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.