A Beautiful Mind Part 14

Phantom of Fine Hall Princeton, 1970s Princeton, 1970s

Much Madness is divinest Sense - To a discerning Eye... .

- EMILY D d.i.c.kINSON, Number 435 Number 435

AN IMPERSONAL NEW GRANITE-CLAD TOWER, built with defense dollars at the height of the Vietnam War, had replaced the old Fine Hall and neighboring Jadwin Hall. built with defense dollars at the height of the Vietnam War, had replaced the old Fine Hall and neighboring Jadwin Hall.1 Math and physics majors spent most of their waking hours below ground where the architects had situated the library - which had formerly occupied the highest floor of Old Fine - as well as the new computer center. Within a few days or weeks, the embryo scientist or mathematician would discover "a very peculiar, thin, silent man walking the halls, night and day," "with sunken eyes and a sad, immobile face." Math and physics majors spent most of their waking hours below ground where the architects had situated the library - which had formerly occupied the highest floor of Old Fine - as well as the new computer center. Within a few days or weeks, the embryo scientist or mathematician would discover "a very peculiar, thin, silent man walking the halls, night and day," "with sunken eyes and a sad, immobile face."2 On rare occasions, they might catch a glimpse of the wraith - usually clad in khaki pants, plaid s.h.i.+rt, and bright red high-top Keds - printing painstakingly on one of the numerous blackboards that lined the subterranean corridors linking Jadwin and New Fine. On rare occasions, they might catch a glimpse of the wraith - usually clad in khaki pants, plaid s.h.i.+rt, and bright red high-top Keds - printing painstakingly on one of the numerous blackboards that lined the subterranean corridors linking Jadwin and New Fine.3 More often, students would emerge from an 8:00 More often, students would emerge from an 8:00 A.M A.M. lecture to find an enigmatic epistle written the night before: "Mao Tse-Tung's Bar Mitzvah was 13 years, 13 months and 13 days after Brezhnev's circ.u.mcision," for example.4 Or "I agree with Harvard: There is a brain flat." Or "I agree with Harvard: There is a brain flat."5 Or a letter from Nikita Khrushchev to Moses with arcane mathematical statements involving the factoring of very long, ten- to fifteen-digit numbers into two large primes. Or a letter from Nikita Khrushchev to Moses with arcane mathematical statements involving the factoring of very long, ten- to fifteen-digit numbers into two large primes.6 "n.o.body knew where they came from," recalled Mark Reboul, who graduated in 1977. "n.o.body knew what they meant." "n.o.body knew where they came from," recalled Mark Reboul, who graduated in 1977. "n.o.body knew what they meant."7 Eventually, some soph.o.m.ore or junior would clue in the newcomer that the author of the messages, aka the Phantom, was a mathematical genius who had "flipped" while giving a lecture; while trying to solve an impossibly difficult problem; after discovering that someone else had scooped him on a major result; or upon learning that his wife had fallen in love with a mathematical rival.8 He had friends in high places at the university, the older student would add. Students were not to bother him. He had friends in high places at the university, the older student would add. Students were not to bother him.9 Among the students, the Phantom was often held up as a cautionary figure: Anybody who was too much of a grind or who lacked social graces was warned that he or she was "going to wind up like the Phantom." Anybody who was too much of a grind or who lacked social graces was warned that he or she was "going to wind up like the Phantom."10 Yet if a new student complained that having him around made him feel uncomfortable, he was immediately warned: "He was a better mathematician than you'll ever be!" Yet if a new student complained that having him around made him feel uncomfortable, he was immediately warned: "He was a better mathematician than you'll ever be!"11 Few students ever exchanged a word with the Phantom, although some of the brasher ones occasionally b.u.mmed a cigarette or asked for a light, for the Phantom was now a heavy smoker. One new physics student once erased two or three of the messages only to encounter the Phantom in front of the blackboard writing a few days later, "sweating, trembling, and practically crying." The student never erased another.12 Students and young faculty members studied the Phantom's messages and sometimes copied them down verbatim. The messages created an aura around the Phantom and confirmed the legends of his genius. Frank Wilczek, a physicist at the Inst.i.tute for Advanced Study who lives in Einstein's old house on Mercer Street, was an a.s.sistant professor at the university at the time. He remembered feeling "intrigued and impressed" and "in the presence of a great mind."13 Mark Schneider, a physics professor at Grinnell who was a graduate student in 1979, recalled: "We all found the remarkable connections, level of detail, and breadth of knowledge ... exceptional, which is why I ... collected a few dozen of the best of these." Mark Schneider, a physics professor at Grinnell who was a graduate student in 1979, recalled: "We all found the remarkable connections, level of detail, and breadth of knowledge ... exceptional, which is why I ... collected a few dozen of the best of these."14 Shortly after Hironaka won a Fields prize for his brilliant proof of the resolution of singularities, one of Nash's messages read: N5 + I + I5 + X + X5 + O + Os + N + N5 = 0 = 0 Can Hironaka resolve this singularity?15 Some of the messages seemed purely mathematical, at least until one looked at them more closely, as in this 1979 message: Open Letter to Prof. Heisuke Hironaka

The above algebraic variety of dimension 6, represented in affine 7s.p.a.ce is singular, having a point singularity at the origin (0,0,0,0,0,0,0) of the coordinates.

The question is: How singular comparatively, is the above 6-variety, that is, what is the comparative degree of its singularity, compared with other singularities of such a sort as to provide standards of comparison?16

Others contained indirect references to past events: Indian Limbo B = (RX)7 + (MO) + (MO)6 + (OP) + (OP)5 + (QU) + (QU)4 + (ME) + (ME)3 + (OT) + (OT)2 + AAP + AAP

OT suggests "Occupational Therapy" - as in Dr. O.T. Beetle, M.D.

AAP = P R (2) - 1, as a number.17 And still others were slyly humorous: True or False Question Statement: President Jimmy Carter is suffering from the disease of xanthochromatosis, the same disease which previously affected the careers of Nixon and Agnew, so that the disease has presumably jumped the gap of the apparently immune northern republicans Ford and Rockefeller and reinfected Air Force One via the person of Jimmy Carter.

The above statement is true.

The above statement is false.18 During one period, all the messages featured a commentator named Ya Ya Fontana who made mysterious p.r.o.nouncements about current events, princ.i.p.ally in the Middle East.19 In another period, Alexandre Grothendieck's name appeared frequently. In another period, Alexandre Grothendieck's name appeared frequently.20 In still another, Diophantine equations - equations like In still another, Diophantine equations - equations like x xn + y + yn = z = zn- dominated.21 Margaret Wertheim, author of Pythagoras' Trousers, Pythagoras' Trousers, a history of mathematics, has pointed out that "people look to the order of numbers when the world falls apart." a history of mathematics, has pointed out that "people look to the order of numbers when the world falls apart."22 Nash's romance with numerology blossomed when his world was falling apart, suggesting once again that delusions - like "mystical, cultic religious efflorescence" - aren't merely the ravings of madmen but conscious, painstaking, and often desperate attempts to make sense out of chaos. Nash's romance with numerology blossomed when his world was falling apart, suggesting once again that delusions - like "mystical, cultic religious efflorescence" - aren't merely the ravings of madmen but conscious, painstaking, and often desperate attempts to make sense out of chaos.

