John Nash (1928- )
When the young Nash had applied to graduate school at Princeton in 1948, his old Carnegie Tech professor, R.J. Duffin, wrote only one line on his letter of recommendation: "This man is a genius".
It was at Princeton that Nash encountered the theory of games, then recently launched by John von Neumann and Oskar Morgenstern. However, they had only managed to solve non-cooperative games in the case of "pure rivalries" (i.e. zero-sum). The young Nash turned to rivalries with mutual gain. His trick was the use of best-response functions and a recent theorem that had just emerged - Kakutani's fixed point-theorem.
His main result, the "Nash Equilibrium", was published in 1950 in the Proceedings of the National Academy of Sciences. He followed this up with a paper which introduced yet another solution concept - this time for two-person cooperative games - the "Nash Bargaining Solution" (NBS) in 1950. A 1951 paper attached his name to yet another side of economics - this time, the "Nash Programme", reflecting his methodological call for the reduction of all cooperative games into a non-cooperative framework.
His contributions to mathematics were no less remarkable. As an undergraduate, he had inadvertently (and independently) proved Brouwer's fixed point theorem. Later on, he went on to break one of Riemann's most perplexing mathematical conundrums. From then on, Nash provided breakthrough after breakthrough in mathematics.
In 1958, on the threshold of his career, Nash got struck by paranoid schizophrenia. He lost his job at MIT in 1959 (he had been tenured there in 1958 - at the age of 29) and was virtually in capicated by the disease for the next two decades or so. He roamed about Europe and America, finally, returning to Princeton where he became a sad, ghostly character on the campus - "the Phantom of Fine Hall" as Rebecca Goldstein described him in her novel, Mind-Body Problem.
The disease began to evaporate in the early 1970s and Nash began to gradually to return to his work in mathematics. However, Nash himself associated his madness with his living on an "ultra logical" plane, "breathing air too rare" for most mortals, and if being "cured" meant he could no longer do any original work at that level, then, Nash argued, a remission might not be worthwhile in the end. As John Dryden once put it:Great wits are sure to madness near allied, And thin partitions do their bounds divide.
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