A Beautiful Mind (26 page)

His meeting with Scott did nothing to ease his anxiety. The board was already working through its list of twenty-two-year-olds. Now that the board knew that he was no longer a graduate student, he might very well be in the next call, which was scheduled for the twentieth of the month, less than two weeks away. Nash mentioned that he was doing classified research for the military, and described both his affiliation with RAND and the ONR project at Princeton. Scott did not rule out the possibility of granting an occupational deferment, but he expressed some skepticism that a young mathematician could be indispensable, except in uniform, in a national emergency. Nash felt slightly better about his meeting with Dickason, who had taught math and physics before the war and appeared to be impressed by Nash’s Princeton degree and associates. It was probably Dickason who tipped Nash off to the fact that merely filing an application for a II-A, an occupational deferment, would temporarily halt the wheels of the draft machinery and take him out of the pool of potential draftees at least until the board had time to consider his II-A application.

Nash wasted no time. In Bluefield, he went to the library and read the Selective Service law. He thought about the board’s psychology. He wrote to Tucker, to the Office of Naval Research in Washington, and no doubt also to Williams at RAND, though there is no record of such a letter.
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(A letter from the
Office of Naval Research in Washington, received by Al Tucker on September 15, begins, “John Nash has written me asking if ONR can help get him a draft deferment.”) Nash asked them to request a II-A deferment, but urged them to state only the bare facts, promising more information later — so that “heavier guns may be later rolled out without the appearance” of merely repeating the initial statements.
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He was intent on buying as much time as possible. Later on, in other circumstances, Nash would repeatedly express his dislike and resentment of “politics” and “politicking.” But, impractical, childish, and detached from everyday concerns as he was in some ways, he was quite capable of plotting strategy, ferreting out necessary facts, making use of his father’s connections, and most of all, marshaling allies and supporters.

Tucker, the university, the Navy, and RAND responded sympathetically and promptly, claiming in unison that he was irreplaceable, it would take years to train a substitute, and his work was “essential to the welfare and security of this nation.”
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Fred D. Rigby at the Office of Naval Research in Washington advised Tucker that the best route to take was for a university officer to ask the New York branch of the ONR to write to the Bluefield draft board. “This process is said to work well. Normally, it takes place after the man is put in 1-A, but there is no rule against its use in advance of that event.”
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Rigby also noted that “this kind of question is coming up frequently these days,” suggesting that Nash was hardly alone among young academics with Defense Department affiliations seeking to avoid the draft. Rigby also promised that, should the branch office action fail, “we will then make a second try directly with the national selective service organization,” adding, however, that in all likelihood “this will not be necessary.”
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The concerted effort to save Nash from the draft was not much different from similar efforts made for a great many other young scientists at the time. The Korean War did not inspire the same patriotic fervor as World War II.
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Many academics regarded defense research as a kind of alternative service and the notion of exempting especially accomplished and valuable individuals had antecedents even in World War II.
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Kuhn remembers trying but failing to join the Navy’s V-12 program, which would have allowed him to spend the war attending the same classes at Caltech that he would have attended as a civilian, only in uniform. He wound up in the infantry only because he failed the Navy’s tougher physical.
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Korea did not prompt the massive draft evasion of the Vietnam era, de facto a working-class war, but among a certain elite in Nash’s generation there was a sense of entitlement and a lack ’of embarrassment about obtaining special treatment.

The urgency of Nash’s efforts to avoid the draft suggests deeper fears than those related to career ambitions or personal convenience. His was a personality for which regimentation, loss of autonomy, and close contact with strangers were not merely unpleasant, but highly threatening. With some justification, Nash would later blame the onset of his illness partly on the stress of teaching, a far milder form of regimentation than military life. His fear of being drafted remained acute long after the Korean War ended and after he turned twenty-six (the age
cut-off for draft eligibility). It eventually reached delusional proportions and helped drive him to attempt to abandon his American citizenship and seek political asylum abroad.

Interestingly, Nash’s gut instinct has since been validated by schizophrenia researchers.
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None of the life events known to produce mental disorders such as depression or anxiety neurosis — combat, death of a loved one, divorce, loss of a job — have ever been convincingly implicated in the onset of schizophrenia. But several studies have since shown that basic military training during peacetime can precipitate schizophrenia in men with a hitherto unsuspected vulnerability to the illness.
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Although the study subjects were all carefully screened for mental illnesses, hospitalization rates for schizophrenia turned out to be abnormally high, especially for draftees.

Rigby’s prediction was soon borne out. A handwritten note dated September 15 from the files of Princeton’s dean of faculty, Douglas Brown, records a telephone call from Agnes Henry, the mathematics department secretary, who informed the dean’s secretary that John Nash had telephoned her asking the dean to write to the Office of Naval Research.
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A few days later Nash filled out a university form, “Information Needed in a National Emergency,” in which he stated that he was registered at Local Board 12 in Bluefield, that his current classification was I-A, and that he had a “chance for 2-A, application pending.”
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The form noted that Nash was engaged in project 727, Tucker’s ONR logistics grant. In response to the question “Are you engaged in any other research work or consultation of possible national interest?” Nash responded yes and listed “consultant for RAND corporation.” A note, added perhaps by the head of Princeton’s grants office, mentioned that Nash had spent “3 years or more on the theory of games and related fields. Wrote paper in this field when at Carnegie Tech as undergraduate. Two years to get Ph.D. at Princeton. Dr. Rigby has already told NY to support.”