Nash was making up numbers out of names and was often extremely worried about what he found. "He was quite agitated when he thought that the numbers were portents of something serious," recalled Peter Cziffra, the head librarian at Fine Hall. Hale Trotter, a mathematician on the Princeton faculty, recalled, "I'd say h.e.l.lo and he'd initiate a conversation. I remember one in which he was very concerned about the similarity of the telephone number of the United States Senate and the telephone number of the Kremlin. He was doing the arithmetic correctly but the reasoning for it was crazy."23 Nash did a lot of telephoning in those years. Early on, Peter Cziffra remembers, Nash tried to call public figures as well as people at the university: "It was a little odd... . He wanted to talk about something that had been in the paper. A crisis in Russia that he wanted to talk about with somebody."24 William Browder, who was now chairman of the mathematics department, recalled: Nash was the greatest numerologist the world has ever seen. He would do these incredible manipulations with numbers. One day he called me and started with the date of Khrushchev's birth and worked right through to the Dow Jones average. He kept manipulating and putting in new numbers. What he came out with at the end was my Social Security number. He didn't say it was my Social Security number and I wouldn't admit that it was. I tried not to give him satisfaction. Nash was never trying to convince anyone of anything. He was doing things from a scholarly point of view. Everything he talked about always had a very scientific flavor. He was trying to gain an understanding of something. It was pure numerology, not applied.25

One has a distinct sense that Nash's condition had stabilized. To go to the blackboard took courage. To share ideas that Nash felt were important, and yet that might seem crazy to others, implied a willingness to make connections with the community at large. To stay in one place and not to run away, to labor at articulating his delusions in a way that attracted an audience that valued them must be seen as evidence of some progression back to consensual forms of reality and behavior. And, at the same time, to have his delusions seen not just as bizarre and unintelligible, but as having an intrinsic value, was surely one aspect of these "lost years" that paved the way for an eventual remission.

As James Gla.s.s, the author of Private Terror/Public Places Private Terror/Public Places and and Delusion, Delusion, put it upon hearing about Nash's years in Princeton: "It seemed to serve as a containing place for his madness." put it upon hearing about Nash's years in Princeton: "It seemed to serve as a containing place for his madness."26 It is obvious that, for Nash, Princeton functioned as a therapeutic community. It was quiet and safe; its lecture halls, libraries, and dining halls were open to him; its members were for the most part respectful; human contact was available, but not intrusive. Here he found what he so desperately wanted in Roanoke: safety, freedom, friends. As Gla.s.s put it, "Being freer to express himself, without fearing that someone would shut him up or fill him up with medication, must have helped pull him out of his disastrous retreat into hermetic linguistic isolation." It is obvious that, for Nash, Princeton functioned as a therapeutic community. It was quiet and safe; its lecture halls, libraries, and dining halls were open to him; its members were for the most part respectful; human contact was available, but not intrusive. Here he found what he so desperately wanted in Roanoke: safety, freedom, friends. As Gla.s.s put it, "Being freer to express himself, without fearing that someone would shut him up or fill him up with medication, must have helped pull him out of his disastrous retreat into hermetic linguistic isolation."27 Roger Lewin, a psychiatrist at Shepherd Pratt in Baltimore, said, "It seems that Nash's schizophrenia diminished in the way it appeared to others and that his madness became confined to intellectual and delusional projections rather than to wrapping him completely in behavioral expressions."28 These are descriptions similar to those Nash himself has given of these years in Princeton: "I thought I was a Messianic G.o.dlike figure with secret ideas. I became a person of delusionally influenced thinking but of relatively moderate behavior and thus tended to avoid hospitalization and the direct attention of psychiatrists." These are descriptions similar to those Nash himself has given of these years in Princeton: "I thought I was a Messianic G.o.dlike figure with secret ideas. I became a person of delusionally influenced thinking but of relatively moderate behavior and thus tended to avoid hospitalization and the direct attention of psychiatrists."

The immense effort - the reading, computations, and writing - of producing the messages may have played a role in preventing Nash's mental capacities from deteriorating. The messages had their own history and evolved over time. At some point, probably starting in the mid-1970s, Nash began writing epigrams and epistles based on calculations in base 26.29 Base 26, of course, uses twenty-six symbols, the number of letters in the English alphabet, just as the base 10 of everyday arithmetic employs the integers zero through nine. Thus, if a calculation came out "right," it produced actual words. Base 26, of course, uses twenty-six symbols, the number of letters in the English alphabet, just as the base 10 of everyday arithmetic employs the integers zero through nine. Thus, if a calculation came out "right," it produced actual words.

Here was Nash, who as a boy had delighted in inventing secret codes, with his great mathematical ability and mystical preoccupations, and with plenty of time on his hands, taking names, converting them into numbers based on the letter-number correspondence, factoring the resulting numbers, and then comparing the primes in the hope of discovering "secret" messages. Daniel Feenberg, a graduate student of economics who ran into Nash at the computer center around 1975, recalled: "Nash had an obsessive concern with Nelson Rockefeller. He would take the letters, a.s.sign numbers to each letter, get a very large number, and then a.n.a.lyze that number for hidden meaning. It had the same relations.h.i.+p to mathematics as astrology to astronomy."30 This, of course, is not only time This, of course, is not only timerconsuming but remarkably difficult, and the odds of finding meaningful words or combination of words minute.

