John F. Nash, Jr.

Brief Biography

John Forbes Nash, Jr. was a Nobel Prize-winning mathematician whose contributions to the theory of games have had a significant influence on operations research. Born in Bluefield, West Virginia, Nash was the son of an electrical engineer and a former school teacher. He attended Carnegie Institute of Technology in Pittsburgh, originally hoping to study engineering before switching to chemistry and, finally, mathematics. The university’s faculty refereed to him as “a young Gauss”. His supervisor, Richard J. Duffin, wrote a single sentence for Nash’s graduate school letters of recommendation, simply stating: “This man is a genius.” In 1948, Nash enrolled at Princeton University. During his second year as a Princeton graduate student, Nash extended John von Neumann’s minimax theorem for two-person zero sum games. 

Game theory in the 1930s and 1940s was treated as hardly more than an extension of linear inequalities. Nash, however, adopted a different viewpoint. He proved that every finite, n-person, non-cooperative game has at least one equilibrium outcome in mixed strategies. Such an outcome is known as a Nash Equilibrium.   The concept behind the Nash Equilibrium, a collection of strategies by the various players such that no one player can improve the outcome by changing only his  own strategy,  has seen broad applicability in economics, military strategy, political science, the auctioning of radio spectrum,  and even in evolutionary biology. His proof in his dissertation and subsequent papers beautifully applied existing topological fixed point theorems to game theory.

Though there were some issues with the original proofs, Nash’s contributions were solidified when Carlton Lemke and J. T. Howson, Jr devised an ingenious algorithm for the bimatrix case. For opening a new chapter in the theory and practice of games and mathematical programming, Nash was presented the John von Neumann Theory Prize by the Operations Research Society of America in 1978.

Nash finished his dissertation, Non-Cooperative Games, in 1950 under the supervision of Albert W. Tucker. He remained at Princeton for another two years in order to refine his mathematical skills before moving to the Massachusetts Institute of Technology. Nash spent the summers of 1950, 1952, and 1954 as a consultant for the RAND Corporation in Santa Monica, California. Here he dealt with the military application of game theory. Although he was dismissed in 1954 following his arrest in a police operation designed to entrap homosexuals, he continued an association with RAND into the 1960s and 1970s, going through their channels to share the designs of a proposed (but ultimately rejected) computational system with the National Security Agency. Nash resigned his position at MIT in 1959 after being diagnosed as a paranoid schizophrenic.

From 1959 to 1970, Nash moved around to a variety of institutions across the globe, receiving continued care for his condition. From 1960 to 1965, he held a position at Princeton University and with the associated Institute for Advanced Study. He spent the next two years working on research papers at Brandeis University in Boston before moving-in with his mother in Roanoke, Virginia. After his mother’s death in 1970, Nash returned to Princeton, where he became known as the "Phantom of Fine Hall," the mathematics building. Slowly over time, he recovered from his mental illness, and made additional contributions to mathematics beyond the realm of economics and operations research.

Nash was propelled to the spotlight in 1994 when he was jointly awarded the Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel (the Nobel Prize in Economics) with John C. Harsanyi and Reinhard Seltein for “pioneering analysis of equilibria in the theory of non-cooperative games”. His nomination for the award was supported by a group of individuals that included close friend and colleague, Harold Kuhn.

In 2001, renowned film director Ron Howard took Nash’s biography, A Beautiful Mind, by Sylvia Nasar, to the big screen. The film stared decorated actor Russell Crowe as Nash and received eight Academy Award nominations. It won four Oscars, including Best Picture and Best Adapted Screenplay. Kuhn served as the mathematics consultant on the firm.

Nash received numerous other accolades including the Double Helix Prize, the Leroy P. Steele Prize of the American Mathematical Society, and the Abel Mathematics Prize. He was an inaugural fellow of AMS and the Institute for Operations Research and the Management Sciences.  Nash and his wife were killed in a car accident on May 23, 2015. 

Other Biographies

Wikipedia Entry for John Forbes Nash, Jr.

Karstensson L. (2002) Biographical Notes on John Forbes Nash, Jr. (1928 - ). 

A Biographical Note on John Forbes Nash Jr.

Luchetti R. (2011) John F. Nash, Jr. Bartocci C., Betti R., Guerragio A., & Luchetti R. eds. in Mathematical Lives, 137-146. Springer: New York.

Milnor J. (1998) John Nash and "A Beautiful Mind". Notice of the American Mathematical Society, 45(10): 1329-1332. (link)

Nasar S. (1998) A Beautiful Mind. Simon & Schuster: New York.

PBS American Experience. A Brilliant Madness: John Nash (1928 - ). Accessed July 6, 2017. (link)

University of St. Andrews School of Mathematical and Computer Sciences. Nash Biography. Accessed April 2, 2015. (link)

John Nash (2004) Interview by Marika Grieshel, September 1. 1st Meeting of Laureates in Economic Sciences. Lindau, Germany. (video)

PBS American Experience. Brilliant Madness: Supplementary Interview with John Nash. Accessed April 2, 2015. (link)

John Nash (2012) Interview by Harold Kuhn, November 27, 2011.  Simons Foundation Science Lives.  Accessed October 4, 2018 (link)