestrate it.”
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As it turned out, it would take most of the year, and a collective effort, before the final product — which some mathematicians regard as Nash’s most important work — was finally ready to be submitted to a journal.

To complete, it, Nash came as close as he ever had or would to an active collaboration with other mathematicians. “It was like building the atom bomb,” recalled Lennart Carleson, a young professor from the University of Uppsala who was visiting MIT that term. “This was the beginning of nonlinear theory. It was very difficult.”
¹²
Nash knocked on doors, asked questions, speculated out loud, fished for ideas, and at the end of the day, got a dozen or so mathematicians around Cambridge interested enough in his problem to drop their own research long enough to solve little pieces of his puzzle. “It was a kind of factory,” Carleson, who contributed a neat little theorem on entropy to Nash’s paper, said. “He wouldn’t
tell us what he was after, his grand design. It was amusing to watch how he got all these great egos to cooperate.”
¹³

Besides Moser and Carleson, Nash also turned to Eli Stein, now a professor of mathematics at Princeton University but then an MIT instructor. “He wasn’t interested in what I was doing,” recalled Stein. “He’d say, You’re an analyst. You ought to be interested in this.’ ”
¹⁴

Stein was intrigued by Nash’s enthusiasm and his constant supply of ideas. He said, “We were like Yankees fans getting together and talking about great games and great players. It was very emotional. Nash knew exactly what he wanted to do. With his great intuition, he saw that certain things ought to be true. He’d come into my office and say, This inequality must be true.’ His arguments were plausible but he didn’t have proofs for the individual lemmas — building blocks for the main proof.”
¹⁵
He challenged Stein to prove the lemmas.

“You don’t accept arguments based on plausibility,” said Stein in 1995. “If you build an edifice based on one plausible proposition after another, the whole thing is liable to collapse after a few steps. But somehow he knew it wouldn’t. And it didn’t.”
¹⁶

Nash’s thirtieth year was thus looking very bright. He had scored a major success. He was adulated and lionized as never before.
¹⁷
Fortune
magazine was about to feature him as one of the brightest young stars of mathematics in an upcoming series on the “New Math.”
¹⁸
And he had returned to Cambridge as a married man with a beautiful and adoring young wife. Yet his good fortune seemed at times only to highlight the gap between his ambitions and what he had achieved. If anything, he felt more frustrated and dissatisfied than ever. He had hoped for an appointment at Harvard or Princeton.
¹⁹
As it was, he was not yet a full professor at MIT, nor did he have tenure. He had expected that his latest result, along with the offer from Courant, would convince the department to award him both that winter.
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Getting these things after only five years would be unusual, but Nash felt that he deserved nothing less.
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But Martin had already made it clear to Nash that he was unwilling to put him up for promotion so soon. Nash’s candidacy was controversial, Martin had told him, just as his initial appointment had been.
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A number of people in the department felt he was a poor teacher and an even worse colleague. Martin felt Nash’s case would be stronger once the full version of the parabolic equations paper appeared in print. Nash, however, was furious.

Nash continued to brood over the De Giorgi fiasco. The real blow of discovering that De Giorgi had beaten him to the punch was to him not just having to share the credit for his monumental discovery, but his strong belief that the sudden appearance of a coinventor would rob him of the thing he most coveted: a Fields Medal.

Forty years later, after winning a Nobel, Nash referred in his autobiographical essay, in his typically elliptical fashion, to his dashed hopes:

It seems conceivable that if either De Giorgi or Nash had failed in the attack on this problem (or
a priori
estimates of Holder continuity) then that the lone climber reaching the peak would have been recognized with the mathematics’ Fields medal (which has traditionally been restricted to persons less than 40 years old).
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The next Fields Medal would be awarded in August 1958, and as everyone knew, the deliberations had long been under way.

To understand how deep the disappointment was, one must know that the Fields Medal is the Nobel Prize of mathematics, the ultimate distinction that a mathematician can be granted by his peers, the trophy of trophies.
²⁴
There is no Nobel in mathematics, and mathematical discoveries, no matter how vital to Nobel disciplines such as physics or economics, do not in themselves qualify for a Nobel. The Fields is, if anything, rarer than the Nobel. In the fifties and early sixties, it was awarded once every four years and usually to just two recipients at a time. Nobels, by contrast, are awarded annually, with as many as three winners sharing each prize. Tradition demands that recipients of the Fields be under forty years of age, a practice designed to honor the spirit of the prize charter, which stipulates that the purpose of the honor is “to encourage young mathematicians” and “future work.”
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The incentive, incidentally, is of an intangible variety, as the cash involved, in contrast to the Nobel, is negligible, a few hundred dollars. Yet since the Fields is an instant ticket in midcareer to endowed chairs at top universities, ample research funds, and star salaries, this seeming disadvantage is more apparent than real.

