John Nash, an American mathematician and Nobel Prize winner for Economics was born in Bluefield, West Virginia on June 13, 1928. He is also known as John Forbes Nash Jr.
His parents Forbes Nash who was an electric engineer and Margaret Virginia, who worked as a school teacher before marriage, played a great role in Nash’s development as a mathematician. They provided him with the Compton’s Pictured Encyclopedia and many scientific books since a very young age through which Nash learned a lot.
After high school, Nash started studying Chemical Engineering at Carnegie Institute of Technology (now known as Carnegie Mellon University) in Pittsburgh on George Westinghouse Scholarship. But soon he shifted his majors in chemistry and finally in mathematics upon encouragement from his teachers. Due to his outstanding performance, he was awarded a Masters degree in addition to his Bachelor’s degree in 1948. He also received a scholarship at the Princeton University for doctoral in mathematics which he completed in 1950. He then started his career from the same university and became a faculty member there.
After about a year, in 1951, Nash accepted the C.L.E. Moore Instructor position at the Massachusetts Institute of Technology (MIT), with partial difference equation being the topic of his research then.
The Nash Equilibrium or the Nash Solution is one of Nash’s contributions to the game theory. This equilibrium offers solution to such a situation in which a decision is being taken by many people at the same time and reflects upon the effect of one person’s strategy or decision over that of others. A similar form of this solution had been used by a mathematician and economist, Antoine Augustin Cournot in his work on oligopoly (a form of market or industry) earlier in 1838. Later in 1944, John von Neumann and Oskar Morgenstern had brought forth the same solution but in terms of mixed strategies by applying probability distribution. Nash however, went many steps ahead and proposed a mixed-strategy Nash equilibrium for more than just zero-sum games; the special case that limited the work of John von Neumann and Oskar Morgenstern. By adopting this theorem, many principles and strategies were later developed related to various fields like environment, sports, businesses, regulations etc.
Nash also contributed in the field of differential geometry through many theorems. He worked on one of Hilbert’s problem (19th of the 23 problems David Hilbert had presented in 1900) and solved it by the Nash–De Giorgi theorem. Some of his other theorems include the Nash-Moser inverse function theorem and the Nash embedding theorems.
Nash got his first publication while studying at Princeton in 1950, by his paper The Bargaining Problem which was a result of his interest in economics developed through one of his elective courses in International Economics. Nash’s works as a mathematician widely covered many areas of mathematics including algebra and his prominent discoveries in the game theory. His PhD thesis was on Non-Cooperative Games and a paper on the same topic got published in the journal Annals of Mathematics in 1951. The same journal presented his revolutionary research in algebraic geometry through his article Real Algebraic Manifolds in 1952, during his instructorship at MIT.
Besides winning the Nobel Prize for Economics in 1994, Nash also received some other great awards including;
- Abel Prize by Norwegian Academy of Science and Letters for his contributions to partial differential equations in 2015
- John von Neumann Theory Prize in 1978
- The American Mathematical Society’s Leroy P. Steele Prize for a Seminal Contribution to Research in 1999.
John Nash died at the age of 86 on May 23, 2015 in a car accident in New Jersey.