A Beautiful Mind Part 5

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 Was.h.i.+ngton, and no doubt also to Williams at RAND, though there is no record of such a letter.6 (A letter from the (A letter from the Office of Naval Research in Was.h.i.+ngton, 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. Office of Naval Research in Was.h.i.+ngton, 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.7 He was intent on buying as much time as possible. Later on, in other circ.u.mstances, 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. He was intent on buying as much time as possible. Later on, in other circ.u.mstances, 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 subst.i.tute, and his work was "essential to the welfare and security of this nation."8 Fred D. Rigby at the Office of Naval Research in Was.h.i.+ngton 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." Fred D. Rigby at the Office of Naval Research in Was.h.i.+ngton 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."9 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." 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."10 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.11 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. 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.12 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 cla.s.ses 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. 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 cla.s.ses 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.13 Korea did not prompt the ma.s.sive draft evasion of the Vietnam era, de facto a working-cla.s.s war, but among a certain elite in Nash's generation there was a sense of ent.i.tlement and a lack 'of embarra.s.sment about obtaining special treatment. Korea did not prompt the ma.s.sive draft evasion of the Vietnam era, de facto a working-cla.s.s war, but among a certain elite in Nash's generation there was a sense of ent.i.tlement and a lack 'of embarra.s.sment 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 citizens.h.i.+p and seek political asylum abroad. cut-off for draft eligibility). It eventually reached delusional proportions and helped drive him to attempt to abandon his American citizens.h.i.+p and seek political asylum abroad.

Interestingly, Nash's gut instinct has since been validated by schizophrenia researchers.14 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. 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.15 Although the study subjects were all carefully screened for mental illnesses, hospitalization rates for schizophrenia turned out to be abnormally high, especially for draftees. 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.16 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 cla.s.sification was I-A, and that he had a "chance for 2-A, application pending." 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 cla.s.sification was I-A, and that he had a "chance for 2-A, application pending."17 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 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, Was.h.i.+ngton 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."18 The ONR followed, on September 28, with a letter to the draft board saying that Nash was "a key research a.s.sistant" and "this contract is an essential part of the Navy Department's research and development program and is in the interest of national safety." The ONR followed, on September 28, with a letter to the draft board saying that Nash was "a key research a.s.sistant" and "this contract is an essential part of the Navy Department's research and development program and is in the interest of national safety."19 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.20 (Peisakoff's recollection differs from Best's, however; he says he wanted to enlist but that his superiors at RAND wouldn't let him.) (Peisakoff's recollection differs from Best's, however; he says he wanted to enlist but that his superiors at RAND wouldn't let him.)21 "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. "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.22 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."23 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 cla.s.sification and can consider an appeal if this should be rejected." 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 cla.s.sification and can consider an appeal if this should be rejected."24 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. 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.

