A BEAUTIFUL MIND

By Sylvia Nasar.

Illustrated. 459 pp. New York:

Simon & Schuster. $25.



athematics is a young man's game," the mathematician Norbert Wiener wrote, "yet it is not bearable to contemplate a brief distinction and burgeoning of activity ... followed by a lifetime of boredom."

John Forbes Nash Jr., a mathematician who had a genius for solving hard problems in his own distinctive way, found an unusual solution for this one, too. After the dazzling achievements of his youth, he simply departed from the realm of consensual reality.

He lived in a superheated world of schizophrenic delusions for the better part of 30 years. Then he emerged, at least as sane as the average mathematician, just in time to accept, graciously, the 1994 Nobel Prize in Economics.

The story brings to mind the pianist David Helfgott and the movie "Shine." Sylvia Nasar, an economics correspondent for The New York Times, has written a biography of Nash that reads like a fine novel.

Reared in blue-collar Bluefield, W.Va., Nash won a Westinghouse scholarship that brought him to Carnegie Tech, where his mathematical ability paved the way to graduate school at Princeton.

In 1948, Fine Hall at Princeton was for mathematicians what Paris had once been for painters and novelists; the air was so thick with mathematical ideas that, in the words of Einstein's assistant Leopold Infeld, if you put out your hand, you would find "a few formulae are stuck to your palm."

The Protestant Nash, out of place in this largely Jewish setting but not lacking in mathematical talent, wound up graduating on the basis of a slender, 27-page doctoral thesis on the theory of competitive games. It would eventually win him that Nobel Prize, but it was not good enough to get him the position he coveted at Princeton or Harvard.



JOHN FORBES NASH JR., 1994. Credit: Dick Pettersson/Upsala Nya Tidning, from "A Beautiful Mind"

Now in his 20s, he proceeded to knock off a number of impressive theorems, working in an intuitive style in which he saw the result before he could provide the detailed steps. While an MIT colleague named Warren Ambrose wrote a meticulous proof on the blackboard, Nash could be heard muttering "hack, hack" from the back of the room. Perhaps out of revenge, Ambrose asked Nash, "Is it possible to embed any Riemannian manifold in a Euclidian space?"

Ms. Nasar never really explains what that means, but it doesn't matter. Having satisfied himself that it was a problem worthy of his talents, Nash went after it with relentless tenacity, producing at the end of two years what a Princeton mathematician called "one of the most important pieces of mathematical analysis in this century." Mathematicians consider the Nobel-winning work trivial by comparison.

During this same period, Nash had two homosexual relationships that left deep emotional traces; managed to get arrested in a sting operation by the police in Santa Monica, Calif., which cost him his summer consulting job at the Rand Corp.; took a mistress whom he treated with casual, selfish cruelty, a practical nurse named Eleanor Stier, who bore him a son named John; and finally married a beautiful, aristocratic Salvadoran named Alicia Larde, a rare female physics major at MIT.

By the age of 30, he narrowly missed the Fields Medal, the highest honor in mathematics, but he was awarded tenure at MIT, and he had begun his inexorable descent into madness. He had, with Alicia, another son, also named John, who later turned out to be both a formidable mathematician and a paranoid schizophrenic.

Nash resigned his tenured position almost as soon as he'd gotten it, tried to give up his American citizenship, managed to get himself expelled from both Switzerland and France, and suffered a series of involuntary hospitalizations that put him at the mercy of psychiatric crudities like insulin shock therapy.

Nash was tall, handsome, muscular and witty when he courted Alicia in the mid-50s. By the summer of 1960, "he would go into restaurants with bare feet," Ms. Nasar writes. "With dark hair to his shoulders and a bushy black beard, he had a fixed expression, a dead gaze. Women, especially, found him frightening."

During a remission in the 1960s, he managed to write a couple of quite good scientific papers, but the relief was only temporary.

Although he and Alicia were divorced in 1963, she took him back as a boarder in 1970, because no one else would. Given the stable domestic arrangement provided by the hard-working Alicia, he became the gentle ghost of Fine Hall, harmlessly haunting the library and computer room and very gradually drifting back in the general direction of sanity. Nash learned, he says, to discard the paranoid thoughts the way a dieter stays off sweets.

Ms. Naser has managed to tease out the super-secret story of the deliberations at the Swedish Academy that led to Nash's Nobel Prize. This set piece alone will be a feast for Nobel junkies, full of drama, politics and snobbery. The controversy was so bitter, it almost put an end to the economics prize.

She has a special knack for recreating the atmosphere of places like Fine Hall, and for thumbnail sketches of the characters who march through these pages, including many giants of 20th-century mathematics. If you don't know what a Nash equilibrium is, you won't understand it after reading this book, but that hardly detracts from the pleasure it gives.

There are numerous loose ends. (Alicia at one point is pregnant with a second child who is never mentioned again.) But in a messy life like Nash's, there are bound to be loose ends.

By the end of the book he no longer has to wonder whether he will be permitted to enter the Princeton Faculty Club. The rest of us feel as if we've been sitting there all along, happily gossiping about him.

