# John Nash

**Topics:**Game theory, Nash equilibrium, Carnegie Mellon University

**Pages:**6 (1861 words)

**Published:**November 6, 2010

Nash is the subject of the Hollywood movie A Beautiful Mind. The film, loosely based on the biography of the same name, focuses on Nash's mathematical genius and struggle with paranoid schizophrenia.[1][2] Contents

Early life

Nash was born on June 13, 1928 in Bluefield, West Virginia. His father, after whom he is named, was an electrical engineer for the Appalachian Electric Power Company. His mother, Margaret, had been a school teacher prior to marriage. Nash's parents pursued opportunities to supplement their son's education with encyclopedias and even allowed him to take advanced mathematics courses at a local college while still in high school. Nash accepted a scholarship to Carnegie Institute of Technology (now Carnegie Mellon University) and graduated with a Master's Degree in only three years.[3] Post-graduate life

Nash's advisor and former Carnegie Tech professor, R.J. Duffin, wrote a letter of recommendation consisting of a single sentence: "This man is a genius."[4] Nash was accepted by Harvard University, but the chairman of the mathematics department of Princeton, Solomon Lefschetz, offered him the John S. Kennedy fellowship, which was enough to convince Nash that Harvard valued him less.[5] Thus he went to Princeton where he worked on his equilibrium theory. He earned a doctorate in 1950 with a 28 page dissertation on non-cooperative games.[6] 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". These studies led to four articles:

* "Equilibrium Points in N-person Games", Proceedings of the National Academy of Sciences 36 (1950), 48–49. MR0031701 * "The Bargaining Problem", Econometrica 18 (1950), 155–162. MR0035977 * "Non-cooperative Games", Annals of Mathematics 54 (1951), 286–295. [1] * "Two-person Cooperative Games", Econometrica 21 (1953), 128–140. MR0053471

Nash did ground-breaking work in the area of real algebraic geometry:

* "Real algebraic manifolds", Annals of Mathematics 56 (1952), 405–421. MR0050928 See Proc. Internat. Congr. Math. (AMS, 1952, pp 516–517).

His most famous work in mathematics is the Nash embedding theorem, which shows that any abstract Riemannian manifold can be isometrically realized as a submanifold of Euclidean space. He made contributions to the theory of nonlinear parabolic partial differential equations, and to singularity theory. Personal life

Per Nash's biography, from 1951 onwards, he had a liaison with a nurse, named Eleanor Stier. She bore a child named John David Stier. Though Nash had thought of marrying her, he later decided against it and left them.

In 1955, Nash went to the Massachusetts Institute of Technology as a C. L. E. Moore Instructor in the mathematics faculty. There, he met Alicia López-Harrison de Lardé (born January 1, 1933), a physics student from El Salvador, whom he married in February 1957. She admitted Nash to a mental hospital in 1959 for schizophrenia; their son, John Charles Martin Nash, was born soon afterward, but remained nameless for a year because his mother felt that her husband should have a say in the name.

Nash and de Lardé divorced in 1963, though after his final hospital discharge in 1970 Nash lived in de Lardé's house. In 1994 Nash won the Nobel Memorial...

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