*A Beautiful Mind*By Sylvia Nasar

Simon and Schuster; 336 pages; $25

People with high IQs tend to be nearsighted. This is not because they read a lot or stare at computer screens too much. That common-sense hypothesis has been discredited by research. Rather, it is a matter of genetics. The same genes that tend to elevate IQ also tend to affect the shape of the eyeball in a way that leads to myopia. This relationship–known in genetics as “pleiotropy”–seems to be completely accidental, a quirk of evolution.

Could there be a similar pleiotropy between madness and mathematics? Reading this absolutely fascinating biography by Sylvia Nasar, an economics writer for the *New York Times*, I began to wonder. Its subject, John Nash, is a mathematical genius who went crazy at the age of 30 and then, after several decades of flamboyant lunacy, was awarded the Nobel Prize in economics for something he had discovered as a graduate student. (He is now about to turn 70.) Nash is among the latest in a long and distinguished line of mathematicians–stretching back to that morbid paranoiac, Isaac Newton–who have been certifiably insane during parts of their lives.

Just in the last 100 years or so, most of the heroic figures in the foundations of mathematics have landed in mental asylums or have died by their own hand. The greatest of them, Kurt Gödel, starved himself to death in the belief that his colleagues were putting poison in his food. Of the two pioneers of game theory–the field in which Nash garnered his Nobel–one, Ernst Zermelo, was hospitalized for psychosis. The other, John Von Neumann, may not have been clinically insane, but he did serve as the real-life model for the title character in Stanley Kubrick’s *Dr. Strangelove*.

So maybe there is an accidental, pleiotropic connection between madness and mathematics. Or maybe it isn’t so accidental. Mathematicians are, after all, people who fancy that they commune with perfect Platonic objects–abstract spaces, infinite numbers, zeta functions–that are invisible to normal humans. They spend their days piecing together complicated, scrupulously logical tales about these hallucinatory entities, which they believe are vastly more important than anything in the actual world. Is this not a kind of a *folie à* n (where *n* equals the number of pure mathematicians worldwide)?

ABeautiful Mind reveals quite a lot about the psychic continuum leading from mathematical genius to madness. It is also a very peculiar redemption story: how three decades of raging schizophrenia, capped by an unexpected Nobel Prize, can transmute a cruel shit into a frail but decent human being.

As a boy growing up in the hills of West Virginia, Nash enjoyed torturing animals and building homemade bombs with two other unpopular youngsters, one of whom was accidentally killed by a blast. (Given Nash’s childhood keenness for explosives and his later penchant for sending odd packages to prominent strangers through the mail, it’s a wonder the FBI never got on to him as a Unabomber suspect.) He made his way to Carnegie Tech, where he was a classmate of Andy Warhol’s, and thence to Princeton–the world capital of mathematics at the time–at the age of 20.

In sheer appearance, this cold and aloof Southerner stood out from his fellow math prodigies. A “beautiful dark-haired young man,” “handsome as a god,” he was 6 feet 1 inch tall, with broad shoulders, a heavily muscled chest (which he liked to show off with see-through Dacron shirts), a tapered waist, and “rather limp and beautiful hands” accentuated by long fingernails. Within two years of entering Princeton, Nash had framed and proved the most important proposition in the theory of games.

Mathematically, this was no big deal. Game theory was a somewhat fashionable pursuit for mathematicians in those postwar days, when it looked as if it might do for military science and economics what Newton’s calculus had done for physics. But they were bored with it by the early 1950s. Economists, after a few decades of hesitation, picked it up in the ‘80s and made it a cornerstone of their discipline.

Agame is just a conflict situation with a bunch of participants, or “players.” The players could be poker pals, oligopolists competing to corner a market, or nuclear powers trying to dominate each other. Each player has several strategy options to choose from. What Nash showed was that in every such game there is what has become known as a “Nash equilibrium”: a set of strategies, one for each player, such that no player can improve his situation by switching to a different strategy. His proof was elegant but slight. A game is guaranteed to have a Nash equilibrium, it turns out, for the same reason that in a cup of coffee that is being stirred, at least one coffee molecule must remain absolutely still. Both are direct consequences of a “fixed-point theorem” in the branch of mathematics known as topology. This theorem says that for any continuous rearrangement of a domain of things, there will necessarily exist at least one thing in that domain that will remain unchanged–the “fixed point.” Nash found a way of applying this to the domain of all game strategies so that the guaranteed fixed point was the equilibrium for the game–clever, but the earlier topological theorem did all the work. Still, for an economics theorem, that counts as profound. Economists have been known to win Nobel Prizes for rediscovering theorems in elementary calculus.

