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**John Forbes Nash Jr. was an American mathematician who made fundamental contributions to game theory, differential geometry, and the study of partial differential equations. **

Differential geometry is a mathematical discipline that uses the techniques of differential calculus, integral calculus, linear algebra and multilinear algebra to study problems in geometry.

In mathematics, a partial differential equation is a differential equation that contains unknown multivariable functions and their partial derivatives.

A mathematician is someone who uses an extensive knowledge of mathematics in his/her work, typically to solve mathematical problems.

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**Nash's work has provided insight into the factors that govern chance and decision-making inside complex systems found in everyday life.
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A complex system is a system composed of many components which may interact with each other.

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**His theories are widely used in economics. **

Economics is a social science concerned with the factors that determine the production, distribution, and consumption of goods and services.

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**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. **

The Nobel Memorial Prize in Economic Sciences, commonly referred to as the Nobel Prize in Economics, is an award for outstanding contributions to the field of economics, and generally regarded as the most prestigious award for that field.

Reinhard Justus Reginald Selten was a German economist, who won the 1994 Nobel Memorial Prize in Economic Sciences.

Princeton University is a private Ivy League research university in Princeton, New Jersey, United States.

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**In 2015, he also shared the Abel Prize with Louis Nirenberg for his work on nonlinear partial differential equations.
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The Abel Prize is a Norwegian prize awarded annually by the Government of Norway to one or more outstanding mathematicians.

Louis Nirenberg is a Canadian American mathematician, considered one of the outstanding analysts of the 20th century.

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**John Nash is the only person to be awarded both the Nobel Memorial Prize in Economic Sciences and the Abel Prize.
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**In 1959, Nash began showing clear signs of mental illness, and spent several years at psychiatric hospitals being treated for paranoid schizophrenia. **

Psychiatric hospitals, also known as mental hospitals, mental asylums or simply asylums, are hospitals or wards specializing in the treatment of serious mental illness, such as clinical depression, schizophrenia, and bipolar disorder.

Schizophrenia is a mental disorder characterized by abnormal social behavior and failure to understand what is real.

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**After 1970, his condition slowly improved, allowing him to return to academic work by the mid-1980s. **

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**His struggles with his illness and his recovery became the basis for Sylvia Nasar's biography, A Beautiful Mind, as well as a film of the same name starring Russell Crowe as Nash.
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Sylvia Nasar is a Uzbek German-born American journalist, best known for her biography of John Forbes Nash, Jr., A Beautiful Mind.

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**On May 23, 2015, Nash and his wife Alicia were killed in a car crash while riding in a taxi on the New Jersey Turnpike.**

The New Jersey Turnpike, known colloquially as "the Turnpike", is a toll road in New Jersey, maintained by the New Jersey Turnpike Authority.