A Beautiful Mind

by Sylvia Nasar

  Putting classic unsolved problems on exams was another of Nash’s favorite tricks, Aumann recalled: “The students were supposed to show that pi is an irrational number. Later, when Nash was upbraided by the chairman of the department for putting the equivalent of Fermat’s Last Theorem on a final, he responded by saying that people have a mental picture that this is a difficult problem. Maybe that’s the stumbling block. Maybe, if people didn’t realize that the problem was ’hard,’ they could solve it.”8

  On another occasion, one of Nash’s graders actually confronted him after he put the following question on a test:

  If you make up a bunch of fractions of pi 3.141592… . If you start from the decimal point, take the first digit, and place decimal point to the left, you get.1

  Then take the next 2 digits .41

  Then take the next 3 digits .592

  And so on and so on.

  You get a sequence of fractions between 0 and 1.

  What are the limit points of this set of numbers?

  (A limit point is a point such that in any open interval containing it, however small, there are an infinite number of numbers from the sequence.)9

  The grader immediately realized that it was a question that nobody had ever answered. The decimal expansion of pi isn’t a famous outstanding problem, but it’s the kind of thing mathematicians ask each other, not undergraduates. Only one fact has been proved, namely, that it has to have at least one limit point. It was clear that the students should know that there was at least one limit. But Nash thought that he knew, intuitively, that every number between 0 and 1 should be a limit point. He felt strongly that he knew the answer intuitively, which is of course quite different from having a solid proof. “It was a sort of strange thing to do,” said the grader, in 1996.

  Nash’s propensity for tricks of this kind was so well known that it became the occasion of a small joke on him, George Whitehead, a topologist in the department at the time, recalled in a conversation in 1995.10 Nash was teaching a large section of the same freshman calculus course that several graduate students were also teaching. All the sections had a prescribed and identical final and all the tests were graded together. A test, signed J. Forbes Hacker, Jr., with all wrong answers, came back, “hacker” being a double-entendre referring both to Nash’s favorite putdown, which was “hack,” and MIT slang for jokester. (It was hackers, for example, who one night removed a car belonging to Donald Spencer, who was briefly an instructor at MIT before the war, from its parking space on Massachusetts Avenue, deconstructed it, and left it for him to find when he walked into his classroom the next morning, once again fully assembled.) On another occasion, messages appeared on several blackboards around Building Two: THIS IS HATE JOHN NASH DAY!11

  Still, Nash could be charming to students he regarded as mathematically talented, and such students found much to admire. To a select few, often undergraduates, Nash made himself “very, very available for chatting about mathematics,” Barry Mazur, a number theorist at Harvard who first encountered Nash during his freshman year at MIT recalled. “It was amazing what he was willing to talk about. There was a sense of infinite time in every conversation.”

  Once Mazur and Nash were chatting in the common room. Someone mentioned a classical theorem by a disciple of Gauss, Peter Gustave Lejeune Dirichlet, that states that there are an infinite number of prime numbers in certain arithmetic progressions. “It’s the kind of thing that one just accepts or perhaps goes off and looks up afterwards,” Mazur said. Nash, however, jumped up, went to the board, and “for hours and hours elegantly thought through the proof from first principles” for Mazur’s benefit.12

  Outside the classroom, Nash alternated between the sort of behavior for which he was famous at Princeton — pacing in Building Two’s cavernous hallways whistling Bach — and bouts of sociability. By day, he spent very little time in the office suite that he shared with the other Moore Instructors. Mostly, he spent his time in the mathematics common room — a far cry from the one in Fine Hall, a ratty and nondescript lounge directly below the instructors’ offices, at the bottom of a flight of stairs.

  The social atmosphere of the MIT common room resembled some of the more raucous scenes from the cult movie If, about a British public school that is taken over by its “boys.” Nash imported the Princeton practice of a regular tea hour to MIT, but not any of its more genteel customs.13 “He wanted to be the quickest,” Isadore M. Singer, a fellow Moore Instructor, recalled in 1994. “He was a real competitor.”14 Just as he had at Princeton, Nash liked jumping into a conversation, throwing out challenges and being challenged. He liked solving problems.

