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 M.I.T. in 1959 (he had been tenured there in 1958 - at the age of 29) and was virtually incapicated 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 "ultralogical" 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.
约翰·纳什生于1928 年6 月13 日。父亲是电子工程师与教师，第一次世界大战的老兵。纳什小时孤独内向，虽然父母对他照顾有加，但老师认为他不合群不善社交。 纳什的数学天分大约在14 岁开始展现。他在普林斯顿大学读博士时刚刚二十出头，但他的一篇关于非合作博弈的博士论文和其他相关文章，确立了他博弈论大师的地位。在20 世纪50 年代末，他已是闻名世界的科学家了。
然而，正当他的事业如日中天的时候，30 岁的纳什得了严重的精神分裂症。他的妻子艾利西亚———麻省理工学院物理系毕业生，表现出钢铁一般的意志：她挺过了丈夫被禁闭治疗、孤立无援的日子，走过了惟一儿子同样罹患精神分裂症的震惊与哀伤……漫长的半个世纪之后，她的耐心和毅力终于创下了了不起的奇迹：和她的儿子一样，纳什教授渐渐康复，并在1994 年获得诺贝尔奖经济学奖。