CHAPTER 15

A Beautiful Theorem Princeton, 195051 Princeton, 195051

STRANGE AS IT MAY NOW SEEM, the dissertation that would one day win Nash a n.o.bel wasn't highly regarded enough to a.s.sure 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. the dissertation that would one day win Nash a n.o.bel wasn't highly regarded enough to a.s.sure 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.1 Even his biggest fan, Tucker, had concluded that while Nash could "hold his own in pure mathematics," it was not "his real strength." Even his biggest fan, Tucker, had concluded that while Nash could "hold his own in pure mathematics," it was not "his real strength."2 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.3 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 a.n.a.lysts of his day and a fine lecturer, used to walk into his graduate cla.s.ses, 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." 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 a.n.a.lysts of his day and a fine lecturer, used to walk into his graduate cla.s.ses, 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."4 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 s.p.a.ce. 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 a.s.sortment - 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 compet.i.tion in which Poincare 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. 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 a.s.sortment - 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 compet.i.tion in which Poincare 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.5 Nash became fascinated with the subject of manifolds at Carnegie.6 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 n.o.bel autobiography, Nash says that, right around the time that he got his equilibrium result for 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 n.o.bel autobiography, Nash says that, right around the time that he got his equilibrium result for n n-person games, that is, in the fall of 1949, he also made "a nice discovery relating to manifolds and real algebraic varieties."7 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. 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, Poincare, Wiener - have also worked in this way.8 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." 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."9 With Steenrod's encouragement,10 Nash gave a short talk on his theorem at the International Congress of Mathematicians in Cambridge in September 1950. Nash gave a short talk on his theorem at the International Congress of Mathematicians in Cambridge in September 1950.11 Judging from the published abstract, however, Nash was still missing essential elements of his proof. Nash planned to complete it at Princeton. Unfortunately for Nash, Steenrod was on leave in France. Judging from the published abstract, however, Nash was still missing essential elements of his proof. Nash planned to complete it at Princeton. Unfortunately for Nash, Steenrod was on leave in France.12 Lefschetz, who undoubtedly was pressing Nash to have the paper ready before the annual job market got under way in February, urged Nash to go to Donald Spencer, the visiting professor who had been on Nash's generals committee and had just been hired away from Stanford, and to use Spencer as a sounding board for completing the paper. Lefschetz, who undoubtedly was pressing Nash to have the paper ready before the annual job market got under way in February, urged Nash to go to Donald Spencer, the visiting professor who had been on Nash's generals committee and had just been hired away from Stanford, and to use Spencer as a sounding board for completing the paper.13 As a visiting professor, Spencer occupied a tiny office squeezed between Artin's huge corner office and an equally grand study belonging to William Feller. Spencer, as Lefschetz wrote to the dean of faculty, was "probably the most attractive mathematician in America at that moment," as well as "one of the most versatile American born mathematicians." as Lefschetz wrote to the dean of faculty, was "probably the most attractive mathematician in America at that moment," as well as "one of the most versatile American born mathematicians."14 A doctor's son, Spencer grew up in Colorado and was admitted to Harvard, where he intended to study medicine. Instead, he wound up at MIT studying theoretical aerodynamics and then at Cambridge, England, where he became a student of J. E. Littlewood, Hardy's great coauthor. A doctor's son, Spencer grew up in Colorado and was admitted to Harvard, where he intended to study medicine. Instead, he wound up at MIT studying theoretical aerodynamics and then at Cambridge, England, where he became a student of J. E. Littlewood, Hardy's great coauthor.15 Spencer did brilliant work in complex a.n.a.lysis, a branch of pure mathematics that has widespread engineering applications. Spencer did brilliant work in complex a.n.a.lysis, a branch of pure mathematics that has widespread engineering applications.16 He was a much sought-after collaborator, his most celebrated collaboration being with the j.a.panese mathematician Kunihiko Kodaira, a Fields medalist. He was a much sought-after collaborator, his most celebrated collaboration being with the j.a.panese mathematician Kunihiko Kodaira, a Fields medalist.17 Spencer himself won the Bocher Prize. Spencer himself won the Bocher Prize.18 Although he primarily worked in highly theoretical fields, he nonetheless had some applied interests, namely hydrodynamics. Although he primarily worked in highly theoretical fields, he nonetheless had some applied interests, namely hydrodynamics.19 A lively, voluble man, Spencer was "sometimes daunting in his reckless energy."20 His appet.i.te for difficult problems was boundless, his powers of concentration impressive. He could drink enormous quant.i.ties of alcohol - five martinis out of "bird bath" gla.s.ses - and still talk circles around other mathematicians. His appet.i.te for difficult problems was boundless, his powers of concentration impressive. He could drink enormous quant.i.ties of alcohol - five martinis out of "bird bath" gla.s.ses - and still talk circles around other mathematicians.21 A man whose natural exuberance hid a darker tendency toward depression and introspection, Spencer's appet.i.te for abstraction was accompanied by an extraordinary empathy for colleagues who were in trouble. A man whose natural exuberance hid a darker tendency toward depression and introspection, Spencer's appet.i.te for abstraction was accompanied by an extraordinary empathy for colleagues who were in trouble.22 He did not, however, suffer fools gladly. The first draft of Nash's paper gave Spencer little confidence that the younger mathematician was up to the task he'd set for himself. "I didn't know what he was going to do, really. But I didn't think he was going to get anywhere."23 But for months, Nash showed up at Spencer's door once or twice a week. Each time he would lecture Spencer on his problem for an hour or two. Nash would stand at the blackboard, writing down equations and expounding his points. Spencer would sit and listen and then shoot holes in Nash's arguments. But for months, Nash showed up at Spencer's door once or twice a week. Each time he would lecture Spencer on his problem for an hour or two. Nash would stand at the blackboard, writing down equations and expounding his points. Spencer would sit and listen and then shoot holes in Nash's arguments.

Spencer's initial skepticism slowly gave way to respect. He was impressed by the calm, professional way that Nash responded to his most outrageous challenges and his fussiest objections. "He wasn't defensive. He was absorbed in his work. He responded thoughtfully." He also liked Nash for not being a whiner. Nash never talked about himself, Spencer recalled. "Unlike other students who felt underappreciated," he said, "Nash never complained." The more he listened to Nash, moreover, the more Spencer appreciated the sheer originality of the problem. "It was not not a problem that somebody gave Nash. People didn't a problem that somebody gave Nash. People didn't give give Nash problems. He was highly original. n.o.body else could have thought of this problem." Nash problems. He was highly original. n.o.body else could have thought of this problem."

Many breakthroughs in mathematics come from seeing unsuspected relations.h.i.+ps between objects that seem intractable and ones that mathematicians have already got their arms around.

Nash had in mind a very broad category of manifolds, all manifolds that are compact (meaning that they are bounded and do not run off into infinity the way a plane does, but are self-enclosed like a sphere) and smooth (meaning that they have no sharp bends or corners, as there are, for example, on the surface of a cube). His "nice discovery," essentially, was that these objects were more manageable than they appeared at first glance because they were in fact closely related to a simpler cla.s.s of objects called real algebraic varieties, something previously unsuspected. have no sharp bends or corners, as there are, for example, on the surface of a cube). His "nice discovery," essentially, was that these objects were more manageable than they appeared at first glance because they were in fact closely related to a simpler cla.s.s of objects called real algebraic varieties, something previously unsuspected.

