A Beautiful Mind (29 page)

—
F
RIEDRICH
N
IETZSCHE
,
The Will to Power

N
ASH WAS
just twenty-three years old when he became an MIT instructor. He was not only the youngest member of the faculty, but younger than many of the graduate students: His boyish looks and adolescent behavior won him nicknames like Li’l Abner and the Kid Professor.
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By MIT standards of that time, the teaching duties of C. L. E. Moore instructors were light. But Nash found them irksome nonetheless — as he did everything that interfered with his research or smacked of routine. Later, he would be one of the few active researchers on the faculty who avoided giving courses in his own research area. Partly, it was a matter of temperament, partly a matter of calculation. He shrewdly realized that his advancement did not depend on how well or poorly he performed in front of students. He’d advise other instructors, “If you’re at MIT, forget about teaching. Just do research.”
²

Perhaps for this reason, Nash was mostly assigned required courses for undergraduates. In the seven years of his teaching career at MIT, he seems to have taught only three graduate courses, all introductory, one in logic in his second year, one in probability, and a third, in the fall of 1958, in game theory.
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Mostly, it seems, he taught different sections of undergraduate calculus.

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

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

In his first year at MIT, Nash taught an analysis course for advanced undergraduates. The course was supposed to be an introductory look at calculus in which students weren’t just learning manipulations but rather absolutely solid proofs of statements and how to construct such proofs. Between the first and second semesters of the yearlong course, the number of students dwindled from about thirty to five.

Kohn recalled: “He gave a one-hour test. He handed out blue books where you filled in your name and the course number on the cover. When the bell rang, you were supposed to turn over the exam sheet and start working on the test. There were four problems. Problem number one was What is your name?’ The other three problems were fairly hard. Since I knew by then how his mind worked, I made sure to write next to number one, ‘My name is Joseph Kohn.’ People who assumed that writing their name on the cover was enough got twenty-five points taken off.”
⁷

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.”
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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.
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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.
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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.
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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.
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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.”
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Levinson, whose daughter suffered from manic depression, hated psychiatrists. Nash adopted a similarly vehement stance against the profession.
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Warren Ambrose detested conventional greetings like “How are you?” Nash followed suit.
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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 view 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.
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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.
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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.