John Forbes Nash

John Forbes Nash Jr. (English: John Forbes Nash Jr., June 13, 1928 - May 23, 2015), often called John Nash, was an American mathematician and former Moore Honorary Lecturer at MIT. He mainly studied game theory, differential geometry and partial differential equations. In his later years, he was a senior research mathematician at Princeton University. In 1950, Nash received a doctorate from Princeton University in the United States. He proposed an important concept in a doctoral thesis of only 28 pages, which became an important breakthrough in game theory. This concept is called "Nash equilibrium" and is widely used in economics, computer science, evolutionary biology, artificial intelligence, accounting, policy and military theory. In 1994, he and two other game theorists, John Harsanyi and Reinhard Selten, won the Nobel Prize in Economic Sciences. Nash's most important mathematical achievements were in the fields of differential geometry and partial differential equations, especially the results of isometric embedding of Riemannian manifolds into Euclidean space. For his contributions to nonlinear partial differential equations, he jointly received the 2015 Abel Prize with Louis Nirenberg. Geometer Mikhail Gromov commented on Nash's work: "He had tremendous analytical (referring to mathematical analysis) ability combined with geometric insight. ... His geometric work, whether it is his results, techniques, or ideas used, were contrary to anyone's original expectations. ... What he did in geometry, in my opinion, is incomparably much greater than what he did in economics, by many orders of magnitude." After 1959, his research career was interrupted due to the emergence of mental symptoms. He entered the hospital for recuperation twice in 1959 and 1961 and was diagnosed with schizophrenia. Nash refused to receive psychotropic medication. After 1970, his symptoms gradually improved and he returned to academic research. His experiences during this period were written as a biography by Sylvia Nasa and remade into the movie "Beautiful Realm", making his deeds widely known.