John F. Nash Jr.
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| John F. Nash Jr. | |
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| Name | John F. Nash Jr. |
| Birth date | June 13, 1928 |
| Birth place | Bluefield, West Virginia, United States |
| Death date | May 23, 2015 |
| Death place | Monroe Township, New Jersey, United States |
| Nationality | American |
| Fields | Mathematics, Economics |
| Institutions | Princeton University, Massachusetts Institute of Technology, RAND Corporation, Carnegie Mellon University, Yale University |
| Alma mater | Carnegie Mellon University, Princeton University |
| Doctoral advisor | Alonzo Church |
| Known for | Nash equilibrium, differential geometry, game theory |
John F. Nash Jr. was an American mathematician and economist whose work on non-cooperative game theory transformed economics and influenced evolutionary biology, computer science, sociology, and political science. He produced fundamental results in partial differential equations, differential geometry, and equilibrium concepts that bear his name. His life included a prolonged struggle with schizophrenia and a later recovery that attracted wide attention in both academic and popular culture.
Early life and education
Nash was born in Bluefield, West Virginia and raised in Kingston, West Virginia; his parents were Charles S. Nash and Margaret Virginia Nash. He attended Carnegie Institute of Technology (now Carnegie Mellon University), transferring after initial studies to pursue advanced mathematics; there he encountered faculty such as Norbert Wiener and curricula connected to Princeton University's graduate programs. He received a scholarship to Princeton University where he completed a doctoral dissertation under Alonzo Church on nonlinear partial differential equations and game theory topics. During graduate studies at Princeton University, Nash associated with scholars like John von Neumann, Albert Einstein at nearby institutions, and contemporaries including Paul Erdős and Marston Morse.
Academic career and contributions
Nash held positions at institutions including Massachusetts Institute of Technology, Princeton University, Yale University, and worked as a consultant at the RAND Corporation. His 1950 paper introduced the concept later named the Nash equilibrium, a fixed-point result building on work by Kurt Gödel, Brouwer, and John von Neumann; this concept reshaped economics and informed analyses in evolutionary biology, military strategy, international relations, auction theory, mechanism design, and algorithmic game theory. He made foundational contributions to real algebraic geometry and proved results in differential geometry now associated with embedding theorems that influenced work by Shiing-Shen Chern and S. S. Chern. Nash also produced influential results in nonlinear partial differential equations, contributing to the study of elliptic operators, regularity theory, and problems related to the Navier–Stokes equations and calculus of variations. His collaborations and intellectual intersections included figures like Lars Onsager, Richard H. Weyl, Stephen Smale, Michael Artin, and John Milnor.
Mental health and recovery
In the late 1950s and 1960s Nash experienced a prolonged episode of paranoid schizophrenia, resulting in periods of hospitalization at facilities connected to medical centers in Boston and Newark, New Jersey. His delusions and delusional system drew attention from contemporaries such as Ralph A. Lewin and clinicians influenced by the work of Eugen Bleuler and Emil Kraepelin. During recovery he reduced psychiatric medication and returned to academic life, interacting with colleagues at Princeton University and MIT, and resuming research communications with scholars including John Harsanyi and Reinhard Selten. His recovery and continued work attracted public interest alongside portrayals in media inspired by the biography from Sylvia Nasar and the film directed by Ron Howard featuring actors Russell Crowe and Jennifer Connelly.
Personal life and family
Nash married Alicia Larde in the 1950s; they had a son, John David Stier, and later reconciled after periods of separation. He had relationships and interactions with figures in academic and cultural circles including Harvard University affiliates and fellow mathematicians such as Eugene Wigner and Isadore Singer. His family life intersected with legal and academic institutions in New Jersey and New York City, and his domestic circumstances were affected by his medical treatment and later honors. Nash maintained friendships with colleagues at Princeton University and participated in seminars where attendees included Paul Samuelson, Kenneth Arrow, and Robert Lucas Jr..
Awards and honors
Nash received numerous awards including the Nobel Memorial Prize in Economic Sciences in 1994 shared with John C. Harsanyi and Reinhard Selten for work on equilibrium in non-cooperative games; laureates such as Amartya Sen and Joseph Stiglitz commented on the prize. He was elected to the National Academy of Sciences and received honors from institutions like Princeton University, Harvard University, and Massachusetts Institute of Technology. Other recognitions included the John von Neumann Theory Prize, fellowships linked to the Institute for Advanced Study, and an honorary doctorate from Harvard University; his life and work were documented by Sylvia Nasar in a biography and popularized by creative works including a film by Ron Howard and a score featuring compositions referencing Johann Sebastian Bach and Ludwig van Beethoven.
Death and legacy
Nash and his wife Alicia died in a traffic accident on the New Jersey Turnpike near Monroe Township, Middlesex County, New Jersey in 2015. His mathematical and economic legacy endures across disciplines, influencing researchers in computer science, evolutionary biology, neuroscience, statistics, operations research, finance, political science, and philosophy. Institutions such as Princeton University, the Institute for Advanced Study, and the RAND Corporation continue to teach and develop concepts he championed, and his equilibrium concept remains central in textbooks by authors like Kenneth Arrow, John Rawls, Paul Krugman, and Hal Varian. His life is commemorated in biographies, academic symposia, and curricular materials across departments at universities including MIT, Harvard, Yale University, Stanford University, and University of California, Berkeley.
Category:American mathematicians Category:Nobel laureates in Economics Category:People from West Virginia