Algebraic varieties are, like manifolds, also geometric objects, but they are objects defined by a locus of points described by one or more algebraic equations. Thus x x2 + Y + Y2 = 1 represents a circle in the plane, while = 1 represents a circle in the plane, while xy xy = 1 represents a hyperbola. Nash's theorem states the following: Given any smooth compact = 1 represents a hyperbola. Nash's theorem states the following: Given any smooth compact K K-dimensional manifold M, M, there exists a real algebraic variety there exists a real algebraic variety V V in R in R2k + 1 and a connected component and a connected component W W of of V V so that so that W W is a smooth manifold diffeomorphic to M. is a smooth manifold diffeomorphic to M.24 In plain English, Nash is a.s.serting that for any manifold it is possible to find an algebraic variety one of whose parts corresponds in some essential way to the original object. To do this, he goes on to say, one has to go to higher dimensions. In plain English, Nash is a.s.serting that for any manifold it is possible to find an algebraic variety one of whose parts corresponds in some essential way to the original object. To do this, he goes on to say, one has to go to higher dimensions.

Nash's result was a big surprise, as the mathematicians who nominated Nash for members.h.i.+p in the National Academy of Sciences in 1996 were to write: "It had been a.s.sumed that smooth manifolds were much more general objects than varieties."25 Today, Nash's result still impresses mathematicians as "beautiful" and "striking" - quite apart from any applicability. "Just to conceive of the theorem was remarkable," said Michael Artin, professor of mathematics at MIT. Today, Nash's result still impresses mathematicians as "beautiful" and "striking" - quite apart from any applicability. "Just to conceive of the theorem was remarkable," said Michael Artin, professor of mathematics at MIT.26 Artin and Barry Mazur, a mathematician at Harvard, used Nash's result in a 1965 paper to estimate periodic points of a dynamical system. Artin and Barry Mazur, a mathematician at Harvard, used Nash's result in a 1965 paper to estimate periodic points of a dynamical system.27 Just as biologists want to find many species distinguished by only minor differences to trace evolutionary patterns, mathematicians seek to fill in the gaps in the continuum between bare topological s.p.a.ces at one end and very elaborate structures like algebraic varieties at the other. Finding a missing link in this great chain - as Nash did with this result - opened up new avenues for solving problems. "If you wanted to solve a problem in topology, as Mike and I did," said Mazur recently, "you could climb one rung of the ladder and use techniques from algebraic geometry."28 What impressed Steenrod and Spencer, and later on, mathematicians of Artin and Mazur's generation, was Nash's audacity. First, the notion that every manifold could be described by a polynomial equation is a larger-than-life thought, if only because the immense number and sheer variety of manifolds would seem to make it inherently unlikely that all could be described in so relatively simple a fas.h.i.+on. Second, believing that one could prove such a thing also involves daring, even hubris. The result Nash was aiming for would have seemed "too strong" and therefore improbable and unprovable. Other mathematicians before Nash had spotted relations.h.i.+ps between some manifolds and some algebraic varieties, but had treated these correspondences very narrowly, as highly special and unusual cases.29 By early winter, Spencer and Nash were satisfied that the result was solid and that the various parts of the lengthy proof were correct. Although Nash did not get around to submitting a final draft of his paper to the Annals of Mathematics Annals of Mathematics until October 1951, until October 1951,30 Steenrod, in any case, vouched for the results that February, Steenrod, in any case, vouched for the results that February, referring to "a piece of research which he has nearly completed, and with which I am well acquainted since he used me as a sounding board." referring to "a piece of research which he has nearly completed, and with which I am well acquainted since he used me as a sounding board."31 Spencer thought game theory was so boring that he never bothered to ask Nash in the course of that whole year what it was that he had proved in his thesis. Spencer thought game theory was so boring that he never bothered to ask Nash in the course of that whole year what it was that he had proved in his thesis.32 Nash's paper on algebraic manifolds - the only one he was ever truly satisfied with, though it was not his deepest work33 - established Nash as a pure mathematician of the first rank. It did not, however, save him from a blow that fell that winter. - established Nash as a pure mathematician of the first rank. It did not, however, save him from a blow that fell that winter.

Nash hoped for an offer from the Princeton mathematics department. Although the department's stated policy was not to hire its own students, it did not, as a matter of practice, pa.s.s up ones of exceptional promise. Lefschetz and Tucker very likely dropped hints that an offer was a real possibility. Although most of the faculty other than Tucker neither understood nor displayed any interest in his thesis topic, they were aware that it had been greeted with respect by economists.34 In January, Tucker and Lefschetz made a formal proposal that Nash be offered an a.s.sistant professors.h.i.+p.35 Bochner and Steenrod were strongly in favor, although Steenrod, of course, was not present at the discussion. The proposal, however, was doomed to failure. No appointment could be made without unanimous support in a department as small as Princeton's, and at least three members of the faculty, including Emil Artin, voiced strong opposition. Artin simply did not feel that he could live with Nash, whom he regarded as aggressive, abrasive, and arrogant, in such a small department. Bochner and Steenrod were strongly in favor, although Steenrod, of course, was not present at the discussion. The proposal, however, was doomed to failure. No appointment could be made without unanimous support in a department as small as Princeton's, and at least three members of the faculty, including Emil Artin, voiced strong opposition. Artin simply did not feel that he could live with Nash, whom he regarded as aggressive, abrasive, and arrogant, in such a small department.36 Artin, who supervised the honors calculus program in which Nash taught for a term, also complained that Nash couldn't teach or get along with students. Artin, who supervised the honors calculus program in which Nash taught for a term, also complained that Nash couldn't teach or get along with students.37 So the appointment wasn't offered. It was a bitter moment. The thought must have occurred to Nash that he was being rejected less on the basis of his work than on the basis of his personality. It was an even greater blow because the same faculty made it clear that it hoped that John Milnor, only a junior by this time, would one day become part of the Princeton faculty.38 The job market, while not as bad as in the Depression, was nonetheless rather bleak, the Korean War having cut into university enrollments. Having been turned down by Princeton, Nash knew he would be lucky to get a temporary instructors.h.i.+p in a respectable department.