  Students and an occasional professor played games, including go, chess, a great favorite of Wiener’s despite lack of skill at the game,15 and bridge. (Nash, Singer recalled, was hopeless at bridge. “It was absurd,” Singer said. “He had no sense of the laws of probability in cards.”)16 Many of the games, however, were made up on the spur of the moment. One day a group made up an index of eccentricity by which various department members were ranked. Wiener, not Nash, drew the highest score.17 Another time, everyone played a version of charades that involved drawing abstract pictures representing people around the department. A graduate student drew a highly elaborate picture of what appeared to be a taxi. Nobody could guess who it was supposed to be. The picture, it turned out, was meant to be a Nash, the car manufactured in the 1940s and 1950s, and was supposed to signify Nash the Hack, again, a reference to Nash’s favorite putdown of those he regarded as plodders.18

  The crowd in the common room was dominated by a handful of fast-talking, wisecracking veterans of Stuyvesant High School and the Bronx High School of Science math teams and the City College “Math Table” — a once-famous table in City’s cafeteria at which an entire generation of math students, mostly working-class Jews and immigrants, honed their skills in problem solving and repartee.19

  It was a brasher, rougher crowd, less uptight and more tolerant than the one in Fine Hall, and an audience more to Nash’s liking. Showing off wasn’t regarded as a crime if you knew your stuff. Lack of social graces was considered part and parcel of being real mathematicians. “Their attitudes were famously nonbourgeois, exhibitionistic, dissolute,” Felix Browder recalled.20 If anything, all of them placed a certain premium on eccentricity and outrageousness, although by today’s standards what went for unconventional behavior and manners was, by and large, mild — depending on certain turns of phrase, brands of humor, and little deviations in dress. One fellow insisted on wearing pants with fly buttons with a button or two undone.21 One graduate student recalled: “At that time we thought of eccentricity and being good in math as going together. We were all enjoying ourselves by being a little bit wild. We thought of ourselves as taking advantage of being bright by ignoring conventions we didn’t like. We turned ourselves a little bit into characters.”22

  In this circle, Nash learned to make a virtue of necessity, styling himself selfconsciously as a “free thinker.” He announced that he was an atheist.23 He created his own vocabulary.24 He began conversations in midstream with “Let’s take this aspect.” He referred to people as “humanoids.”

  Nash picked up the mannerisms of other eccentric geniuses. For example, Wiener, who was terribly nearsighted, would keep one of his fingers in the groove in the walls between the wall tiles and the plaster, as he navigated his way hesitantly through the corridors. Nash did the same thing.25 D. J. Newman condemned all music after Beethoven. Nash would stalk into the music library and tell anyone who was listening to anything more modern, “That’s junk.”26 Levinson, whose daughter suffered from manic depression, hated psychiatrists. Nash adopted a similarly vehement stance against the profession.27 Warren Ambrose detested conventional greetings like “How are you?” Nash followed suit.28

  Marvin Minsky, whom Nash had known during his final year in Princeton and whom he regarded as the most intelligent “humanoid” of all, recalled: “We shared a similarly cynical vie
w of the world. We’d think of a mathematical reason for why something was the way it was. We thought of radical, mathematical solutions to social problems. At one point, Nash suggested a complete transfusion for something. If there was a problem, we were good at finding a really ridiculously extreme solution.”29 One time he said that parents should “self-destruct,” that is, commit suicide, and hand over all their holdings to their children. It would be not only convenient but principled, Nash said, according to Herta Newman, the wife of Nash’s friend Donald Newman.30 Another time he told a class of undergraduates that American citizens’ voting rights should be made proportional to their income (or perhaps it was wealth).’31 In many ways Nash’s views were more suited to nineteenth-century England’s elitist political landscape than to the predominantly left-wing counterculture of the MIT math department of the 1950s.

  Nevertheless, he adopted a touch of flamboyance about his dress. He wore translucent white Dacron shirts sans undershirt, others thought, to show off his powerful physique.32 He bought a camera and spent much of his time browsing through photography books.33 For a time, he read and talked a great deal about experimenting with mind-altering drugs like heroin — although there is no evidence that he ever tried any.34 His growing heterogeneity of interests and heterodoxy could, with hindsight, be seen as the first overt signs of a growing alienation from convention and society that would later evolve into a radical sense of separateness and disconnection.

