Excerpt from A Beautiful Mind by Sylvia Nasar, plus links to reviews, author biography & more

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A Beautiful Mind

The Life of Mathematical Genius and Nobel Laureate John Nash

By Sylvia Nasar

A Beautiful Mind

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While Nash the man remained frozen in a dreamlike state, a phantom who haunted Princeton in the 1970s and 1980s scribbling on blackboards and studying religious texts, his name began to surface everywhere -- in economics textbooks, articles on evolutionary biology, political science treatises, mathematics journals. It appeared less often in explicit citations of the papers he had written in the 1950s than as an adjective for concepts too universally accepted, too familiar a part of the foundation of many subjects to require a particular reference: "Nash equilibrium," "Nash bargaining solution," "Nash program," "De Giorgi-Nash result," "Nash embedding," "Nash-Moser theorem," "Nash blowing-up." When a massive new encyclopedia of economics, The New Palgrave, appeared in 1987, its editors noted that the game theory revolution that had swept through economics "was effected with apparently no new fundamental mathematical theorems beyond those of von Neumann and Nash."

Even as Nash's ideas became more influential -- in fields so disparate that almost no one connected the Nash of game theory with Nash the geometer or Nash the analyst -- the man himself remained shrouded in obscurity. Most of the young mathematicians and economists who made use of his ideas simply assumed, given the dates of his published articles, that he was dead. Members of the profession who knew otherwise, but were aware of his tragic illness, sometimes treated him as if he were. A 1989 proposal to place Nash on the ballot of the Econometric Society as a potential fellow of the society was treated by society officials as a highly romantic but essentially frivolous gesture -- and rejected. No biographical sketch of Nash appeared in The New Palgrave alongside sketches of half a dozen other pioneers of game theory.

At around that time, as part of his daily rounds in Princeton, Nash used to turn up at the institute almost every day at breakfast. Sometimes he would cadge cigarettes or spare change, but mostly he kept very much to himself, a silent, furtive figure, gaunt and gray, who sat alone off in a corner, drinking coffee, smoking, spreading out a ragged pile of papers that he carried with him always.

Freeman Dyson, one of the giants of twentieth-century theoretical physics, one-time mathematical prodigy, and author of a dozen metaphorically rich popular books on science, then in his sixties, about five years older than Nash, was one of those who saw Nash every day at the institute. Dyson is a small, lively sprite of a man, father of six children, not at all remote, with an acute interest in people unusual for someone of his profession, and one of those who would greet Nash without expecting any response, but merely as a token of respect.

On one of those gray mornings, sometime in the late 1980s, he said his usual good morning to Nash. I see your daughter is in the news again today, Nash said to Dyson, whose daughter Esther is a frequently quoted authority on computers. Dyson, who had never heard Nash speak, said later: "I had no idea he was aware of her existence. It was beautiful. I remember the astonishment I felt. What I found most wonderful was this slow awakening. Slowly, he just somehow woke up. Nobody else has ever awakened the way he did."

More signs of recovery followed. Around 1990, Nash began to correspond, via electronic mail, with Enrico Bombieri, for many years a star of the Institute's mathematics faculty. Bombieri, a dashing and erudite Italian, is a winner of the Fields Medal, mathematics' equivalent of the Nobel. He also paints oils, collects wild mushrooms, and polishes gemstones. Bombieri is a number theorist who has been working for a long time on the Riemann Hypothesis. The exchange focused on various conjectures and calculations Nash had begun related to the so-called ABC conjecture. The letters showed that Nash was once again doing real mathematical research, Bombieri said:

He was staying very much by himself. But at some point he started talking to people. Then we talked quite a lot about number theory. Sometimes we talked in my office. Sometimes over coffee in the dining hall. Then we began corresponding by e-mail. It's a sharp mind...all the suggestions have that toughness...there's nothing commonplace about those....Usually when one starts in a field, people remark the obvious, only what is known. In this case, not. He looks at things from a slightly different angle.

A spontaneous recovery from schizophrenia -- still widely regarded as a dementing and degenerative disease -- is so rare, particularly after so long and severe a course as Nash experienced, that, when it occurs, psychiatrists routinely question the validity of the original diagnosis. But people like Dyson and Bombieri, who had watched Nash around Princeton for years before witnessing the transformation, had no doubt that by the early 1990s he was "a walking miracle."

Copyright © 1998 by Sylvia Nasar.

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