Both MIT and Chicago, it turns out, were interested in hiring Nash as an instructor.39 Bochner had the ear of William Ted Martin, the new chairman of the MIT mathematics department, and strongly urged Martin to offer Nash an instructors.h.i.+p. Bochner had the ear of William Ted Martin, the new chairman of the MIT mathematics department, and strongly urged Martin to offer Nash an instructors.h.i.+p.40 Bochner urged Martin to ignore the gossip about Nash's supposedly difficult personality. Tucker, meanwhile, was pus.h.i.+ng Chicago to do the same. Bochner urged Martin to ignore the gossip about Nash's supposedly difficult personality. Tucker, meanwhile, was pus.h.i.+ng Chicago to do the same.41 When MIT offered Nash a C. L. E. Moore instructors.h.i.+p, Nash, who liked the idea of living in Cambridge, accepted. When MIT offered Nash a C. L. E. Moore instructors.h.i.+p, Nash, who liked the idea of living in Cambridge, accepted.42

CHAPTER 16

MIT

BY THE END OF J JUNE, Nash was in Boston living in a cheap room on the Boston side of the Charles.1 Every morning he walked across the Harvard Bridge, over the yellow-gray river to east Cambridge where MIT s modern, aggressively utilitarian campus lay sprawled between the river and a swath of factories and warehouses. Even before he reached the far side, he could smell the factory smells, including the distinct odors of chocolate and soap mingling together from a Necco candy factory and a P&G detergent plant. Every morning he walked across the Harvard Bridge, over the yellow-gray river to east Cambridge where MIT s modern, aggressively utilitarian campus lay sprawled between the river and a swath of factories and warehouses. Even before he reached the far side, he could smell the factory smells, including the distinct odors of chocolate and soap mingling together from a Necco candy factory and a P&G detergent plant.2 As he turned right onto Memorial Drive, he could see Building Two looming ahead, a featureless block of cement painted an "alarming brown," just to the right of the new library, then under construction. As he turned right onto Memorial Drive, he could see Building Two looming ahead, a featureless block of cement painted an "alarming brown," just to the right of the new library, then under construction.3 His office was on the third floor next to the stairwell in a corner suite a.s.signed to several instructors, a spare, narrow room with a high ceiling, overlooking the river and the low Boston skyline beyond. His office was on the third floor next to the stairwell in a corner suite a.s.signed to several instructors, a spare, narrow room with a high ceiling, overlooking the river and the low Boston skyline beyond.4 In 1951, before Sputnik Sputnik and Vietnam, MIT was not exactly an intellectual backwater, but it was nothing like what it is today. The Lincoln Laboratory was famous for its wartime research, but its future academic superstars were still relatively unknown youngsters, and powerhouse departments for which it has since become known - economics, linguistics, computer science, mathematics - were either infants or gleams in some academic's eye. It was, in spirit and in fact, still very much the nation's leading engineering school, not a great research university. and Vietnam, MIT was not exactly an intellectual backwater, but it was nothing like what it is today. The Lincoln Laboratory was famous for its wartime research, but its future academic superstars were still relatively unknown youngsters, and powerhouse departments for which it has since become known - economics, linguistics, computer science, mathematics - were either infants or gleams in some academic's eye. It was, in spirit and in fact, still very much the nation's leading engineering school, not a great research university.5 An environment more ant.i.thetical to the hothouse atmosphere of Princeton is hard to imagine. MIT's large scale and modern contours made it feel like the behemoth state universities of the Midwest. The military, as well as industry, loomed awfully large, so large that MIT's armed, plainclothes campus security force existed solely for the purpose of guarding the half-dozen "cla.s.sified" sites scattered around the campus and preventing those without proper security clearances and identification from wandering in. ROTC and courses in military science were required of all MIT's two-thousand-plus undergraduate men.6 The academic departments like mathematics and economics existed pretty much to cater to the engineering student - in Paul Samuelson's words, "a pretty crude animal." The academic departments like mathematics and economics existed pretty much to cater to the engineering student - in Paul Samuelson's words, "a pretty crude animal."7 All counted as "service departments," gas stations where engineers pulled up to get their tanks filled with obligatory doses of fairly elementary mathematics, physics, and chemistry. All counted as "service departments," gas stations where engineers pulled up to get their tanks filled with obligatory doses of fairly elementary mathematics, physics, and chemistry.8 Economics, for example, had no graduate program at all until the war. Economics, for example, had no graduate program at all until the war.9 Physics had no n.o.bel Laureates on its faculty at the time. Physics had no n.o.bel Laureates on its faculty at the time.10 Teaching loads were heavy - sixteen hours a week was not uncommon for senior faculty - and Teaching loads were heavy - sixteen hours a week was not uncommon for senior faculty - and were weighted toward large introductory courses like calculus, statistics, and linear algebra. were weighted toward large introductory courses like calculus, statistics, and linear algebra.11 Its faculty were younger, less well known, and less credentialed than Harvard's, Yale's, or Princeton's. Its faculty were younger, less well known, and less credentialed than Harvard's, Yale's, or Princeton's.