  But, at the moment, these postures enhanced rather than detracted from Nash’s social appeal. Nash’s status as an instructor and his growing reputation as a mathematician brought him newfound respect. He was now considered interesting company. His arrogance was seen as evidence of his genius, and so was his eccentricity, a source of both amusement and grudging respect, the other side of the genius coin, as it were. Fagi Levinson, the department’s den mother, said in 1996: “For Nash to deviate from convention is not as shocking as you might think. They were all prima donnas. If a mathematician was mediocre he had to toe the line and be conventional. If he was good, anything went.”35

  Jerome Neuwirth, a graduate student at MIT, said, “When your solution turns out to be right, we give you your due. We give you a lot of leeway. Had Nash been less of a mathematician, he wouldn’t have gotten away with his nastiness.”36 Donald Newman added, “People were annoyed with him because he was flippant, but not really annoyed. They considered him a bad boy, but a great one, a great golden boy.”37

  The gang around Nash included Newman, aka D.J., a Harvard graduate student who spent most of his time at MIT hanging out with his old friends from City College and with Nash, because “Harvard was too snooty.”38 Other members of the group included Walter Weissblum, a brilliant sad sack, drunk, and hunchback with a heart of gold, who never finished his degree;39 Harry Gonshor, who later became a professor at Rutgers, an oddball who wore Coke-bottle glasses, looked as if he were floating on air, and once proved a theorem so that it could be stated as “AFL = CIO”;40 Gustave Solomon, the most humane of the group, later a coinventor of the Reed-Solomon code;41 Leopold “Poldy” Flatto, an inveterate people-watcher and storyteller;42 and, after 1952, Jacob Leon Bricker, the group’s Woody Allen.43

  Neuwirth, a latecomer to the group, said, “Who were we? What were we trying to do? Every group has its own currency. Our only currency is what we were thinking. Who’s smart? Who’s doing what? What can you solve? How far did you get? It doesn’t sound nice but it was exciting.”44

  Nash’s closest equal, in brains, competitiveness, and general superciliousness, was Newman. Newman was considered a genius and the best problem solver of the group.45 A big, brash, blond swaggerer, Newman had the distinction, very impressive to Nash, of being a three-time Putnam winner. He was already a husband and father, with responsibilities that, however, did little to cramp his flamboyant style. He drove a flashy white Thunderbird with red leather seats that he liked to drag race along Memorial Drive in the middle of the night. As an undergraduate at City College, he’d been famous for stunts like turning up in the class of some unfortunate mathematics professor bearing an enormous tree branch, leaves and all, that he claimed was for a biology class.

  Nash and Newman immediately recognized each other as kindred spirits. “They loved to spark each other,” Arthur Singer recalled.46 “They admired each other’s sarcasm,” said Mattuck. “It was all good-natured. But D.J. could make cracks much faster. He had instant recall when it came to mathematics. People used to say that D.J. could solve any problem that could be done in twenty-four hours. Newman didn’t have the power of Nash’s sustained concentration. Nash could think about a problem for half a year.”47

  Newman went to a seminar given by Nash. “I sat in on some of Nash’s lectures,” said Newman, who was intrigued rather than put off. “It was different, kind of exciting. He wandered, unlike most lecturers, because he liked to explore a lot of things at once. It was kind of nice… . We chewed each other out,” Newman recalled. “Nash and I were friendly friends.”48

  Thanks to the acceptance of Newman and his friends, Nash acquired a real social life. The crowd often ate lunch together in Walker Memorial, but it also gathered after hours at various cheap restaurants, coffee shops, and beer halls that were as plentiful in 1950s Cambridge and Boston as they are today, places that didn’t mind if you nursed a beer all night and were willing to write separate checks.49 They included famous Boston restaurants like Durgin Park, which served generous helpings of traditional New England dishes, including a sinfully delicious roast beef and Indian pudding; Jake Wirth, an old-style German establishment with a mammoth oak bar; and the Wursthaus in Harvard Square. Other favorites were Cronin’s, Chez Dreyfus, and the Newbury Steakhouse. The Hayes-Bickford and the Waldorf, which were both Horn & Hardart-style coffee shops, open most of the night, were also frequent gathering places. At other times, everybody would hang out at some graduate student’s apartment, or go to parties given by the Martins, Levinsons, and in the mid-1950s, the Minskys.