The university immediately wrote to ONR stating that “this project is considered by the Logistics Branch of ONR, Washington as a very important contribution in the present national emergency. Dr. Nash is a key member of our staff in this project and is one of the very few individuals in the country who have been trained in this field.”
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The ONR followed, on September 28, with a letter to the draft board saying that Nash was “a key research assistant” and “this contract is an essential part of the Navy Department’s research and development program and is in the interest of national safety.”
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RAND protected Nash as well. RAND’s former manager of security, Richard Best, recalls writing letters for Nash and another mathematician from Princeton, Mel Peisakoff, to “save” them from the draft.
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(Peisakoff’s recollection differs from Best’s, however; he says he wanted to enlist but that his superiors at RAND wouldn’t let him.)
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“We had a lot of reservists and a great many young people,” said Best. “In 1948, the average age was 28.35 years. The personnel office wasn’t well [equipped to handle the situation]. I wrote some form letters to the draft board for Nash,” he recalled.
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Nash’s lobbying campaign worked, though he was not immediately granted the desired II-A. By October 6, the university informed Nash that “you seem to be safe until June 30.”
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Apparently, the board had simply postponed the designation for active service until June 30, 1951. The university advised Nash, “I would suggest that we defer any further action until next spring, at which time, we can again apply for a II-A classification and can consider an appeal if this should be rejected.”
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But, at least for now, he had prevented the military from wrecking his plans. More important, by protecting his personal freedom, Nash may have protected the integrity of his personality and won the ability to function well for longer than he might otherwise have.

15
A Beautiful Theorem
Princeton, 1950–51

S
TRANGE AS IT MAY NOW SEEM,
the dissertation that would one day win Nash a Nobel wasn’t highly regarded enough to assure him an offer from a top academic department. Game theory did not inspire much interest or respect among the mathematical elite, von Neumann’s prestige notwithstanding. Indeed, Nash’s mentors at Carnegie and Princeton were vaguely disappointed in him; they had expected the youngster who had re-proved theorems of Brouwer and Gauss to tackle a really deep problem in an abstract field like topology.
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Even his biggest fan, Tucker, had concluded that while Nash could “hold his own in pure mathematics,” it was not “his real strength.”
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Having successfully sidestepped the threat of the draft, Nash now began working on a paper that he hoped would win him recognition as a pure mathematician.
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The problem concerned geometric objects called manifolds, which were of great interest to mathematicians at that time. Manifolds were a new way of looking at the world, so much so that even defining them sometimes tripped up eminent mathematicians. At Princeton, Salomon Bochner, one of the leading analysts of his day and a fine lecturer, used to walk into his graduate classes, start to give a definition of a manifold, get hopelessly bogged down, and finally give up, saying with an exasperated air, before moving on, “Well, you all know what a manifold is.”
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In one dimension, a manifold may be a straight line, in two dimensions a plane, or the surface of a cube, a balloon, or a doughnut. The defining feature of a manifold is that, from the vantage point of any spot on such an object, the immediate vicinity looks like perfectly regular and normal Euclidean space. Think of yourself shrunk to the size of a pinpoint, sitting on the surface of a doughnut. Look around you, and it seems that you’re sitting on a flat disk. Go down one dimension and sit on a curve, and the stretch nearby looks like a straight line. Should you be perched on a three-dimensional manifold, however esoteric, your immediate neighborhood would look like the interior of a ball. In other words, how the object appears from afar may be quite different from the way it appears to your nearsighted eye.

By 1950, topologists were having a field day with manifolds, redefining every
object in sight topologically. The diversity and sheer number of manifolds is such that today, although all two-dimensional objects have been defined topologically, not all three- and four-dimensional objects — of which there is literally an infinite assortment — have been so precisely described. Manifolds turn up in a wide variety of physical problems, including some in cosmology, where they are often very hard to cope with. The notoriously difficult three-body problem proposed by King Oskar II of Sweden and Norway in 1885 for a mathematical competition in which Poincaré took part, which entails predicting the orbits of any three heavenly bodies — such as the sun, moon, and earth — is one in which manifolds figure largely.
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Nash became fascinated with the subject of manifolds at Carnegie.
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But it is likely that his ideas did not crystallize until after he came to Princeton and began having regular conversations with Steenrod. In his Nobel autobiography, Nash says that, right around the time that he got his equilibrium result for
n
-person games, that is, in the fall of 1949, he also made “a nice discovery relating to manifolds and real algebraic varieties.”
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This is the result that he had considered writing up as a dissertation after von Neumann’s cool reaction to his ideas about equilibrium for games with many players.

The discovery came long before Nash had worked out the laborious steps of the actual proof. Nash always worked backward in his head. He would mull over a problem and, at some point, have a flash of insight, an intuition, a vision of the solution he was seeking. These insights typically came early on, as was the case, for example, with the bargaining problem, sometimes years before he was able, through prolonged effort, to work out a series of logical steps that would lead one to his conclusion. Other great mathematicians — Riemann, Poincaré, Wiener — have also worked in this way.
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One mathematician, describing the way he thought Nash’s mind worked, said: “He was the kind of mathematician for whom the geometric, visual insight was the strongest part of his talent. He would see a mathematical situation as a picture in his mind. Whatever a mathematician does has to be justified by a rigorous proof. But that’s not how the solution presents itself to him. Instead, it’s a bunch of intuitive threads that have to be woven together. And some of the early ones present themselves visually.”
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