Raw genius is often required to intuit the hidden connections between an established mathematical truth and an unsuspected result, and arrogant self-confidence to undertake the formal proof. But the disturbing implication of A Beautiful Mind, a masterful biography of the Nobel Prize-winning mathematician John Nash, is that these same qualities may leave their holders unusually prone to mental illness-especially the mysterious disorder known as paranoid schizophrenia. Unchecked insight detects hidden connections everywhere, Nash’s case suggests, and unchecked egotism spawns grandiose delusions.

Nash was a mathematical prodigy who earned his Ph.D. from Princeton in 1950, at the age of 21. His thesis on game theory transformed the field from an academic curiosity into one of the foundations of modern economics, sociobiology and business strategy. He proved that not only for noncooperative zero-sum games, where players’ interests always conflict, but also for the far more common class of cooperative, non-zero-sum games, where players have both common and conflicting interests, it is always possible to predict each player’s most rational strategy.

By the time Nash was 31, his ingenuity and persistence in the face of daunting problems, as well as his air of superiority and his frequently adolescent behavior, had already made him a legend in the mathematical community. But that was when Nash lost his own grip on rationality. According to this vivid, unsparing account by Sylvia Nasar, an economics correspondent for The New York Times, Nash ceased doing mathematics and fixated on the idea that he should form a world government. He delved deeply into numerology, finding messages meant for him in other people’s names and in newspaper articles, and turned against his wife and family. “Where once he had ordered his thoughts and modulated them,” Nasar writes, “he was now subject to their peremptory and insistent commands”-a good pocket definition of schizophrenia.

Nash’s sudden descent-and the three decades he subsequently spent as a patient in mental hospitals, a world traveler on a bizarre quest for political asylum and a wraith haunting the halls of Princeton-both horrified and fascinated his colleagues. “All you have is your brain,” one former Princeton economics professor told Nasar. “The idea that anything could go wrong with it…[is] threatening for everybody, of course, but for academics that’s all of it.”

Yet Nasar doesn’t let the lurid spectacle of Nash’s mental disintegration eclipse the larger themes in his life that may have prepared the way for his illness: loneliness and fear of intimacy, disdain for social and scholarly conventions, propensity to live in a world inside his own head, repressed homosexuality. And she doesn’t neglect the story’s remarkable dnouement: Nash’s gradual recovery from schizophrenia in the 1980s, and his selection, along with two other pioneers in game theory, as a winner of the 1994 Nobel Prize in economics. This happy conclusion to Nash’s wasted years, so different from the endings of other troubled geniuses such as British mathematician Alan Turing, scores one for hope over despair, and elevates Nasar’s well-told story to the level of high drama.