Nash was born at Bluefield, West Virginia. His father was an electrical engineer and his mother was a teacher. He originally studied chemical engineering at Carnegie Tech. in Pittsburgh but moved courses, first to chemistry and then, encouraged by the mathematics faculty, to mathematics.

Nash then entered Princeton on a fellowship as a graduate student. At Carnegie he had taken a course on international economics and this had led to a paper on what he called ‘The Bargaining Problem’. At Princeton, he developed this further using the ideas of game theory first discussed by von Neumann and Morgenstern. The result was Nash's theory of non-cooperative games, which he wrote up for his PhD thesis. The theory, which could be applied to any finite number of players, later found applications in economics.

Nash was not certain that this work would be an acceptable topic for a thesis and, during this period, he also made certain discoveries in pure mathematics concerning manifolds. This work was published later when he was an instructor at the Massachusetts Institute of Technology, a post he took up in 1951. At MIT he also worked on problems in differential geometry, which were relevant to general relativity theory.

At this point Nash seemed set for a brilliant mathematical career but, early in 1959, he began to suffer mental problems. In his own words, it was “the time of my change from scientific rationality of thinking into the delusional thinking characteristic of persons who are psychiatrically diagnosed as ‘schizophrenic’ or ‘paranoid schizophrenic’”. He resigned his academic post and spent periods in mental hospitals. After some 25 years Nash appeared to have recovered and to have started serious mathematical work again. In 1997 he was awarded the Nobel Prize for economics for the work he had done as a young man many years before on noncooperative game theory. He was awarded the Abel Prize for 2015 along with Louis Nirenberg “for striking and seminal contributions to the theory of nonlinear partial differential equations and its applications to geometric analysis.”