"There were advantages," said Samuelson. "A lot of the MIT faculty didn't have Ph.D.'s. I came without a formal degree. S.olow came before he had a formal degree. We were treated magnificently. It was more of a meritocracy." He added, "People would say, doesn't everybody do that? Not up the river, we'd answer. How do you explain that? We're Avis, we try harder."12 Socially, MIT was dominated by an old guard not of high-society intellectuals, but of middle-cla.s.s Republicans and engineers. "It certainly was not a faculty club populated by cultivated Brahmins," said Samuelson, who was then twenty-five years old: "When I came [in 1940] it was 85 percent engineering, 15 percent science."13 MIT also had a less exclusionary tradition than Harvard or even Princeton. By the 1950s, perhaps 40 percent of the mathematics faculty and students at MIT were Jewish.14 Bright youngsters from New York City public schools, effectively barred even then from attending Princeton as undergraduates, went there. Princeton was "out of the question for a Jew," recalls Joseph Kohn, who enrolled as a freshman at MIT in 1950. "At Brooklyn Tech the greatest thing in the world was sending a student to MIT." Bright youngsters from New York City public schools, effectively barred even then from attending Princeton as undergraduates, went there. Princeton was "out of the question for a Jew," recalls Joseph Kohn, who enrolled as a freshman at MIT in 1950. "At Brooklyn Tech the greatest thing in the world was sending a student to MIT."15 Still smarting from his rejection by Princeton, Nash arrived at Building Two with something of a chip on his shoulder, a feeling that he was a swan among ducks. MIT was already changing, however. Indeed, bringing a brilliant young researcher like Nash on board in the mathematics department was itself a sign of that s.h.i.+ft.

There was money all of a sudden, not just for teaching the exploding numbers of students, but for research.16 The amounts were small by post- The amounts were small by post-Sputnik standards or even those of today, but huge by prewar standards. Support for science, initially fueled by the successes during World War II, was now growing because of the Cold War. It came not just from the Army, Navy, and Air Force but from the Atomic Energy Commission and the Central Intelligence Agency. MIT wasn't unique. Other inst.i.tutions, from the big state universities in the upper Midwest to Stanford, grew up the same way. There was also the talent. Physics got many of the Los Alamos people. Electrical engineering was becoming a magnet for the first generation of computer scientists, an eclectic group of neurobiologists, applied mathematicians, and a.s.sorted visionaries like Jerome Lettvin and Walter Pitts, who saw the computer as a model for studying the architecture and functioning of the human brain. standards or even those of today, but huge by prewar standards. Support for science, initially fueled by the successes during World War II, was now growing because of the Cold War. It came not just from the Army, Navy, and Air Force but from the Atomic Energy Commission and the Central Intelligence Agency. MIT wasn't unique. Other inst.i.tutions, from the big state universities in the upper Midwest to Stanford, grew up the same way. There was also the talent. Physics got many of the Los Alamos people. Electrical engineering was becoming a magnet for the first generation of computer scientists, an eclectic group of neurobiologists, applied mathematicians, and a.s.sorted visionaries like Jerome Lettvin and Walter Pitts, who saw the computer as a model for studying the architecture and functioning of the human brain.17 "It was very much a growing environment and science was a growing sphere," said Samuelson, adding that after the war, the 85 percent-15 percent split between engineering and science had s.h.i.+fted to 50 percent-50 percent. He added: "It was the upswing in money ... that made this possible. That was part of the whole postwar pattern." "It was very much a growing environment and science was a growing sphere," said Samuelson, adding that after the war, the 85 percent-15 percent split between engineering and science had s.h.i.+fted to 50 percent-50 percent. He added: "It was the upswing in money ... that made this possible. That was part of the whole postwar pattern."18 Mathematics was on the verge of becoming an important department, although that was not obvious to everyone at the time. The department had one famous name, Norbert Wiener (who wound up at MIT largely thanks to Harvard's anti-Semitism), and two or three first-rate younger men, including the topologist George Whitehead and the a.n.a.lyst Norman Levinson. But otherwise, mathematics consisted largely of competent teachers rather than great researchers - "a few giants but a lot of mediocrities." anti-Semitism), and two or three first-rate younger men, including the topologist George Whitehead and the a.n.a.lyst Norman Levinson. But otherwise, mathematics consisted largely of competent teachers rather than great researchers - "a few giants but a lot of mediocrities."19 The man who changed all that was appointed chairman of the department in 1947. William Ted Martin, called Ted by everyone who knew him, was the tall, skinny, loquacious son of an Arkansas country doctor. Blond and blue-eyed with a sunny disposition and a ready grin, Martin was married to the granddaughter of a president of Smith College and revved up with ambition. A man whose innate decency would turn him into one of Nash's protectors after Nash became ill, Martin would soon endure his own trial by fire. At the height of the McCarthy witch hunt, Martin's secret past as an underground member of the Communist Party in the late 1930s and early 1940s would be exposed, threatening both his career and his vision for the department.20 But in 1951 the past was still safely buried. A "sparkplug of a chairman," his real talent was for making things happen, wheedling money out of the MIT administration, the Navy, and the Air Force, and using it to great, indeed astounding, effect. But in 1951 the past was still safely buried. A "sparkplug of a chairman," his real talent was for making things happen, wheedling money out of the MIT administration, the Navy, and the Air Force, and using it to great, indeed astounding, effect.21 One of Martin's strokes of genius was figuring out that the cheapest and quickest way to upgrade the department was not to reel in a few more big names, but to lure young hotshots there for a year or two and handle them, as much as possible, with kid gloves. Copying Harvard's Benjamin Pierce Fellows, Martin created C. L. E. Moore Instructors.h.i.+ps, so called in honor of MIT's most distinguished mathematician in the 1920s.22 Moore Instructors weren't expected to join the permanent faculty. The idea was to get a stream of talent that would act as a catalyst, firing up MIT's humdrum atmosphere and attracting better students, the best of whom now automatically went to the Ivies and Chicago. Moore Instructors weren't expected to join the permanent faculty. The idea was to get a stream of talent that would act as a catalyst, firing up MIT's humdrum atmosphere and attracting better students, the best of whom now automatically went to the Ivies and Chicago.