  Within his new circle, Nash strove to constantly underscore his own uniqueness, superiority, and self-sufficiency. “I’m Nash with a capital N!” his whole manner shouted.50 He was always saying that only one or two people in the department — Wiener was always one of these — were up to his standard. His putdowns were legendary. “You’re a child,” was a favorite expression. “You don’t know crap. How trivial! How stupid! You’ll never do anything!” he would say.51

  He loved to perform. At parties, he acted rather than conversed. Once, at the Minskys’, Nash demanded that his listeners challenge him with a difficult mathematical problem. He said, “I’ve had a few drinks. Are my thinking powers stronger or weaker on drink?”52

  He was not above dissembling slightly to wow an audience.53 He would pout if he was bested in an argument.54 And he hated being challenged by someone he considered to be an inferior. One day in the common room, a group of students was talking about a famous World War II logistics puzzle, the “Jeep” problem.55 The essence of the Jeep problem is that you want to cross the two-thousand-mile-wide Sahara desert but the Jeep’s gas tank holds only enough gas to travel two hundred miles. The only way to cross the desert is to follow a two-steps-forward, one-step-back strategy: to load up the Jeep with cans of gasoline, drive, say, one hundred miles, drop off the cans, and go back to the starting point. Then you get more cans of gas, go one hundred miles, unload some and use some to top off the gas in the tank, go another one hundred miles, and go back, picking up some more gasoline. The question is, how many gallons would be needed?

  There is no optimal solution to the problem, as it turns out. Everybody was proposing solutions. Nash threw out a number. Nash’s grader that term, Seymour Haber, proposed a number half as big. Nash contemptuously dismissed Haber’s solution. When Haber insisted that he prove it, Nash said, “My solution’s much better.”

  Haber recounted: “I didn’t see it. I insisted that he prove it. He didn’t want to. He said it was obvious.
I still wouldn’t accept his assertion. So he did the calculation. He turned out to be mostly right, but he was extremely annoyed with me. He was angry for my having forced him to do this grungy work when it was perfectly clear all along what the answer was. He was angry with me for some period afterward.”

  Nor was he above putting the audience down. A typical example: at lunch one day, a graduate student was describing an axiomatic approach to a problem outlined by one of his professors. Nash fairly exploded, “Don’t give me all that crap! Tell me how you’d solve the problem. You haven’t learned anything. All these concepts don’t mean a thing.”56

  Nash’s putdowns of other mathematicians earned him the sobriquet “Gnash.” Nash responded, “G obviously stands for genius. In fact, there are few geniuses these days here at MIT. Me, of course, and also Norbert Wiener. Even Norbert may no longer be a genius, but there is evidence that he once was.” After that, he referred to Gnu (Newman) and G-squared (Andrew Gleason, a young Harvard professor who had just solved Hilbert’s fifth problem).57

  When John McCarthy, whom Nash knew from Princeton, gave a seminar in the department, Nash pulled him aside afterward and said, “There are too many journals. There are too many trashy papers being published. There are too many guys doing research. Only a few of us should be in research. The rest of them should be in sin x” — a snide reference to the tables at the back of high-school trigonometry books.58

  Nash flaunted his social snobbery, a legacy of his Bluefield upbringing. He implied that he came from old money.59 He would sniff wine at a party and say, “This is an adequate Chianti.”60 Nowhere was his snobbery more evident than in his reaction to being “a non-Jew in a definitely Jewish atmosphere.”61 Later, when Nash became paranoid and embraced all sorts of strange delusions, he wrote letters to Newman and others addressed to “Jewboy,” became obsessed with the state of Israel, and talked about “Krypto-Zionist conspiracies.”62 But in the early 1950s, his attitude was merely one of social superiority. He frequently told Newman that he looked “too Jewish.”63 Like Groucho Marx, he was inclined not to admire any club that accepted him. Nash displayed a contempt for people and things he considered beneath him. As Fred Brauer, another instructor at MIT, put it forty years later, “That covered a lot of territory.”64