Nash worked on one of those old-fas.h.i.+oned Friden-Marchant calculators with a tiny2 glowing, green CRT. glowing, green CRT.31 He must have written an algorithm for doing base 26 arithmetic. Performing these calculations would have been tremendously tedious and would have required writing down intermediate results as he went along, since these calculators had very little storage capacity and weren't programmable. Generating the equations that const.i.tuted the core of his blackboard messages was not just fancy arithmetic, however. As one of the former physics students remarked, "It would have taken deep abstraction of the sort that real mathematicians perform." He must have written an algorithm for doing base 26 arithmetic. Performing these calculations would have been tremendously tedious and would have required writing down intermediate results as he went along, since these calculators had very little storage capacity and weren't programmable. Generating the equations that const.i.tuted the core of his blackboard messages was not just fancy arithmetic, however. As one of the former physics students remarked, "It would have taken deep abstraction of the sort that real mathematicians perform."32 On one occasion, Feenberg wrote a computer program for Nash: He asked me if computer programming was something he should do. He'd seen me working with computers. He wanted to factor a twelve-digit number, which he felt was a composite number. He had already tested it against the first seventy thousand primes on a desk calculator. He had done it twice. He'd found no mistake, but he hadn't found a factor. I said we could do it. It took only about five minutes to write the program and test it. The answer came back: His number was a composite number that was the product of two primes.33

Nash was beginning to develop an interest in learning how to use the computer. (If one spent time in the computing center one had to sit at those ancient desk calculators by the hour, shuffling decks of computer cards.) Hale Trotter, who was working half-time in the computer center in those days, described it: "It was the old days. We fed cards into the computer. There was a large 'ready room' with a big counter, a card reader, table, and chairs and another room with a calculator. There was always lots of paper around." desk calculators by the hour, shuffling decks of computer cards.) Hale Trotter, who was working half-time in the computer center in those days, described it: "It was the old days. We fed cards into the computer. There was a large 'ready room' with a big counter, a card reader, table, and chairs and another room with a calculator. There was always lots of paper around."34 At the time, Trotter recalled, he kept track of people's computer time but n.o.body was billed. At some point the administration decided that he had to charge individual research accounts. Students and faculty alike had to open accounts and get pa.s.swords. Trotter initially told Nash that Nash could use his account number. At weekly meetings, the subject of regularizing the situation with Nash came up. Some students were wondering what was going on with Trotter's name on Nash's output. Someone suggested, said Trotter, "Why not give him his own account?" Everybody agreed to give him a free account. "He never, never made any trouble. If anything, he was embarra.s.singly diffident. Sometimes if one was having a conversation with Nash, it was hard to break away."

For most of the 1970s, Nash conducted his elaborate researches in the reference room of Firestone Library, where he was known to successive generations of students as "the library crazy man" and later as "the mad genius of Firestone."35 In the late 1970s, he was often the last to leave the library at midnight. He spent evenings in the reference room, his floppy golf hat on the broad wooden table with a neat pile of books. He could spend two or three hours standing at the card catalog. In the late 1970s, he was often the last to leave the library at midnight. He spent evenings in the reference room, his floppy golf hat on the broad wooden table with a neat pile of books. He could spend two or three hours standing at the card catalog.

Charles Gillespie, a historian of science and editor of the Dictionary of Scientific Biography, Dictionary of Scientific Biography, had an office on the third floor of Firestone Library. Every day Nash would arrive at Firestone, marching down the walk, eyes straight ahead and briefcase in hand. He almost always headed for the third floor stacks, in a section of the library devoted to religion and philosophy. Gillespie always said good morning. Nash was always silent. had an office on the third floor of Firestone Library. Every day Nash would arrive at Firestone, marching down the walk, eyes straight ahead and briefcase in hand. He almost always headed for the third floor stacks, in a section of the library devoted to religion and philosophy. Gillespie always said good morning. Nash was always silent.36 Nash did, however, occasionally strike up acquaintances.h.i.+ps, as when he got to know two Iranian students during the summer of 1975. Amir a.s.sadi, a big, smiling bear of a man, now on the mathematics faculty at the University of Wisconsin, recalled: My brother spent the summer with me while I was studying for my generals. He used to wait for me in the common room. I'd seen Nash around and heard about him, but one day when I walked in he and my brother were talking intensely and I joined him. After that, I always said h.e.l.lo and we talked occasionally. He was extremely gentle and very shy. He seemed just so lonely. We were among the few people who talked to him. But he spoke freely to my brother. I suppose he saw a lonely foreigner.

Usually the conversations were quite short, but sometimes he would go on and on. It seemed scholarly to us. He didn't act bizarre. He used to read the on and on. It seemed scholarly to us. He didn't act bizarre. He used to read the Encyclopaedia Britannica. Encyclopaedia Britannica. He had enormous knowledge. Nash was interested in Zoroastrian religion. Zarathustra was an ancient Iranian prophet. He wasn't mad. He wasn't someone who "had a yellow camel [i.e., crazy]." The religion he founded was based on three principles: good deeds, good thoughts, good expressions. Fire was holy. Light and darkness were always locked in struggle. Fires always burn in Zoroastrian temples. They are monotheists. Nash would ask us to verify this and that. Occasionally we went and really read something. He had enormous knowledge. Nash was interested in Zoroastrian religion. Zarathustra was an ancient Iranian prophet. He wasn't mad. He wasn't someone who "had a yellow camel [i.e., crazy]." The religion he founded was based on three principles: good deeds, good thoughts, good expressions. Fire was holy. Light and darkness were always locked in struggle. Fires always burn in Zoroastrian temples. They are monotheists. Nash would ask us to verify this and that. Occasionally we went and really read something.

In Iran the sense of sympathy and deep regret for a person being lonely is very great. We felt sorry.37

Nash's daily rounds in those years followed a predictable pattern. He would get up, not too early, and ride the d.i.n.ky into town, buy a copy of The New York Times, The New York Times, walk over to Olden Lane, eat breakfast or lunch at the Inst.i.tute, and wander back to the university, where he could be found either in Fine or in Firestone. For some time, he became a regular at Fine Hall teas. The year Joseph Kohn became chairman of the math department, 1972, Kohn spent "many sleepless nights" over Nash. Some of the math department secretaries had come to him at various times saying that Nash's behavior worried them. walk over to Olden Lane, eat breakfast or lunch at the Inst.i.tute, and wander back to the university, where he could be found either in Fine or in Firestone. For some time, he became a regular at Fine Hall teas. The year Joseph Kohn became chairman of the math department, 1972, Kohn spent "many sleepless nights" over Nash. Some of the math department secretaries had come to him at various times saying that Nash's behavior worried them.38 Kohn couldn't remember exactly what the behavior was but guessed that it involved staring. In any case, he brushed the women's complaints aside, saying that there was nothing to worry about, but privately he wasn't so sure. Kohn couldn't remember exactly what the behavior was but guessed that it involved staring. In any case, he brushed the women's complaints aside, saying that there was nothing to worry about, but privately he wasn't so sure.

