A BEAUTIFUL MIND, by Sylvia Nasar. Simon & Schuster, 459 pp., $25.

On an October afternoon in 1994, the mathematician John Nash gave a brief speech at a

champagne party in Princeton's Fine Hall that was being held to celebrate his

Nobel Prize in economics. Unaccustomed to addressing such gatherings, he spoke

with a frankness one seldom hears on these occasions. He praised game theory -

for which he had been awarded the prize - in an ironic tone that betrayed his

skepticism about the field's ultimate importance. Now that he had won the Nobel,

he added, he hoped he could finally get a credit card. And although he knew he

was supposed to say he was happy to share the prize with two other recipients,

he confessed that he wished he alone had won it since he was in desperate

financial straits.

Aside from Nash's bluntness, the most remarkable thing about his speech was

what he neglected to mention: namely, that he had only recently recovered from a

35-year bout with paranoid schizophrenia - an illness that had left him a ghost

of his former self. Although Nash spent most of that time at Princeton, he was

not a member of the faculty and had not held any academic position since 1958,

when he resigned from MIT to pursue his various delusional quests, such as

establishing a world government and deciphering the encrypted messages sent to

him by aliens and foreign governments. After leaving MIT Nash even rejected a

tenured job at the University of Chicago, because he believed he was about to

become the Emperor of Antarctica. In and out of mental institutions, with brief

periods of semi-lucidity in which his genius came to the fore, Nash was

virtually unknown to those beyond the small circle of mathematicians who looked

after him.

The irony is that during the years that he was mentally incapacitated, his

theory - the "Nash Equilibrium," which showed how a decentralized

decision-making process could, in fact, be coherent - became a virtual fixture

of economics, evolutionary biology, political science and a variety of other

disciplines. Despite his importance, most who heard that he had received the

Nobel knew nothing of his struggle until the publication of New York Times

reporter Sylvia Nasar's fascinating article, which she has now expanded into "A

Beautiful Mind," a completely engrossing study of Nash's life. The book is a

triumph of intellectual biography in which one finds not only the tragic story

of one man's genius, madness and reawakening, but also an intriguing portrait

the arcane world of high-powered mathematics.

Born in Bluefield, W. Va., in 1928, Nash was an odd and intellectually

precocious child who was nicknamed "Big Brains" by his friends. After high

school, he attended the Carnegie Institute of Technology, where he would show

off his prowess by sitting in a chair and fielding math problems other students

hurled at him. Nash was courted by every prestigious graduate school in the

country and decided to study math at Princeton, which was then considered to be

the center of the mathematical universe. As Nasar writes: "Princeton in 1948 was

to mathematics what Paris once was to painters and novelists, Vienna to

psychoanalysts and architects, and ancient Athens to philosophers and

playwrights."

In particular, Princeton was the center of the "game theory" revolution

taking place in mathematics. Two hundred years after Adam Smith's "The Wealth of

Nations" coined the metaphor of the "invisible hand" of economics, Princeton's

mathematicians were attempting to construct a systematic theory of rational

human behavior by using games as an analogy. Drawing on his intuitive

mathematical brilliance, as well as his atomistic vision of humans as "out of

touch with one another and acting on their own," Nash devised an equilibrium

point "where every player independently chose his best response to the other

players' best strategies," writes Nasar.

The fact that a man capable of conceiving of a nuanced theory of rationality

could then descend into madness gives "A Beautiful Mind" an exquisite sense of

dramatic tension. We watch in horror and fascination as the brilliant

mathematician degenerates into a paranoid numerologist (as one colleague tells

it, "One day he called me and started with the date of Krushchev's birth and

worked right through to the Dow Jones average"). "His longstanding conviction

that the universe was rational evolved into a caricature of itself, turning into

an unshakable belief that everything has meaning, everything has a reason,

nothing was random or coincidental," Nasar writes.

Was Nash's madness a break from his genius or simply a tragic, but logical,

continuation of it? This is the question that haunts Nasar's book. Nash claims

to have willed his recovery, to have finally "just said no" to the paranoid

thoughts and imaginary voices that hector him even today. Indeed the

epistemological similarities between Nash's delusions and his academic work is

chilling. When asked how such a great intellectual could have come to believe in

aliens, he replied: "Because the ideas I had about supernatural beings came to

me the same way that my mathematical ideas did. So I took them seriously." That

Nash is currently (in Nasar's well-wrought phrase) "within the normal range for

the mathematical personality' " may say less about John Nash than about the

profession that trained him.

I think it's safe to say that even general readers who consider themselves

fluent in the argot of the culture wars are probably ignorant about developments

in cutting-edge mathematics. Given this, Nasar has made a heroic, and largely

successful, attempt to write about the fine points of game theory and

mathematical arcana in an engaging and accessible style. "A Beautiful Mind" is

the kind of book that makes even a hard-core humanist want to learn a little

more about math.

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