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 . 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 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 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 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.

　　約翰 納什(1928-)

　　約翰 納什生于1928 年6月13日。父親是電子工程師與教師，第一次世界大戰(zhàn)的老兵。納什小時(shí)孤獨(dú)內(nèi)向，雖然父母對(duì)他照顧有加，但老師認(rèn)為他不合群不善社交。 納什的數(shù)學(xué)天分大約在14歲開(kāi)始展現(xiàn)。他在普林斯頓大學(xué)讀博士時(shí)剛剛二十出頭，但他的一篇關(guān)于非合作博弈的博士論文和其他相關(guān)文章，確立了他博弈論大師的地位。在20 世紀(jì)50年代末，他已是聞名世界的科學(xué)家了。

　　然而，正當(dāng)他的事業(yè)如日中天的時(shí)候，30歲的納什得了嚴(yán)重的精神分裂癥。他的妻子艾利西亞 麻省理工學(xué)院物理系畢業(yè)生，表現(xiàn)出鋼鐵一般的意志：她挺過(guò)了丈夫被禁閉治療、孤立無(wú)援的日子，走過(guò)了惟一的兒子同樣罹患精神分裂癥的震驚與哀傷 漫長(zhǎng)的半個(gè)世紀(jì)之后，她的耐心和毅力終于創(chuàng)下了了不起的奇跡：和她的兒子一樣，納什教授漸漸康復(fù)，并在1994 年獲得諾貝爾獎(jiǎng)經(jīng)濟(jì)學(xué)獎(jiǎng)。

　　如今，納什已經(jīng)基本恢復(fù)正常，并重新開(kāi)始科學(xué)研究。他現(xiàn)在是普林斯頓大學(xué)數(shù)學(xué)教授，但已經(jīng)不再任教。學(xué)校經(jīng)濟(jì)學(xué)系經(jīng)常會(huì)舉辦有關(guān)博弈論的論壇，納什有時(shí)候會(huì)參加，但是他幾乎從不發(fā)言，每次都是靜靜地來(lái)，靜靜地走。

　　關(guān)于納什還有一部獲得奧斯卡最佳電影獎(jiǎng)的影片《美麗心靈》，感興趣的同學(xué)可以找來(lái)觀看，可能會(huì)對(duì)納什戰(zhàn)勝精神分裂癥的故事有更好的體會(huì)。納什的例子可以用于討論天才與毅力的關(guān)系，討論環(huán)境的影響等話題。

　　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 . 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 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 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 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.

　　約翰 納什(1928-)

　　約翰 納什生于1928 年6月13日。父親是電子工程師與教師，第一次世界大戰(zhàn)的老兵。納什小時(shí)孤獨(dú)內(nèi)向，雖然父母對(duì)他照顧有加，但老師認(rèn)為他不合群不善社交。 納什的數(shù)學(xué)天分大約在14歲開(kāi)始展現(xiàn)。他在普林斯頓大學(xué)讀博士時(shí)剛剛二十出頭，但他的一篇關(guān)于非合作博弈的博士論文和其他相關(guān)文章，確立了他博弈論大師的地位。在20 世紀(jì)50年代末，他已是聞名世界的科學(xué)家了。

　　然而，正當(dāng)他的事業(yè)如日中天的時(shí)候，30歲的納什得了嚴(yán)重的精神分裂癥。他的妻子艾利西亞 麻省理工學(xué)院物理系畢業(yè)生，表現(xiàn)出鋼鐵一般的意志：她挺過(guò)了丈夫被禁閉治療、孤立無(wú)援的日子，走過(guò)了惟一的兒子同樣罹患精神分裂癥的震驚與哀傷 漫長(zhǎng)的半個(gè)世紀(jì)之后，她的耐心和毅力終于創(chuàng)下了了不起的奇跡：和她的兒子一樣，納什教授漸漸康復(fù)，并在1994 年獲得諾貝爾獎(jiǎng)經(jīng)濟(jì)學(xué)獎(jiǎng)。

　　如今，納什已經(jīng)基本恢復(fù)正常，并重新開(kāi)始科學(xué)研究。他現(xiàn)在是普林斯頓大學(xué)數(shù)學(xué)教授，但已經(jīng)不再任教。學(xué)校經(jīng)濟(jì)學(xué)系經(jīng)常會(huì)舉辦有關(guān)博弈論的論壇，納什有時(shí)候會(huì)參加，但是他幾乎從不發(fā)言，每次都是靜靜地來(lái)，靜靜地走。

　　關(guān)于納什還有一部獲得奧斯卡最佳電影獎(jiǎng)的影片《美麗心靈》，感興趣的同學(xué)可以找來(lái)觀看，可能會(huì)對(duì)納什戰(zhàn)勝精神分裂癥的故事有更好的體會(huì)。納什的例子可以用于討論天才與毅力的關(guān)系，討論環(huán)境的影響等話題。