Nash’s breakthrough in game theory got him recruited by the Rand Corp., which was then a secretive military think tank in Santa Monica (its name is an acronym for “research and development”). However, the achievement did not greatly impress his fellow mathematicians. To do that, Nash, on a wager, disposed of a deep problem that had baffled the profession since the 19^{th} century: He showed that any Riemannian manifold possessing a special kind of “smoothness” can be embedded in Euclidean space. Manifolds, one must understand, are fairly wild and exotic beasts in mathematics. A famous example is the Klein bottle, a kind of higher-dimensional Moebius strip whose inside is somehow the same as its outside. Euclidean space, by contrast, is orderly and bourgeois. To demonstrate that “impossible” manifolds could be coaxed into living in Euclidean space is counterintuitive and pretty exciting. Nash did this by constructing a bizarre set of inequalities that left his fellow mathematicians thoroughly befuddled.

That about marked the end of Nash’s career as a mathematical genius. The next year, he was expelled from Rand as a security risk after local police caught him engaging in a lewd act in a public men’s room near Muscle Beach. At MIT, where he had been given a teaching job, he hardly bothered with undergraduates and humiliated graduate students by solving their thesis problems. He carried on affairs with several men and a mistress, who bore him a son he refused to lift a finger to support. His cruel streak extended to the woman he married, a beautiful physics student named Alicia who was awed by this “genius with a penis.” Once, at a math department picnic, he threw her to the ground and put his foot on her throat.

All the while, Nash was showing an intense interest in the state of Israel–often a sign of incipient insanity, at least in a non-Jew. Geniuses slipping into madness also tend to disrobe in public (I learned this from a volume on chess prodigies, who have a proclivity for disrobing on public buses). Nash showed up for an MIT New Year’s Eve party clad only in a diaper. And then, of course, there was the *New York Times*, that old mainstay of psychotic delusion–Nash thought aliens were sending him encrypted messages through its pages (come to think of it, that could explain the *Times*’ odd prose).

When the big breakdown came, it was properly mathematical. Fearing his powers might be waning as he approached 30, Nash decided he would solve the most important unresolved problem in mathematics: the Riemann Zeta conjecture. This bold guess about the solutions to a certain complex-valued infinite series (made by the incomparable Bernhard Riemann in 1859) would, if true, have far-reaching implications for the structure of the most basic of entities, the natural numbers. Before an eager audience of hundreds of mathematicians at Columbia University in 1959, Nash presented his results: a farrago of mathematical lunacy. “Nash’s talk wasn’t good or bad,” said one mathematician present. “It was horrible.” Some weeks before, Nash had declined a University of Chicago offer of an endowed chair on the grounds that he was scheduled to become the emperor of Antarctica.

Such ebullitions of insanity continued for three decades, becoming more rococo. Nash went to Europe to form a world government, attempting repeatedly to renounce his U.S. citizenship. He did stints in tony asylums, hanging out with Robert Lowell, and in dismal state institutions, where he was subjected daily to insulin-induced comas. He believed himself to be a Palestinian refugee called C.O.R.P.S.E.; a great Japanese shogun, C1423; Esau; the prince of peace; *l’homme d’Or*; a mouse. As Nasar observes, his delusions were weirdly inconsistent. He felt himself simultaneously to be the epicenter of the universe–“I am the left foot of God on earth”–and an abject, persecuted petitioner.

He returned to the Princeton area in the 1970s, where he was taken care of by the long-suffering Alicia, now his ex-wife (she supported him partly through computer programming, partly on welfare). He haunted the campus, where students began to call him “the Phantom.” They would come to class in the morning to find runic messages he had written on the blackboard at night: “Mao Tse-Tung’s Bar Mitzvah was 13 years, 13 months, and 13 days after Brezhnev’s circumcision.”

Then, in the ‘90s, inexplicably, the voices in Nash’s head began to quiet down. (Nasar gives an interesting account of just how rare such remissions are among those diagnosed with schizophrenia.) At the same time, the Nobel committee in Stockholm was deciding it was about time to award the prize in economics for game theory. Dare they make a known madman into a laureate? What might he say to King Gustav at the ceremony? Nasar shows her mettle as a reporter here by penetrating the veil of secrecy surrounding the Nobel and revealing the back-stage machinations for and against Nash’s candidacy. He did fine at the ceremony, by the way.

Indeed, he has evolved into a “very fine person,” according to his ex-wife–humbled by years of psychotic helplessness, buoyed up by the intellectual world’s highest accolade. The Nobel has a terrible effect on the productivity of many recipients, paralyzing them with greatness. For Nash it was pure therapy. Then, too, there is the need to take care of his son by Alicia, who–pleiotropically?–inherited both his mathematical promise and his madness. (His older son, the one born out of wedlock, got neither.) The Nobel money bought a new boiler for the little bungalow across from the Princeton train station inhabited by this shaky menage. (When *Vanity Fair* published an excerpt of *A Beautiful Mind*, Nash probably became the only person ever featured in that magazine to live in a house clad in “insulbrick.”)

The eeriest thing I discovered while reading this superb book was that Nash and I came within a couple of years of crossing paths in a Virginia mental hospital. I was actually *working* there, but psychiatric aides pick up so many mannerisms of the patients that it’s hard to tell the difference after a while. A few years after that I found myself in a mathematics Ph.D. program. You’ll be glad to know that I’m in remission.