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A Beautiful Math: John Nash, Game Theory, and the Modern Quest for a Code of Nature
Brilliant but odd, intellectually sophisticated but socially awkward, Nash dazzled the world of mathematics in the 1950s with astounding and original results in several arenas. He rattled the routines at Princeton University and the Rand Corporation in California with both his mental magnificence and his disruptive behavior. By now, the subsequent tragic aspects of Nash’s life story are familiar to millions of people, thanks to the Oscar-winning movie starring Russell Crowe, and Sylvia Nasar’s A Beautiful Mind, the acclaimed book on which the movie was based. Yet while book and movie probed the conflicting complexities in Nash the man, neither delved deeply into Nash’s math. So for most people today, his accomplishments remain obscure. Within the world of science, though, Nash’s math now touches more disciplines than Newton’s or Einstein’s. What Newton’s and Einstein’s math did for the physical universe, Nash’s math may now be accomplishing for the biological and social universe.
Indeed, had mental illness not intervened, Nash’s name might today be commonly uttered in the same breath with those scientific giants of the past. As it is, he made important contributions to a few mathematical specialties. But he achieved his greatest fame in economics, the field in which he shared the 1994 Nobel Prize with John Harsanyi and Reinhard Selten for their seminal work on the theory of games—the math that analyzes how people make choices in contests of strategy.
Game theory originated in efforts to understand parlor games like poker and chess, and was first fully formulated as a mathematical tool for describing economic behavior. But in principle, game theory encompasses any situation involving strategic interaction—from playing tennis to waging war. Game theory provides the mathematical means of computing the payoffs to be expected from various possible choices of strategies. So game theory’s math specifies the formulas for making sound decisions in any competitive arena. As such, it is “a tool for investigating the world,” as the economist Herbert Gintis points out. But it is much more than a mere tool. “Game theory is about how people cooperate as much as how they compete,” Gintis writes. “Game theory is about the