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.
约翰 纳什(1928-)
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,走过了惟一的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。
如今,纳什已经基本恢复正常,并重新开始科学研究。他现在是普林斯顿大学数学教授,但已经不再任教。学校经济学系经常会举办有关博弈论的论坛,纳什有时候会参加,但是他几乎从不发言,每次都是静静地来,静静地走。
关于纳什还有一部获得奥斯卡最佳电影奖的影片《美丽心灵》,感兴趣的同学可以找来观看,可能会对纳什战胜精神分裂症的故事有更好的体会。纳什的例子可以用于讨论天才与毅力的关系,讨论环境的影响等话题。
雅思考试六个月备考计划--适合基础较差的烤鸭
雅思一个月复习备考计划--适合基础较好的烤鸭
剖析雅思阅读Heading题的段落结构
在雅思考试中如何安排阅读时间
解读雅思考试阅读中的对应关系
雅思阅读答题时的注意事项有哪些?
2014年的雅思阅读备考指南
怎样做好雅思段落与信息匹配题
雅思阅读技巧有哪些
7大答题技巧助你拿下雅思阅读简答题
雅思阅读答题技巧
通过把握雅思阅读文章结构 做标题选择题
雅思阅读判断题中的否定词
雅思阅读技巧小贴士
提升雅思阅读实力应着眼四个方面
雅思阅读成绩提高方法三步走
雅思阅读成绩总是上不去的原因剖析
雅思阅读的最高境界:摆脱单词的束缚
雅思阅读背景知识介绍:数字13为什么不吉利
雅思阅读提高方法有哪些
雅思阅读备考误区
着眼雅思阅读中的常见关系词 把握雅思阅读技巧
雅思阅读的猜词技巧
雅思阅读高分三大步骤
雅思阅读:如何提高雅思阅读能力
怎样高效利用雅思阅读真题
雅思考试三个月备考计划--适合基础一般的烤鸭
雅思阅读中常见的省略句形式
雅思阅读真经介绍
揭秘雅思阅读的文章来源和分类
不限 |
英语教案 |
英语课件 |
英语试题 |
不限 |
不限 |
上册 |
下册 |
不限 |