With a few exceptions, such as Trotter, the faculty tended to avoid him. Claudia Goldin, who was on the economics faculty at the time, recalled: He was an intriguing mystery. He just seemed to be around. Here was this giant and all of us were standing on his shoulders. But what kind of shoulders were they? For academics, there's always this fear. All you have is your brain. The idea that anything could go wrong with it is so threatening. It's threatening for everybody, of course, but for academics that's all of it.39

Mostly it was students who knew a bit of his legend, who generally found him nonthreatening, who sought him out. Feenberg, for example, had lunch with Nash. "Everyone knew he was a great man and just having lunch was an interesting experience. It was sad also. Here was this presence, this very famous person in our midst that people outside of Princeton often thought was dead."40 In 1978, largely thanks to the kindness of his old cla.s.smate from graduate school and RAND, Lloyd Shapley, Nash was finally awarded a mathematical prize. He was awarded the John von Neumann Theory Prize by the Operations Research Society and the Inst.i.tute for Management Science jointly with Carl Lemke, a mathematician, of Rensselaer Polytechnic Inst.i.tute. mathematician, of Rensselaer Polytechnic Inst.i.tute.41 Nash won for his invention of noncooperative equilibrium; Lemke for his work in computing Nash equilibria. Nash won for his invention of noncooperative equilibrium; Lemke for his work in computing Nash equilibria.42 Lloyd Shapley was on the prize committee. It was his idea. "I felt sentiment and nostalgia," he recalled.43 Shapley, having received the honor himself the year before, thought: "Here's a chance to do something for Nash." He was motivated, he later said, by the hope that honoring Nash would somehow help Alicia and Johnny. "My sentiment, such as it was, was based on picturing him growing up. Here's this kid growing up and his dad isn't there. This might do something to increase his self-esteem. His father isn't there, but he's great, his work is being recognized." Shapley, having received the honor himself the year before, thought: "Here's a chance to do something for Nash." He was motivated, he later said, by the hope that honoring Nash would somehow help Alicia and Johnny. "My sentiment, such as it was, was based on picturing him growing up. Here's this kid growing up and his dad isn't there. This might do something to increase his self-esteem. His father isn't there, but he's great, his work is being recognized."44 Nash was not, however, invited to the prize ceremony in Was.h.i.+ngton.45 Instead, Alan Hoffman, a mathematician at IBM and the second member of the prize committee, went down to Princeton to present Nash with the award. Instead, Alan Hoffman, a mathematician at IBM and the second member of the prize committee, went down to Princeton to present Nash with the award.46 He said: "We gathered in Al Tucker's office. Al and Harold Kuhn were there, so we chatted a while. Nash was sitting in the corner. Let me tell you, seeing this man who was a genius and now functioning at subadolescent level really was tragic. There's a difference between knowing and seeing." He said: "We gathered in Al Tucker's office. Al and Harold Kuhn were there, so we chatted a while. Nash was sitting in the corner. Let me tell you, seeing this man who was a genius and now functioning at subadolescent level really was tragic. There's a difference between knowing and seeing."47

CHAPTER 46

A Quiet Life Princeton, 197090 Princeton, 197090

I have been sheltered here and dins avoided homelessness.

-JOHN N NASH, 1992 1992

WHEN ALICIA OFFERED to let Nash live with her in 1970, she was moved by pity, loyalty, and the realization that no one else on earth would take him in. His mother was dead, his sister unable to accept the burden. Alicia was, divorced or no, his wife. Whatever her reservations about living with her mentally ill ex-husband, they played no role in her thinking: She was simply not prepared to turn her back on him. to let Nash live with her in 1970, she was moved by pity, loyalty, and the realization that no one else on earth would take him in. His mother was dead, his sister unable to accept the burden. Alicia was, divorced or no, his wife. Whatever her reservations about living with her mentally ill ex-husband, they played no role in her thinking: She was simply not prepared to turn her back on him.

Alicia also was moved by the conviction that she had something more to offer Nash than physical shelter. She believed, perhaps somewhat wishfully, that living in an academic community among his own kind, without the threat of further hospitalization, would help him get well. She took Nash's own a.s.sessment of his needs - for safety, freedom, and friends.h.i.+p - literally. In a letter to Martha written at Nash's request in late 1968, when he was convinced that his mother and sister planned to hospitalize him again, Alicia had argued that hospitalization was unnecessary and harmful: "Much of his past hospitalization I now feel was a mistake and had no beneficial permanent effects, rather the opposite. If he is to make a lasting adjustment, I think this has to be done under normal conditions."1 In 1968, Alicia had attributed her change of heart not just to the fact that Nash had relapsed despite aggressive treatment but, more important, to her own experiences since her divorce, which gave her new insights into Nash's plight. She wrote to Martha, "I feel that I now understand his difficulties much better than I ever did in the past, having experienced some of his type of problems personally."2 Like many of those who tried to help Nash, Alicia was moved by a very personal and direct identification with his suffering. Like many of those who tried to help Nash, Alicia was moved by a very personal and direct identification with his suffering.

Alicia's beauty and vulnerability, a mix made even more potent because of her history of personal tragedy, made it likely that someone would fall in love with her. Forty-something, a professor of mathematics, John Coleman Moore might have inhabited the pages of an F. Scott Fitzgerald novel rather than an office at Fine Hall. His dark good looks, formal manners, and custom-made suits distinguished him from the rather scruffy ranks of fellow mathematicians. And his command of French and intimate knowledge of his native New York and a.s.sorted European capitals lent him a sophisticated aura. A bachelor, Moore was also a ladies' man. Forty-something, a professor of mathematics, John Coleman Moore might have inhabited the pages of an F. Scott Fitzgerald novel rather than an office at Fine Hall. His dark good looks, formal manners, and custom-made suits distinguished him from the rather scruffy ranks of fellow mathematicians. And his command of French and intimate knowledge of his native New York and a.s.sorted European capitals lent him a sophisticated aura. A bachelor, Moore was also a ladies' man.

When they returned from their separate years in Paris, Moore, Nash, and Alicia sometimes had dinners a trois. But it wasn't until after the Nashes' divorce, in mid-1963, and after Moore, described by a former girlfriend as "rigid and prim,"3 suffered a devastating mental collapse of his own that the relations.h.i.+p turned romantic. Plagued by alcoholism and severe depression, Moore was hospitalized at a sw.a.n.k, psychoa.n.a.lytically oriented hospital outside Philadelphia. suffered a devastating mental collapse of his own that the relations.h.i.+p turned romantic. Plagued by alcoholism and severe depression, Moore was hospitalized at a sw.a.n.k, psychoa.n.a.lytically oriented hospital outside Philadelphia.4 During two and one-half lonely years in which Moore remained in the hospital, other than Donald Spencer and George Whitehead, his thesis adviser from MIT, Alicia was his only regular visitor. Whitehead, who ran into Alicia a few times there, recalled: "There were lots of people in P-town who didn't come and see him. He was remarkably thankful for visitors." During two and one-half lonely years in which Moore remained in the hospital, other than Donald Spencer and George Whitehead, his thesis adviser from MIT, Alicia was his only regular visitor. Whitehead, who ran into Alicia a few times there, recalled: "There were lots of people in P-town who didn't come and see him. He was remarkably thankful for visitors."5 The friends.h.i.+p, born out of shared experiences and mutual sympathy, blossomed into romance.6 Moore returned to Princeton and his teaching duties in the summer of 1965, about the same time that Nash moved to Boston. He became Alicia's regular escort at Princeton dinner parties, concerts, and the like. Whether it was a great love match, as her marriage to Nash had been, isn't clear. Moore, for all his charm and kindness, had little of the sort of charisma that had attracted Alicia so wildly to Nash. She yearned for someone who could take care of her, though. And for some time it appeared that they would marry. Moore returned to Princeton and his teaching duties in the summer of 1965, about the same time that Nash moved to Boston. He became Alicia's regular escort at Princeton dinner parties, concerts, and the like. Whether it was a great love match, as her marriage to Nash had been, isn't clear. Moore, for all his charm and kindness, had little of the sort of charisma that had attracted Alicia so wildly to Nash. She yearned for someone who could take care of her, though. And for some time it appeared that they would marry.