Since he wouldn't have to live with them for long, or so he thought, Martin wasn't scared of difficult personalities. "Bochner said Nash was worth appointing. 'Don't worry about anything!' " Martin recalled.23 And Martin didn't. He came to value Nash, not just as "a brilliant and creative young man," but as an ally in his quest to make the department great. He would come to particularly rely on Nash's absolute intellectual honesty: "When Nash mentioned somebody [as a potential hire], you didn't wonder if he was a crony or a relative. If Nash said he was top flight, you didn't need much in the way of outside references." And Martin didn't. He came to value Nash, not just as "a brilliant and creative young man," but as an ally in his quest to make the department great. He would come to particularly rely on Nash's absolute intellectual honesty: "When Nash mentioned somebody [as a potential hire], you didn't wonder if he was a crony or a relative. If Nash said he was top flight, you didn't need much in the way of outside references."

The most attractive figure at MIT from Nash's point of view was Norbert Wiener. Wiener was, in some ways, an American John von Neumann, a polymath of great originality who made stunning contributions in pure mathematics up until the beginning of World War II and then embarked on a second and equally astounding career in applied mathematics.24 Like von Neumann, Wiener is known to the public for his later work. He was, among other things, the father of cybernetics, the application of mathematics and engineering to communications and control problems. Like von Neumann, Wiener is known to the public for his later work. He was, among other things, the father of cybernetics, the application of mathematics and engineering to communications and control problems.

Wiener was also famously eccentric. His appearance alone was remarkable. His beard, Samuelson recalled after Wiener's death in 1964, was like "the Ancient Mariner's."25 He puffed on fat cigars. He waddled like a duck, a myopic parody of an absentminded professor. His extraordinary upbringing at the hands of his father, Leo, was the subject of two popular books, He puffed on fat cigars. He waddled like a duck, a myopic parody of an absentminded professor. His extraordinary upbringing at the hands of his father, Leo, was the subject of two popular books, I Am a Genius I Am a Genius and and I Am a Mathematician, I Am a Mathematician, the first of which became a bestseller in the early 1950s. Prolific as he was, Wiener generated as many anecdotes about himself as theorems. He hardly seemed to know where he was. He would ask, for example, "When we met, was I walking to the faculty club or away from it? For in the latter case I've already had my lunch." the first of which became a bestseller in the early 1950s. Prolific as he was, Wiener generated as many anecdotes about himself as theorems. He hardly seemed to know where he was. He would ask, for example, "When we met, was I walking to the faculty club or away from it? For in the latter case I've already had my lunch."26 He was notoriously insecure. If he encountered someone he knew carrying a book under his arm, he would, as likely as not, ask anxiously whether his name was in the book. He was notoriously insecure. If he encountered someone he knew carrying a book under his arm, he would, as likely as not, ask anxiously whether his name was in the book.27 Friends and admirers traced this feature of his personality to his obsessive and overbearing father, who once bragged that he could turn a broomstick into a mathematician, and to Harvard's anti-Semitism, which cost Wiener an appointment in Birkhoff's department. As Samuelson said in a eulogy after Wiener's death: "The exodus from Harvard dealt a lasting psychic trauma to Norbert Wiener. It did not help that his father was a Harvard professor ... or that Norbert's mother regarded his move as a cruel comedown in life." Friends and admirers traced this feature of his personality to his obsessive and overbearing father, who once bragged that he could turn a broomstick into a mathematician, and to Harvard's anti-Semitism, which cost Wiener an appointment in Birkhoff's department. As Samuelson said in a eulogy after Wiener's death: "The exodus from Harvard dealt a lasting psychic trauma to Norbert Wiener. It did not help that his father was a Harvard professor ... or that Norbert's mother regarded his move as a cruel comedown in life."28 Wiener's colleagues at MIT knew that he suffered from periods of manic excitability followed by severe depressions, constantly threatened to resign, and sometimes spoke of suicide. "When he was high he'd run all over MIT telling people his latest theorem," Zipporah "f.a.gi" Levinson, the wife of Norman Levin-son, recalled. "You couldn't stop him."29 At times, he would come to the Levinsons' house, weeping, and say that he wished to kill himself. At times, he would come to the Levinsons' house, weeping, and say that he wished to kill himself.30 One of Wiener's ever-present fears was that he would go mad; his brother Theo, as well as two nephews, suffered from schizophrenia. One of Wiener's ever-present fears was that he would go mad; his brother Theo, as well as two nephews, suffered from schizophrenia.31 Perhaps because of his own psychological struggles, Wiener had an acute empathy for other people's trials. "He was egotistical and childish, but also very sensitive to the real needs of others," Mrs. Levinson recalled.32 When a younger colleague was writing a book but couldn't afford a typewriter, Wiener showed up at his door unannounced with a Royal portable under his arm. When a younger colleague was writing a book but couldn't afford a typewriter, Wiener showed up at his door unannounced with a Royal portable under his arm.

