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S. John Forbes Nash, Jr. (born June 13, 1928) is an American mathematician whose works in game theory, differential geometry, and partial differential equations have provided insight into the forces that govern chance and events inside complex systems in daily life.
His theories are used in market economics, computing, evolutionary biology, artificial intelligence, accounting, politics and military theory.
Serving as a Senior Research Mathematician at Princeton University during the latter part of his life, he shared the 1994 Nobel Memorial Prize in Economic Sciences with game theorists Reinhard Selten and John Harsanyi.
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.
 I later spent times of the order of five to eight months in hospitals in New Jersey, always on an involuntary basis and always attempting a legal argument for release.
And it did happen that when I had been long enough hospitalized that I would finally renounce delusional hypotheses and revert to thinking of myself as a human of more conventional circumstances and return to mathematical research.
In these interludes of, as it were, enforced rationality, I did succeed in doing some respectable mathematical research. Thus there came about the research for "Le problème de Cauchy pour les équations différentielles d'un fluide général"; the idea that Prof.
Hironaka called "the Nash blowing-up transformation"; and those of "Arc Structure of Singularities" and "Analyticity of Solutions of Implicit Function Problems with Analytic Data".
But after my return to the dream-like delusional hypotheses in the later 60's I became a person of delusionally influenced thinking but of relatively moderate behavior and thus tended to avoid hospitalization and the direct attention of psychiatrists.
Thus further time passed. Then gradually I began to intellectually reject some of the delusionally influenced lines of thinking which had been characteristic of my orientation.
This began, most recognizably, with the rejection of politically-oriented thinking as essentially a hopeless waste of intellectual effort.
 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, born Margaret Virginia Martin and known as Virginia, had been a schoolteacher before she married. Both parents pursued opportunities to supplement their son's education, providing him with encyclopedias and even allowing him to take advanced mathematics courses at a local college while still in high school.
" 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.  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.  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: Nash, JF (1950), "Equilibrium Points in N-person Games", Proceedings of the National Academy of Sciences 36 (36): 48–9, doi:10.
 Nash began to show signs of extreme paranoia and his wife later described his behavior as erratic, as he began speaking of characters like Charles Herman and William Parcher who were putting him in danger. Nash seemed to believe that all men who wore red ties were part of a communist conspiracy against him.Nash mailed letters to embassies in Washington, D. C. , declaring that they were establishing a government.
 He was admitted to the McLean Hospital, April–May 1959, where he was diagnosed with paranoid schizophrenia. The clinical picture is dominated by relatively stable, often paranoid, fixed beliefs that are either false, over-imaginative or unrealistic, usually accompanied by experiences of seemingly real perception of something not actually present — particularly auditory and perceptional disturbances, a lack of motivation for life, and mild clinical depression.