At the time that Nash left Princeton, Alicia was still working at RCA. Her mother, who moved in with her after the death of her husband, kept house for Alicia as she had done in Cambridge years earlier. Mrs. Larde also helped take care of Johnny, who had grown into an extremely bright and altogether adorable boy, tall, sweet-faced, and still very blond.

Things started to unravel when Alicia suddenly lost her job at RCA. The company's s.p.a.ce division had been periodically buffeted by contract cancellations and layoffs. Alicia, who was frequently absent, often late, or simply too depressed when she was at work to be effective, was particularly vulnerable.7 She found another job fairly quickly, but it didn't last. She could not seem to get on her feet again. For a grim period that lasted several years, she drifted from job to job and was frequently unemployed, a fact to which she alluded obliquely in her letter to Martha. Alicia was determined to get a job that matched her educational credentials, but few aeros.p.a.ce companies were hiring female engineers in that era, and Alicia was turned down for more than thirty such positions. "There were times when I was going to interviews every day all day," she later recalled. "But I never got any offers. It was very depressing." She found another job fairly quickly, but it didn't last. She could not seem to get on her feet again. For a grim period that lasted several years, she drifted from job to job and was frequently unemployed, a fact to which she alluded obliquely in her letter to Martha. Alicia was determined to get a job that matched her educational credentials, but few aeros.p.a.ce companies were hiring female engineers in that era, and Alicia was turned down for more than thirty such positions. "There were times when I was going to interviews every day all day," she later recalled. "But I never got any offers. It was very depressing."8 Things got so bad after her unemployment benefits ran out that she was forced to go on welfare and to use food stamps.9 Her hope of marrying Moore came to nothing. He backed away, finding the prospect of taking on a stepson as well as a wife "too much." Her hope of marrying Moore came to nothing. He backed away, finding the prospect of taking on a stepson as well as a wife "too much."10 Her mother "held everything together," as Alicia later said, but it was very hard. Her mother "held everything together," as Alicia later said, but it was very hard.11 Alicia and her mother were forced to give up the nice house they were sharing on Franklin Street in the heart of Princeton proper.12 Alicia found a tiny nineteenth-century frame house in Princeton Junction, long ago swathed in Insulbrick, to rent. It was in poor repair, but cheap and convenient for commuting, since it was literally across the road from the railroad station. Johnny, who was twelve by this time, was extremely unhappy over having to leave his school and friends. But Alicia had little choice. Alicia found a tiny nineteenth-century frame house in Princeton Junction, long ago swathed in Insulbrick, to rent. It was in poor repair, but cheap and convenient for commuting, since it was literally across the road from the railroad station. Johnny, who was twelve by this time, was extremely unhappy over having to leave his school and friends. But Alicia had little choice.

Nash moved to the Junction with her, contributing some of his small income from the trust left by Virginia to pay the rent and household expenses. Alicia referred to him as a "boarder,"13 but in fact they ate meals together and Nash spent a fair amount of time with Johnny, sometimes helping him with his homework or playing chess with him. but in fact they ate meals together and Nash spent a fair amount of time with Johnny, sometimes helping him with his homework or playing chess with him.14 Alicia had taught her son, who would later become a chess master, how to play. Alicia had taught her son, who would later become a chess master, how to play.

Nash was very withdrawn, very quiet. "He was not a troublemaker," Odette recalled.15 Haphazardly dressed, his gray hair long, his expression blank, he would wander up and down Na.s.sau Street. Teenagers would taunt him, planting themselves in his path, waving their arms, shouting rude things directly into his startled face. Haphazardly dressed, his gray hair long, his expression blank, he would wander up and down Na.s.sau Street. Teenagers would taunt him, planting themselves in his path, waving their arms, shouting rude things directly into his startled face.16 Alicia was a proud woman, always sensitive to appearances; her loyalty and compa.s.sion outweighed her concern for what others might think. Alicia was a proud woman, always sensitive to appearances; her loyalty and compa.s.sion outweighed her concern for what others might think.

She was patient. She bit her tongue. She made very few demands on Nash. Looking back, her gentle manner probably played a substantial role in his recovery.17 Had she threatened or pressured Nash, he very well might have wound up on the street. This point was made by Richard Keefe, a psychiatrist at Duke University. Contrary to conventional wisdom, which held that families of the mentally ill should "let it all out," more recent research suggests that people with schizophrenia are no more able to tolerate the expression of strong emotion than patients recovering from a heart attack or cancer surgery. Had she threatened or pressured Nash, he very well might have wound up on the street. This point was made by Richard Keefe, a psychiatrist at Duke University. Contrary to conventional wisdom, which held that families of the mentally ill should "let it all out," more recent research suggests that people with schizophrenia are no more able to tolerate the expression of strong emotion than patients recovering from a heart attack or cancer surgery.18 Alicia is a scrupulously honest person. She says of the role she has played in protecting Nash simply, "Sometimes you don't plan things. They just turn out that way."19 She does see that it helped him, though, saying, "Did the way he was treated help him get better? Oh, I think so. He had his room and board, his basic needs taken care of, and not too much pressure. That's what you need: being taken care of and not too much pressure." She does see that it helped him, though, saying, "Did the way he was treated help him get better? Oh, I think so. He had his room and board, his basic needs taken care of, and not too much pressure. That's what you need: being taken care of and not too much pressure."

