During the academic year of 1956 - 1957 he spends a sabbatical at Princeton.

After gaining his degree, he works as an instructor at Princeton for one year.

During the sabbatical at Princeton (1956–57), Nash meets and marries physics student Alicia Lopez-Harrison de Lardé, who was born in El Salvador. They have a son, John Charles Martin, who also became a mathematician. They get divorced in 1963, but married again in 2001.

John Nash shares the 1994 Economics Nobel Prize with John Harsanyi and Reinhard Selten, "for their pioneering analysis of equilibria in the theory of non-cooperative games". In the late 1980s, Nash had begun to use email to gradually link with working mathematicians They formed part of a group that contacted the Nobel committee and vouched for Nash's mental health ability to receive the award in recognition of his early work.

He enters Carnegie Tech in Pittsburgh as a chemical engineering student but soon shifts to chemistry and then to mathematics, flourishing to the extent that he is awarded an MSc as well as his BSc when he graduates. While in Carnegie, he takes a course in economics and as a result writes the paper The Bargaining Problem. This is the start of his game theory studies.

According to himself, Nash is "thinking rationally again in the style that is characteristic of scientists," though he says he also feels more limited. Today John Nash continues his mathematical research at the department of Mathematics at the university of Princeton. His research interests include logic, game theory, cosmology and gravitation. He has also developed work on the role of money in society.

In 1951 he joins the M.I.T. mathematics faculty. There he publishes his work about Real Algebraic Manifolds, which he actually regards as his best work.

John Nash in born on June 13, 1928, in Bluefield, West Virginia. He has a younger sister, Martha. By the time Nash is a high school student he reads advanced mathematics books and proves the classic Fermat theorem. His parents spot his potential and arrange extra lessons.

From 1950 to 1954, Nash spends his summers as a consultant for the RAND corporation, a US think tank. There he works on applying game theory to strategic situations in the Cold War.

Nash is offered fellowships from both Harvard and Princeton and opts for the latter. In Princeton, he develops his ideas about Non-Cooperative Games, and he also makes a mathematical discovery relating to manifolds and real algebraic varieties. With his game theory work, he gains his PhD after just two years in 1950. His theory of non-cooperative games explains the dynamics of threat and action among competitors.

In the spring of 1959, Nash is diagnosed with paranoid schizophrenia and resigns from M.I.T.. He recovers gradually with the passage of time. In his interludes of rationality he continues his mathematical research. The movie “A Beautiful mind” is loosely based on his biography.