When Nash arrived at MIT in 1951, Wiener embraced him enthusiastically and encouraged Nash's growing interest in the subject of fluid dynamics - an interest that eventually led Nash to his most important work. For example, Nash sent Wiener a note in November 1952, inviting him to a seminar Nash was to give on "turbulence via statistical mechanics, collision functions, etc."33 His postscript, saying, "I've found the smoothing effect in definite form now," suggests that Nash talked about his research with Wiener, something he did with almost no one else in the department. Nash saw Wiener, a genius who was at once adulated and isolated, as a kindred spirit and fellow exile. His postscript, saying, "I've found the smoothing effect in definite form now," suggests that Nash talked about his research with Wiener, something he did with almost no one else in the department. Nash saw Wiener, a genius who was at once adulated and isolated, as a kindred spirit and fellow exile.34 He copied some of Wiener's more extreme mannerisms, his own form of homage to the older man. He copied some of Wiener's more extreme mannerisms, his own form of homage to the older man.35

But Nash was to become far closer to Norman Levinson, a first-rate mathematician and a man of extraordinary character, who would play a role in Nash's career similar to those of Steenrod and Tucker at Princeton - a combination of sounding board and father subst.i.tute. Levinson, then in his early forties, was more enigmatic than Martin but far more accessible than Wiener.36 Wiry, of medium height, with craggy features, Levinson was a fine teacher who rarely displayed the slightest facial expression and never referred to his own accomplishments. He suffered from hypochondria and from wide mood swings, long manic periods of intense creative activity followed by months, sometimes years, of depression in which nothing interested him. A former Communist like Martin, Levinson would suffer doubly during the McCarthy years when he endured not only notoriety and threats to his career as a mathematician, but his teenage daughter's slide into mental illness. Wiry, of medium height, with craggy features, Levinson was a fine teacher who rarely displayed the slightest facial expression and never referred to his own accomplishments. He suffered from hypochondria and from wide mood swings, long manic periods of intense creative activity followed by months, sometimes years, of depression in which nothing interested him. A former Communist like Martin, Levinson would suffer doubly during the McCarthy years when he endured not only notoriety and threats to his career as a mathematician, but his teenage daughter's slide into mental illness.37 Despite these burdens, Levinson was, and would long remain, by far the most respected member of the department. Thoughtful, decisive, and attuned to the personal as well as intellectual needs of those around him, Levinson was father confessor and wise elder, the one whose judgments were constantly sought and carried most weight, on everything from research to appointments. Despite these burdens, Levinson was, and would long remain, by far the most respected member of the department. Thoughtful, decisive, and attuned to the personal as well as intellectual needs of those around him, Levinson was father confessor and wise elder, the one whose judgments were constantly sought and carried most weight, on everything from research to appointments.

His personal history was one of individual triumph over bleak beginnings. Born in Lynn, Ma.s.sachusetts, just before World War I, Levinson was the son of a shoe factory worker who earned eight dollars a week and whose education consisted of attending a yes.h.i.+va for a few years. His mother was illiterate. Despite a childhood of desperate poverty and an education that consisted of attending rundown vocational schools, Levinson's brilliance was undeniable. He managed, with the help of Wiener, who spotted his talent, to attend MIT and, later, Cambridge. At Cambridge, he became a protege of G. H. Hardy and embarked on a series of brilliant papers on ordinary differential equations. "He was very uncouth, very provincial," his wife, Zipporah, who met Levinson soon after he returned from England, recalled in 1995. "He was highly opinionated and too ignorant to know that he didn't know everything. But he'd plunge in and make a good paper, despite the fact that he didn't know the literature. Wiener ignored his rough edges."