In 1973, Alicia's circ.u.mstances started to improve. She had filed a s.e.x discrimination suit against Boeing, one of the companies that had turned her down for a job in the late 1960s. job in the late 1960s.20 It was a feisty thing to do, and the suit, which eventually netted her a modest out-of-court settlement, helped boost her morale. She got a programming job at Con Edison in New York City, where her old college friend Joyce Davis was working. It was a feisty thing to do, and the suit, which eventually netted her a modest out-of-court settlement, helped boost her morale. She got a programming job at Con Edison in New York City, where her old college friend Joyce Davis was working.21 It wasn't easy. She got up every morning at four-thirty to make the two-hour commute from Princeton Junction to Con Edison's Gramercy Park headquarters in downtown Manhattan and came home well past eight every evening. She often felt frustrated by the work itself, her boss, Anna Bailey, another acquaintance from MIT, recalled. She felt that her brains and education weren't being sufficiently recognized. It wasn't easy. She got up every morning at four-thirty to make the two-hour commute from Princeton Junction to Con Edison's Gramercy Park headquarters in downtown Manhattan and came home well past eight every evening. She often felt frustrated by the work itself, her boss, Anna Bailey, another acquaintance from MIT, recalled. She felt that her brains and education weren't being sufficiently recognized.22 But now that she was making a good salary again, she was able to enroll Johnny in the Peddie School, a private preparatory school in Hightstown, about ten miles west of Princeton.23 Johnny, who had become moody and difficult at home, was nonetheless an excellent student. By the end of his soph.o.m.ore year, when he won a Rensselaer Medal in a national compet.i.tion, he had a 4.0 average. Johnny, who had become moody and difficult at home, was nonetheless an excellent student. By the end of his soph.o.m.ore year, when he won a Rensselaer Medal in a national compet.i.tion, he had a 4.0 average.24 And he was showing a marked interest in and a talent for mathematics. "John talked to Johnny a lot about mathematics when he was growing up," Alicia later recalled, adding, "If his father hadn't been a mathematician, Johnny would have been a doctor or a lawyer." And he was showing a marked interest in and a talent for mathematics. "John talked to Johnny a lot about mathematics when he was growing up," Alicia later recalled, adding, "If his father hadn't been a mathematician, Johnny would have been a doctor or a lawyer."25 Johnny started hanging around the Fine Hall common room to play chess and go and talk mathematics with various graduate students. Amir a.s.sadi remembered him as "gentle, a nice kid, a tiny bit awkward, like other mathematicians ... until they find their context."26 Johnny was obviously gifted. a.s.sadi recalled that he was studying "very high-powered math books." Sometimes father and son would come to Fine Hall together. Johnny didn't seem embarra.s.sed, but neither did he ever refer to his father when talking to the students. a.s.sadi recalled, "He disappeared one day. When he came back he'd shaved his head and had become a born-again Christian." Johnny was obviously gifted. a.s.sadi recalled that he was studying "very high-powered math books." Sometimes father and son would come to Fine Hall together. Johnny didn't seem embarra.s.sed, but neither did he ever refer to his father when talking to the students. a.s.sadi recalled, "He disappeared one day. When he came back he'd shaved his head and had become a born-again Christian."

In 1976, Solomon Leader was visiting his friend Harry Gonshor - the same Gonshor who had been part of Nash's crowd at MIT, now a professor on the Princeton faculty - at the Carrier Clinic.27 As the orderly ushered Leader through the locked door of the ward, a tall, wild-eyed young man suddenly loomed before him. "Do you know who I am?" he shouted right into Leader's face. "Do you want to be saved?" Leader noticed he was clutching a Bible. Afterward, Gonshor told him that the man was the son of John Nash. As the orderly ushered Leader through the locked door of the ward, a tall, wild-eyed young man suddenly loomed before him. "Do you know who I am?" he shouted right into Leader's face. "Do you want to be saved?" Leader noticed he was clutching a Bible. Afterward, Gonshor told him that the man was the son of John Nash.

By the time Johnny was hospitalized at Carrier at his mother's initiative, he had been truant for nearly a year.28 He had dropped all of his old friends. For many months, he had refused to leave his room. When his mother or grandmother tried to intervene, he lashed out at them. He had begun reading the Bible obsessively and talking about redemption and d.a.m.nation. He had dropped all of his old friends. For many months, he had refused to leave his room. When his mother or grandmother tried to intervene, he lashed out at them. He had begun reading the Bible obsessively and talking about redemption and d.a.m.nation.29 Soon he began hanging out with members of a small fundamentalist sect, the Way Ministry, and handing out leaflets and b.u.t.tonholing strangers on street corners in Princeton. Soon he began hanging out with members of a small fundamentalist sect, the Way Ministry, and handing out leaflets and b.u.t.tonholing strangers on street corners in Princeton.30 It was not immediately obvious to Alicia or her mother that Johnny's troubling behavior was anything more than an outburst of adolescent rebellion. In time it became clear that Johnny was hearing voices and that he believed that he was a great religious figure. When Alicia tried to get him into treatment, he ran away. He stayed away for weeks and Alicia had to go to the police for help in tracking him down and bringing him back. And then, when her son was in Carrier, Alicia learned that the thing she most dreaded, had dreaded all along, was true. Her brilliant son was suffering from the same illness as his father.31 Johnny seemed to improve quickly after the first hospitalization. But he did not return to school for three years.32 Alicia never talked about him at work except when she was forced to ask for time off. Alicia never talked about him at work except when she was forced to ask for time off.33 She never told anyone at Con Edison that John Nash was living with her again. Like Virginia Nash a decade earlier, she treated her woes as her private sorrow. She tried to cope with Johnny's refusal to take medication, his constant running away, his periodic need for hospitalization, and the terrible drain on her slender resources without giving in to her own depression. "You sacrifice so much, you put so much into it, and then it all goes," she said later. She never told anyone at Con Edison that John Nash was living with her again. Like Virginia Nash a decade earlier, she treated her woes as her private sorrow. She tried to cope with Johnny's refusal to take medication, his constant running away, his periodic need for hospitalization, and the terrible drain on her slender resources without giving in to her own depression. "You sacrifice so much, you put so much into it, and then it all goes," she said later.34 As the trouble with Johnny overwhelmed her, Alicia turned to her friend Gaby Borel for support. Gaby accompanied Alicia on visits to Carrier, and later to Trenton Psychiatric, talked with her on the telephone, and invited the Nashes to dinner.35 Moore confirms this: "Gaby is the closest female friend Alicia has around here. Gaby is very good. n.o.body else was around consistently." Moore confirms this: "Gaby is the closest female friend Alicia has around here. Gaby is very good. n.o.body else was around consistently."36 Gaby's tribute to Alicia's stoicism holds true to this day: "At first, you cannot tell anything about her. You do not realize who she is. She has put a sort of s.h.i.+eld around herself. But she is a very brave and faithful woman."37 In 1977, John David Stier made a cameo appearance in Nash's life.38 Father and son had been in touch by letter at least since 1971, John David's senior year in high school. Nash had become quite concerned about his son's college plans, and Alicia had written Arthur Mattuck to ask him to advise John David. Father and son had been in touch by letter at least since 1971, John David's senior year in high school. Nash had become quite concerned about his son's college plans, and Alicia had written Arthur Mattuck to ask him to advise John David.39 John David enrolled at Bunker Hill Community College and supported himself by working as an orderly. John David enrolled at Bunker Hill Community College and supported himself by working as an orderly.40 Four years later, he applied to a number of four-year schools, was offered several scholars.h.i.+ps, and in 1976 transferred to Amherst, one of the most elite liberal arts colleges in the country. Four years later, he applied to a number of four-year schools, was offered several scholars.h.i.+ps, and in 1976 transferred to Amherst, one of the most elite liberal arts colleges in the country.