The prize is administered by the International Mathematical Union, the same organization that organizes the quadrennial world mathematical congresses, and the selection of Fields medalists is, as one recent president of the organization put it, “one of the most important tasks, one of the most taxing responsibilities.”
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Like the Nobel deliberations, the Fields selection process is shrouded in greatest secrecy.

The seven-member prize committee for the 1958 Fields awards was headed by Heinz Hopf, the dapper, genial, cigar-smoking geometer from Zurich who showed so much interest in Nash’s embedding theorem, and included another prominent German mathematician, Kurt Friedrichs, formerly of Göttingen, and then at Courant.
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The deliberations got under way in late 1955 and were concluded early in 1958. (The medalists were informed, in strictest secrecy, in May 1958 and actually awarded their medals at the Edinburgh congress the following August.)

All prize deliberations involve elements of accident, the biggest one being the composition of the committee. As one mathematician who took part in a subsequent committee said, “People aren’t universalists. They’re horse trading.”
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In 1958, there were a total of thirty-six nominees, as Hopf was to say in his award ceremony speech, but the hot contenders numbered no more than five or six.
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That year the deliberations were unusually contentious and the prizes, which ultimately went to René Thorn, a topologist, and Klaus F. Roth, a number theorist, were awarded on a four-three vote.’
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“There were lots of politics in that prize,” one person close to the deliberations said recently.
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Roth was a shoo-in; he had solved a fundamental problem in number theory that the most senior committee member, Carl Ludwig Siegel, had worked on early in his career. “It was a question of Thorn versus Nash,” said Moser, who heard reports of the deliberations from several of the participants.
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“Friedrichs fought very hard for Nash, but he didn’t succeed,” recalled Lax, who had been Friedrichs’s student and who heard Friedrichs’s account of the deliberations. “He was upset. As I look back, he should have insisted that a third prize be given.”
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Chances are that Nash did not make the final round. His work on partial differential equations, of which Friedrichs would have been aware, was not yet published or properly vetted. He was an outsider, which one person close to the deliberations thought “might have hurt him.” Moser said, “Nash was somebody who didn’t learn the stuff. He didn’t care. He wasn’t afraid of moving in and working on his own. That doesn’t get looked at so positively by other people.”
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Besides, there was no great urgency to recognize him at this juncture; he was just twenty-nine.

No one could know, of course, that 1958 would be Nash’s last chance. “By 1962, a Fields for Nash would have been out of the question,” Moser said recently. “It would never have happened. I’m sure nobody even thought about him anymore.”
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A measure of how badly Nash wanted to win the distinction conferred by such a prize is the extraordinary lengths to which he went to ensure that his paper would be eligible for the Bôcher Prize, the only award remotely comparable in terms of prestige to the Fields. The Bôcher is given by the American Mathematical Society only once every five years.
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It was due to be awarded in February 1959, which meant that the deliberations would take place in the latter part of 1958.

Nash submitted his manuscript to
Acta Mathematica,
the Swedish mathematics journal, in the spring of 1958.
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It was a natural choice, since Carleson was the editor and was convinced of the paper’s great importance. Nash let Carleson know he wanted the paper published as quickly as possible and urged Carleson to give it to a referee who could vet the paper in a minimum of time. Carleson gave the manuscript to Hörmander to referee. Hörmander spent two months studying it, verified all the theorems, and urged Carleson to get it into print as quickly as possible. But as soon as Carleson informed Nash of the formal acceptance, which was, in any case, largely a foregone conclusion, Nash withdrew his paper.

When the paper subsequently appeared in the fall issue of the
American Journal of Mathematics,
Hörmander concluded that Nash had always intended to publish the paper there, since the Bôcher restricted eligible papers to those published in American journals — or, worse, had submitted the paper to both journals,
a clear-cut breach of professional ethics. “It turned out that Nash had just wanted to get a letter of acceptance from
Acta
to be able to get fast publication in the
American Journal of Mathematics.”
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Hörmander was angry at what he felt was “very improper and most unusual.”
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It’s possible, though, that Nash had simply submitted the paper to
Acta
before learning that doing so would exclude it from consideration for the Bôcher, but that upon discovering this fact, he was willing to antagonize Carleson and Hörmander in order to preserve his eligibility. He may therefore not have used
Acta
quite so unscrupulously. Withdrawing the paper after it had been promised to
Acta,
and after it had been refereed, would have been unprofessional, but not as clear a violation of ethics as Hörmander’s scenario suggests. However, it still showed how very much winning a prize meant to Nash.

32
Secrets
Summer 1958

It struck me that I knew everything: everything was revealed to me, all the secrets of the world were mine during those spacious hours.

— G
ERARD DE
N
ERVAL

N
ASH TURNED THIRTY
that June. For most people, thirty is simply the dividing line between youth and adulthood, but mathematicians consider their calling a young man’s game, so thirty signals something far more gloomy. Looking back at this time in his life, Nash would refer to a sudden onset of anxiety, “a fear” that the best years of his creative life were over.
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