John Forbes Nash

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John Forbes Nash Jr.

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

The winner of a Westinghouse scholarship, he attended the Carnegie Institute of Technology, where he received both his bachelor's degree and his master's degree in 1948. 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:

"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):

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

This work led to Nash embedding theorem.."Two real algebraic manifolds are equivalent if and only if they are analytically homeomorphic." [1]

He is best known in popular culture as the subject of the Hollywood movie, A Beautiful Mind, about his mathematical genius and his struggles with mental illness.