That fall Norton Starr, a professor of mathematics at Amherst, hired a student to do some yard work for him.41 Afterward, Starr invited him into the house for a cold drink. As they chatted, the young man learned that Starr had done his Ph.D. at MIT. Had he known a mathematician there named John Nash? Only by sight and reputation, Starr replied. "He's my father," the young man said. Starr looked at him searchingly. He looked at the young man again. "My G.o.d, you do look just like him," he said. Shortly afterward, John David drove down to Princeton to visit his father. Alicia was friendly. He met his brother, Johnny, for the first time. Afterward, Starr invited him into the house for a cold drink. As they chatted, the young man learned that Starr had done his Ph.D. at MIT. Had he known a mathematician there named John Nash? Only by sight and reputation, Starr replied. "He's my father," the young man said. Starr looked at him searchingly. He looked at the young man again. "My G.o.d, you do look just like him," he said. Shortly afterward, John David drove down to Princeton to visit his father. Alicia was friendly. He met his brother, Johnny, for the first time.

The following Christmas, Johnny came up to Boston to stay with Eleanor and John David. Eleanor welcomed him warmly, cooked him nice meals, fussed over him. He came without a winter coat, so Eleanor bought him a down jacket. Johnny was well-behaved around his older brother, but could turn nasty when he was alone with her. At the end of the holiday, Eleanor recalled, "he didn't want to let John go. So John took him back to school with him."42 The reunion between Nash and John Stier did not lead to a lasting reconciliation. "It just sort of petered out," John Stier recalled. His father was more interested in talking about his own problems than his son's. "When I asked him for advice, he'd answer with something about Nixon," he said.43 Nash's confidences were unsettling. Nash had some idea that his son, having attained his majority, would play "an essential and significant personal role in my personal long-awaited 'gay liberation.' " Nash's confidences were unsettling. Nash had some idea that his son, having attained his majority, would play "an essential and significant personal role in my personal long-awaited 'gay liberation.' "44 He had waited a long time, as he said at the time, to "tell him about my life and problems and life history." Eleanor Stier recalled that he did so. He had waited a long time, as he said at the time, to "tell him about my life and problems and life history." Eleanor Stier recalled that he did so.45 John David eventually stopped returning his father's calls. The two would not meet again for seventeen years. "I haven't always wanted to have contact with him," John David said. "Having a mentally ill father was rather disturbing." John David eventually stopped returning his father's calls. The two would not meet again for seventeen years. "I haven't always wanted to have contact with him," John David said. "Having a mentally ill father was rather disturbing."

More often than commonly realized, schizophrenia can be an episodic illness, especially in the years following its initial onset. Periods of acute psychosis may be interspersed with periods of relative calm in which symptoms diminish dramatically either as a result of treatment or spontaneously.46 This was the pattern for Johnny. This was the pattern for Johnny.

In 1979, on the first day of the fall semester at Rider College in Lawrenceville, New Jersey, Kenneth Fields, the chairman of the mathematics department, was asked to talk with a freshman who had made a pest of himself at the math orientation session, questioning everything and protesting that the presentation was not rigorous enough.47 "I don't need to take calculus," the young man said when he arrived in Fields's office. "I'm going to major in math." Since Rider rarely attracted students with an interest or background in mathematics, Fields was intrigued. Quizzing the student as they walked around the campus, he quickly concluded that no mathematics course at Rider was advanced enough for this young man and offered to tutor him personally. "By the way, what's your name?" he finally asked. "John Nash," the student replied. Seeing Fields's look of astonishment, he added, "You may have heard of my father. He solved the embedding theorem." For Fields, who had been an undergraduate at MIT in the 1960s and was familiar with the Nash legend, it was an amazing moment. "I don't need to take calculus," the young man said when he arrived in Fields's office. "I'm going to major in math." Since Rider rarely attracted students with an interest or background in mathematics, Fields was intrigued. Quizzing the student as they walked around the campus, he quickly concluded that no mathematics course at Rider was advanced enough for this young man and offered to tutor him personally. "By the way, what's your name?" he finally asked. "John Nash," the student replied. Seeing Fields's look of astonishment, he added, "You may have heard of my father. He solved the embedding theorem." For Fields, who had been an undergraduate at MIT in the 1960s and was familiar with the Nash legend, it was an amazing moment.

Fields proceeded to meet with Johnny weekly. Johnny took a while to buckle down, but he was soon plowing through difficult texts in linear algebra, advanced calculus, and differential geometry. "It was obvious that he was a real mathematician," said Fields. He was also bright and friendly, a fundamentalist Christian who made friends with other religious, intellectually precocious students. He talked to Fields, who has several relatives who suffer from schizophrenia, about his mental illness. Occasionally he would do a riff on extraterrestrials, and on one occasion he threatened a history professor. By and large, said Fields, Johnny's symptoms seemed to be under control. He got straight As and won an academic prize in his soph.o.m.ore year. said Fields. He was also bright and friendly, a fundamentalist Christian who made friends with other religious, intellectually precocious students. He talked to Fields, who has several relatives who suffer from schizophrenia, about his mental illness. Occasionally he would do a riff on extraterrestrials, and on one occasion he threatened a history professor. By and large, said Fields, Johnny's symptoms seemed to be under control. He got straight As and won an academic prize in his soph.o.m.ore year.

Fields soon concluded that Johnny was wasting his time at Rider and belonged in a Ph.D. program. In 1981, despite his lack of a high school or college diploma, Johnny was accepted at Rutgers University with a full scholars.h.i.+p. Once there, he breezed through his qualifying examinations. From time to time he would threaten to drop out of school and Fields would get frantic calls from Alicia begging him to talk to Johnny. When Fields did, Johnny would answer, "Why do I have to do anything? My father doesn't have to do anything. My mother supports him. Why can't she support me?" But he didn't drop out. He succeeded brilliantly.

Melvyn Nathanson, then a professor of mathematics at Rutgers, liked to a.s.sign what he called simple versions of unsolved cla.s.sical problems in his graduate course on number theory.48 "I gave one the first week," he recalled. "Johnny came back with the solution the following week. I gave another one that week and a week later he had that solution too. It was extraordinary." Johnny wrote a joint paper with Nathanson that became the first chapter of his dissertation. "I gave one the first week," he recalled. "Johnny came back with the solution the following week. I gave another one that week and a week later he had that solution too. It was extraordinary." Johnny wrote a joint paper with Nathanson that became the first chapter of his dissertation.49 He then wrote a second paper on his own, which Nathanson called "beautiful" and which also became part of the thesis. He then wrote a second paper on his own, which Nathanson called "beautiful" and which also became part of the thesis.50 His third paper was an important generalization of a theorem proved by Paul Erdos in the 1930s for a special case of so-called B sequences. His third paper was an important generalization of a theorem proved by Paul Erdos in the 1930s for a special case of so-called B sequences.51 Neither Erdos nor anyone else had succeeded in proving that the theorem held for other sequences, and Johnny's successful attack on the problem would generate a flurry of papers by other number theorists. Neither Erdos nor anyone else had succeeded in proving that the theorem held for other sequences, and Johnny's successful attack on the problem would generate a flurry of papers by other number theorists.