Like many promising young Jewish mathematicians of his generation, Levinson had difficulty getting an academic post when he returned to the States, and it was Hardy who, while visiting Harvard in 1937, was ultimately responsible for Levinson's appointment that year at MIT. The university's provost, Vannevar Bush, had turned down Wiener's recommendation that Levinson be offered an a.s.sistant professors.h.i.+p when Hardy, who at that time was both an outspoken opponent of n.a.z.i anti-Semitism and the most prominent member of the German mathematical society, went with Wiener to the provost's office to protest. "Tell me, Mr. Bush, do you think you're running an engineering school or a theological seminary?" he is supposed to have said. When the provost gave a puzzled frown, Hardy went on: "If it isn't, why not hire Levinson?"

Nash was attracted by Levinson's strong personality and by a quality that he both shared and admired, namely Levinson's uncommon willingness to tackle new and difficult problems. Levinson was an early pioneer in the theory of partial differential equations, recognized by a Bocher Prize, and the author of an important theorem in the quantum theory of scattering of particles. Most remarkably, when he was in his early sixties and already suffering from the brain tumor that would eventually kill him, Levinson achieved the most important result of his career, the solution to a part of the famous Riemann Hypothesis. differential equations, recognized by a Bocher Prize, and the author of an important theorem in the quantum theory of scattering of particles. Most remarkably, when he was in his early sixties and already suffering from the brain tumor that would eventually kill him, Levinson achieved the most important result of his career, the solution to a part of the famous Riemann Hypothesis.38 In many ways, Levinson was a role model for Nash. In many ways, Levinson was a role model for Nash.

CHAPTER 17

Bad Boys

People considered him a bad boy - but a great one.

- D DONALD J. N J. NEWMAN, 1995

The Great Man ... is colder, harder, less hesitating, and without fear of "opinion"; he lacks the virtues that accompany respect and "respectability," and altogether everything that is the "virtue of the herd." If he cannot lead, he goes alone... . He knows he is incommunicable: he finds it tasteless to be familiar... . When not speaking to himself, he wears a mask. There is a solitude within him that is inaccessible to praise or blame.

- F FRIEDRICH N NIETZSCHE, The Will to Power The Will to Power

NASH WAS just twenty-three years old when he became an MIT instructor. He was not only the youngest member of the faculty, but younger than many of the graduate students: His boyish looks and adolescent behavior won him nicknames like Li'l Abner and the Kid Professor. just twenty-three years old when he became an MIT instructor. He was not only the youngest member of the faculty, but younger than many of the graduate students: His boyish looks and adolescent behavior won him nicknames like Li'l Abner and the Kid Professor.1 By MIT standards of that time, the teaching duties of C. L. E. Moore instructors were light. But Nash found them irksome nonetheless - as he did everything that interfered with his research or smacked of routine. Later, he would be one of the few active researchers on the faculty who avoided giving courses in his own research area. Partly, it was a matter of temperament, partly a matter of calculation. He shrewdly realized that his advancement did not depend on how well or poorly he performed in front of students. He'd advise other instructors, "If you're at MIT, forget about teaching. Just do research."2 Perhaps for this reason, Nash was mostly a.s.signed required courses for undergraduates. In the seven years of his teaching career at MIT, he seems to have taught only three graduate courses, all introductory, one in logic in his second year, one in probability, and a third, in the fall of 1958, in game theory.3 Mostly, it seems, he taught different sections of undergraduate calculus. Mostly, it seems, he taught different sections of undergraduate calculus.

His lectures were closer to free a.s.sociation than exposition. Once, he described how he planned to teach complex numbers to freshmen: "Let's see ... I'd tell them i i equals square root of minus one. But I'd also tell them that it could be minus the square root of minus one. Then so how would you decide which one... ." He started to wander. Just what freshmen needed, the listener said, in disgusted tones, in 1995. "He didn't care whether the students learned or not, made equals square root of minus one. But I'd also tell them that it could be minus the square root of minus one. Then so how would you decide which one... ." He started to wander. Just what freshmen needed, the listener said, in disgusted tones, in 1995. "He didn't care whether the students learned or not, made outrageous demands, and talked about subjects that were either irrelevant or far too advanced." outrageous demands, and talked about subjects that were either irrelevant or far too advanced."4 He was a tough grader too. He was a tough grader too.

At times his ideas about the cla.s.sroom had more to do with playing mind games than pedagogy. Robert Aumann, who later became a distinguished game theoretician and was then a freshman at MIT, described Nash's escapades in the cla.s.sroom as "flamboyant" and "mischievous."5 Joseph Kohn, later the chairman of the Princeton mathematics department, called him "a bit of a gamester." Joseph Kohn, later the chairman of the Princeton mathematics department, called him "a bit of a gamester."6 During the 1952 Stevenson-Eisenhower race, Nash was convinced, quite rightly as it turned out, that Eisenhower would win. Most of the students supported Stevenson. He made elaborate bets with the students that were constructed so that he would win regardless of who won the election. The very brightest students were amused, but most were frightened away and soon the better-informed students started to avoid his courses altogether. During the 1952 Stevenson-Eisenhower race, Nash was convinced, quite rightly as it turned out, that Eisenhower would win. Most of the students supported Stevenson. He made elaborate bets with the students that were constructed so that he would win regardless of who won the election. The very brightest students were amused, but most were frightened away and soon the better-informed students started to avoid his courses altogether.

In his first year at MIT, Nash taught an a.n.a.lysis course for ad