John Forbes Nash

John Forbes Nash Jr. (born June 13, 1928) is an American mathematician who works in game theory and differential geometry. He shared the 1994 Bank of Sweden Prize in Economic Sciences with two other game theorists, Reinhard Selten and John Harsanyi.

Education

From June 1945-June 1948 Nash studied at the Carnegie Institute of Technology in Pittsburgh (now Carnegie Mellon University), intending to become an engineer like his father. Instead, he developed a deep love for mathematics and what became a lifelong interest in subjects such as number theory, Diophantine equations, quantum mechanics and relativity theory.

Related Topics:
1945 - 1948 - Carnegie Institute of Technology - Pittsburgh - Carnegie Mellon University - Mathematics - Number theory - Diophantine equations - Quantum mechanics - Relativity theory

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He loved solving problems. At Carnegie he became interested in the 'negotiation problem', which John von Neumann had left unsolved in his book The Theory of Games and Economic Behavior (1944), and participated in the game theory group there. His theory, now called the Nash equilibrium, is an extension of the minimax theorem stated earlier by John Von Neumann in 1928.

Related Topics:
John von Neumann - 1944 - Game theory - Nash equilibrium - Minimax theorem - 1928

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From Pittsburgh he went to Princeton University where he worked on his equilibrium theory. He received a Ph.D. in 1950 with a dissertation on non-cooperative games. The thesis, which was written under the supervision of Albert W. Tucker, contained the definition and properties of what would later be called the Nash equilibrium. His studies on this subject led to three articles:

Related Topics:
Princeton University - Ph.D. - 1950 - Albert W. Tucker - Nash equilibrium

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• 'Equilibrium Points in N-person Games', published in the Proceedings of the National Academy of Sciences (USA) (1950);
• The Bargaining Problem (April 1950) in Econometrica, and
• Two-person Cooperative Games (January 1953), also in Econometrica.

John Nash also did important work in the area of Manifolds (complex spatial structures):

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• Real algebraic manifolds, (1952) Ann. Math. 56 (1952), 405?421. (See also Proc. Internat. Congr. Math., 1950, (AMS, 1952), pp. 516?517.)

This work lead to Nash's Embedding Theorem.."Two real algebraic manifolds are equivalent iff they are analytically homeomorphic."

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