When Johnny got his Ph.D. from Rutgers in 1985, said Nathanson, he seemed poised for a long and productive career as a first-rate research mathematician. An offer of a one-year instructors.h.i.+p at Marshall University in West Virginia seemed like the first of the usual steps that eventually carry new mathematics Ph.D.'s to tenured positions somewhere in academia. While Johnny was in graduate school, Alicia Larde returned to El Salvador for good and Alicia Nash moved to a job as a computer programmer at New Jersey Transit in Newark.52 Things seemed rather hopeful. Things seemed rather hopeful.

PART FIVE

The Most Worthy

CHAPTER 47

Remission

As you know, he has had his illness, but right now he's fine. It's not attributable to one or several things. It's just a question of living a quiet life.

- ALICIA N NASH, 1994

PETER S SARNAK, a brash thirty-five-year-old number theorist whose primary interest is the Riemann Hypothesis, joined the Princeton faculty in the fall of 1990. He had just given a seminar. The tall, thin, white-haired man who had been sitting in the back asked for a copy of Sarnak's paper after the crowd had dispersed. a brash thirty-five-year-old number theorist whose primary interest is the Riemann Hypothesis, joined the Princeton faculty in the fall of 1990. He had just given a seminar. The tall, thin, white-haired man who had been sitting in the back asked for a copy of Sarnak's paper after the crowd had dispersed.

Sarnak, who had been a student of Paul Cohen's at Stanford, knew Nash by reputation as well as by sight, naturally. Having been told many times Nash was completely mad, he wanted to be kind. He promised to send Nash the paper. A few days later, at teatime, Nash approached him again. He had a few questions, he said, avoiding looking Sarnak in the face. At first, Sarnak just listened politely. But within a few minutes, Sarnak found himself having to concentrate quite hard. Later, as he turned the conversation over in his mind, he felt rather astonished. Nash had spotted a real problem in one of Sarnak's arguments. What's more, he also suggested a way around it. "The way he views things is very different from other people," Sarnak said later. "He comes up with instant insights I don't know I'd ever get to. Very, very outstanding insights. Very unusual insights."1 They talked from time to time. After each conversation, Nash would disappear for a few days and then return with a sheaf of computer printouts. Nash was obviously very, very good with the computer. He would think up some miniature problem, usually very ingeniously, and then play with it. If something worked on a small scale, in his head, Sarnak realized, Nash would go to the computer to try to find out if it was "also true the next few hundred thousand times."

What really bowled Sarnak over, though, was that Nash seemed perfectly rational, a far cry from the supposedly demented man he had heard other mathematicians describe. Sarnak was more than a little outraged. Here was this giant and he had been all but forgotten by the mathematics profession. And the justification for the neglect was obviously no longer valid, if it had ever been.

That was 1990. In retrospect, it is impossible to say exactly when Nash's miraculous remission, which began to be noted by mathematicians around Princeton roughly at the beginning of this decade, really began. But, in contrast to the onset of his illness, which became full-blown in a matter of months, the remission took place over a period of years. It was, by his own account, a slow evolution, "a gradual tapering off in the 1970s and 1980s."2 Hale Trotter, who saw Nash nearly every day in the computer center during those years, confirms this: "My impression was of a very gradual sort of improvement. In the early stages he was making up numbers out of names and being worried by what he found. Gradually, that went away. Then it was more mathematical numerology. Playing with formulas and factoring. It wasn't coherent math research, but it had lost its bizarre quality. Later it was real research."3 As early as 1983, Nash was beginning to come out of his sh.e.l.l and making friends with students. Marc Dudey, a graduate student in economics, sought Nash out in 1983. "I felt bold enough at the time to want to meet this legend."4 He discovered that he and Nash shared an interest in the stock market. "We'd be walking along Na.s.sau Street and we'd be talking about the market," Dudey recalled. Nash struck Dudey as a "stock picker" and on occasion Dudey followed his advice (with less than stellar results, it must be said). The following year, when Dudey was working on his thesis and was unable to solve the model he wanted to use, Nash helped to bail him out. "The calculation of an infinite product was involved," Dudey recalled. "I was unable to do it, so I showed it to Nash. He suggested I use Stirling's formula to compute the product and then he wrote down a few lines of equations to indicate how this should be done." All during this time, Nash struck Dudey as no odder than other mathematicians he had encountered. He discovered that he and Nash shared an interest in the stock market. "We'd be walking along Na.s.sau Street and we'd be talking about the market," Dudey recalled. Nash struck Dudey as a "stock picker" and on occasion Dudey followed his advice (with less than stellar results, it must be said). The following year, when Dudey was working on his thesis and was unable to solve the model he wanted to use, Nash helped to bail him out. "The calculation of an infinite product was involved," Dudey recalled. "I was unable to do it, so I showed it to Nash. He suggested I use Stirling's formula to compute the product and then he wrote down a few lines of equations to indicate how this should be done." All during this time, Nash struck Dudey as no odder than other mathematicians he had encountered.

By 1985, Daniel Feenberg, who had helped Nash factor a number derived from Rockefeller's name a decade earlier and was now a visiting professor at Princeton, had lunch with Nash. He was deeply struck by the change he saw in Nash. "He seemed so much better. He described his work in the theory of prime numbers. I'm not competent to judge it, but it seemed like real mathematics, like real research. That was very gratifying."5 The changes were for the most part visible only to a few. Edward G. Nilges, a programmer who worked in Princeton University's computer center from 1987 to 1992, recalled that Nash "acted frightened and silent" at first.6 In Nilges's last year or two in Princeton, however, Nash was asking him questions about the Internet and about programs he was working on. Nilges was impressed: "Nash's computer programs were startlingly elegant." In Nilges's last year or two in Princeton, however, Nash was asking him questions about the Internet and about programs he was working on. Nilges was impressed: "Nash's computer programs were startlingly elegant."

And in 1992, when Shapley visited Princeton, he and Nash had lunch and were able, for the first time in many, many years, to have quite an enjoyable conversation. "Nash was quite sharp then," Shapley recalled. "He was free of this distraction. He'd learned how to use the computer. He was working on the Big Bang. I was very pleased."7

That Nash, after so many years of severe illness, was now "within the normal range for the 'ma