# John Forbes Nash

# John Forbes Nash

**1928-**

**American Mathematician**

Mathematician John Forbes Nash was born in Bluefield, West Virginia. He undertook his undergraduate work at Carnegie Mellon University, and his graduate work at Princeton. At age 22 Nash earned his doctorate with papers and a thesis on non-cooperative games.

Nash's thesis work established the theory of equilibria in non-cooperative games, earning him a share of the 1994 Nobel Prize for Economics nearly half a century later. Nash received the Nobel Prize with Hungarian-American economist John C. Harsanyi and German mathematician Reinhard Selten. The Nobel Prize for Economics is designated to recognize substantial and important contributions to political science, psychology, and sociology.

The brilliance of Nash's work was obscured by a three-decade-long battle with paranoid schizophrenia. Despite frequent hospitalizations and the sometimes debilitating symptoms of his illness, Nash continued his work whenever able. However, though Nash strove to continue the excellence of his research, his personal and professional life suffered from his illness. He had a short faculty tenure at MIT until his illness forced him to resign his post. During the height of Cold War political paranoia in McCarthy-era America, Nash lost his security clearance and an opportunity to work for several strategic think-tanks that employed eminent mathematicians outside of academia.

During the late 1950s and early 1960s, Nash eventually faced destitution and homelessness until his ex-wife and friends within the mathematical community brought him back to Princeton, where Nash worked in obscurity while he maintained tenuous and informal links to the scholarly community between hospitalizations for his illness. By 1970 Nash had became an enigmatic figure on the Princeton campus. Nash would leave mathematical notations and writings scrawled on empty classroom blackboards in the Princeton mathematics building.

The significance of Nash's work was not limited to mathematics. Non-cooperative game theory is viewed by many as one of the most important developments in twentieth-century economic and social science. Game theory has found application in the development of strategy for modern warfare, governmental science (including political campaigns and lobbying efforts), and business strategy.

In essence, game theory is a division of mathematics that sets out theories regarding the behavior of rival competitors operating with a mixture of interests and goals. Nash provided a solution—known now as the Nash equilibrium—that allowed prediction of the dynamic interchange of needs, wants, and threats among competitors. Most importantly, game theory offers important insights into how people and entities (governments and corporations) arrange affairs and make strategic choices.

Critics of game theory, however, contend that its influence is still debatable and that one of the great flaws of the theory is its inability to make predictions in addition to offering explanations of human behavior (for example, how players react). Some critics contend that game theory, rather than being broadly applicable, is relevant to only a few selected problems that have a limited number of competitors. Other critics contend that game theory is incompatible with the idea of free economic competition because the theory assumes an inability of players to influence eventual outcomes.

Supporters of game theory maintain that it is a useful tool for both simple and complex problems, and cite the successful incorporation of game theory in the lucrative action of telecommunication frequencies in the 1990s.

Despite the recognition accorded as a Nobel laureate, many scholars contend that social and academic prejudices regarding Nash's illness prevented him from receiving greater acclaim for work that influenced two generations of scholars in the formulation of mathematical models concerning human conflict and cooperation. Game theory, supporters contend, offers the best opportunity to study economic behavior ranging from price wars to illegal collusion.

Prior to receiving the Nobel Prize, Nash made a sudden recovery from his illness. In addition to his work on game theory, he made significant contributions to the study of real algebraic varieties, differential equations, and geometry.

**ADRIENNE WILMOTH LERNER**

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**John Forbes Nash**