A Beautiful Mind

by Sylvia Nasar

  Eventually, some sophomore 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.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.”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!”11

  Few students ever exchanged a word with the Phantom, although some of the brasher ones occasionally bummed 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 Institute for Advanced Study who lives in Einstein’s old house on Mercer Street, was an assistant 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.”14

  Shortly after Hironaka won a Fields prize for his brilliant proof of the resolution of singularities, one of Nash’s messages read:

  N5 + I5 + X5 + Os + N5 = 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 7–space 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)6 + (OP)5 + (QU)4 + (ME)3 + (OT)2 + 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 pronouncements about current events, principally in the Middle East.19 In another period, Alexandre Grothendieck’s name appeared frequently.20 In still another, Diophantine equations — equations like xn + yn = zn— dominated.21

  Margaret Wertheim, author of Pythagoras’ Trousers, 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 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 hello 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 Glass, the author of Private Terror/Public Places and Delusion, 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 Glass 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 godlike 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 i
n 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.

  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, assign numbers to each letter, get a very large number, and then analyze that number for hidden meaning. It had the same relationship to mathematics as astrology to astronomy.”30 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-fashioned Friden-Marchant calculators with a tiny2 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 constituted 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.”34

  At the time, Trotter recalled, he kept track of people’s computer time but nobody 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 passwords. 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 embarrassingly 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.

  Charles Gillespie, a historian of science and editor of the 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.36

  Nash did, however, occasionally strike up acquaintanceships, as when he got to know two Iranian students during the summer of 1975. Amir Assadi, 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 hello 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 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.

  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 Dinky into town, buy a copy of The New York Times, walk over to Olden Lane, eat breakfast or lunch at the Institute, 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.

  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 classmate 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 Institute for Management Science jointly with Carl Lemke, a mathematician, of Rensselaer Polytechnic Institute.41 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 t
he 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 Washington.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.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.”47

  46

  A Quiet Life Princeton, 1970–90

  I have been sheltered here and dins avoided homelessness.

  —JOHN NASH, 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.