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[数学] 请介绍一位你所最了解的数学大师----进入

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mli 发表于 2006-12-24 11:42:36 | 显示全部楼层
 
David Hilbert (Born: 23 Jan 1862 in Königsberg, Prussia (now Kaliningrad, Russia). Died: 14 Feb 1943 in Göttingen, Germany): Hilbert's work in geometry had the greatest influence in that area after Euclid. A systematic study of the axioms of Euclidean geometry led Hilbert to propose 21 such axioms and he analysed their significance. He made contributions in many areas of mathematics and physics.
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mli 发表于 2006-12-24 11:44:45 | 显示全部楼层
 
Augustin Louis Cauchy (Born: 21 Aug 1789 in Paris, France. Died: 23 May 1857 in Sceaux (near Paris), France): Cauchy pioneered the study of analysis, both real and complex, and the theory of permutation groups. He also researched in convergence and divergence of infinite series, differential equations, determinants, probability and mathematical physics.
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mli 发表于 2006-12-24 11:49:20 | 显示全部楼层
 
Hölder (Born: 22 Dec 1859 in Stuttgart, Germany. Died: 29 Aug 1937 in Leipzig, Germany)

Hölder worked on the convergence of Fourier series and in 1884 he discovered the inequality now named after him. He became interested in group theory through Kronecker and Klein and proved the uniqueness of the factor groups in a composition series.
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mli 发表于 2006-12-24 11:50:19 | 显示全部楼层
 
Hermann Minkowski:

After earning his doctorate in 1885, Minkowski taught mathematics at the Universities of Bonn (1885–94), Königsberg (1894–96), Zürich (1896–1902), and Göttingen (1902–09). Together with Hilbert, he pursued research on the electron theory of the Dutch physicist Hendrik Lorentz and its modification in Einstein's special theory of relativity. In Raum und Zeit (1907; “Space and Time”) Minkowski gave his famous four-dimensional geometry based on the group of Lorentz transformations of special relativity theory. His major work in number theory was Geometrie der Zahlen (1896; “Geometry of Numbers”). His works were collected in David Hilbert (ed.), Gesammelte Abhandlungen, 2 vol. (1911; “Collected Papers”).
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sonny991011 发表于 2007-1-13 01:47:53 | 显示全部楼层
 
我推荐数学之王David hilbert
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rmatrix 发表于 2007-1-14 15:57:44 | 显示全部楼层
 
不过,朱喜平和曹怀东现正遭受质疑!!
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mathmao 发表于 2007-2-1 21:03:27 | 显示全部楼层

范剑青:把数学作为解决社会问题的工具

 
范剑青:把数学作为解决社会问题的工具

弗雷德里克·L·摩尔(Frederick L. Moore)是美国普林斯顿大学1918年的毕业生,一位著名的银行家,他先锋性地投资开发了加拿大西部石油和煤气资源,投资并策划了沃特·迪斯尼公司股票的上市。他的学生爱德华·B·古德诺(Edward B. Goodnow) 1947年从普林斯顿大学毕业。2004年,古德诺向母校捐款500万美元设立Frederick L. Moore'18金融教授席位。2006年,经全校性评选,范剑青成为第一位、也是唯一一位Frederick L. Moore'18金融教授。对于这个头衔,范剑青淡淡地说:“好处就是不用解释我在普林斯顿做得怎么样。”



2006年10月的一天,正在北京开会的范剑青接受了《科学时报》记者长达4个小时的采访。谈到为何如此慷慨地给记者时间,他说:“统计科学是为社会服务的,希望更多的人能了解、热爱并支持统计科学,希望统计科学在中国有更多的应用。”“数学科学在解决有重大影响的社会问题的挑战中会得到更强劲的发展,对实践方法的推敲和完善将促进理论、方法和应用的良性循环,从而推动它们的共同进步。”



今年43岁的范剑青已是国际统计科学界的领军人物。2000年,哈佛大学教授Marvin Zelen在向他颁发统计学最高奖——考普斯总统奖时称:范剑青对统计有巨大、广泛的贡献。



范剑青这次回国是参加四年一度的概率统计年会并作全会报告,这是他今年第四次回国。在海外身负重任,为何还不辞辛劳为祖国服务呢?他说:“为国家做一些事情,这是一种感情。”



陪同采访的中国科学院数学与系统科学院副院长陈敏说:“无论是做人的品质、做学问的态度还是对祖国的热爱,范剑青都是我们的楷模。他是国际统计方向的领军人,却时时不忘帮助祖国。在担任香港中文大学统计系教授和系主任期间,他积极推动大陆学者访问计划和博士培养项目。现在,在完成普林斯顿的工作后,他将主要精力放在国内。”



“你应该侧重于应用”



1978年,年仅15岁的范剑青以数理化几乎满分的成绩考入复旦大学数学系。1982年大学毕业后,他认为自己的数学功底不错,但数学只是一个好工具,而他自己一直想做与社会相关的事情,因此选择了“与数学接近,又与实际结合”的学科——统计学,成为中国科学院应用数学所研究员方开泰的研究生。



1985年,范剑青硕士毕业后考上在职博士。当时,他并不想出国,因为“觉得自己的研究做得挺好,已经在国内一流期刊上发表了约10篇论文”;但另一方面,范剑青也深深感到“我的研究局限在自己了解的知识之内,技巧多但想法不多”。



20世纪80年代中期,国内的“出国风”冲击着范剑青,他开始想到国际统计学的前沿——美国,然而当时他和外界并没什么联系。但他非常幸运,得到了著名的国际理论统计学权威、加州大学伯克利分校教授Lucient Le Cam的赏识,获得加州大学校董会奖学金,来到伯克利攻读博士。



当时,范剑青希望跟随Le Cam做博士,但Le Cam说自己年龄大了,将他推荐给一位29岁的专家大卫·道能浩(David L. Donoho)。道能浩后来获得麦克阿瑟天才奖和考普斯总统奖,并当选美国科学院院士。但当时尚未出道的他对范剑青说,“你跟我做学问可以,但我毕竟年轻,你以后要走自己的路,还需要有资深的人指导”。于是,道能浩又将范剑青推荐给伯克利的另一位统计学大师、美国科学院院士彼得·毕克(Peter J .Bickel),范剑青因此有了两位导师。毕克是考普斯总统奖的第一位获得者,也是获得麦克阿瑟天才奖的四位统计学家之一,他在数学技巧、为人处事等方面都给范剑青以指导。



范剑青认为,自己在伯克利最大的收获就是从老师那里学到很多科学思想和科学哲学。他说:“我把我的数学结果拿给老师看,但他说'不用看,我知道你们中国人做数学可能比我都好,我就跟你去喝咖啡,聊聊数学,教你怎么做有创意的研究,探讨什么是知识创新’。”



博士毕业时,道能浩对他说:“中国人的数学功夫不错,但做学问没有自己的特色就永远没有出路,我侧重理论,而你应该侧重应用。”



范剑青说,做数学有两种方向,一种是“向里走”,解决数学自身的内在联系或难题;另一种是“向外走”,用数学去解决经济学、生物学、社会学等科学领域里的问题。他说:“我的兴趣是用数学去揭开自然的奥秘,归纳社会现象,发展统计科学理论和应用,而不是解决数学难题。理论、方法、应用是融为一体的。学术价值的关键是知识创新的程度。”



“只要问题够复杂我就做”



纵览范剑青长达24页的简历,很难用简略的语言概括他的学术成就,但是他解决的问题却有一些共性——复杂、开创性、革命性。许多数学问题由于过于复杂曾被认为只限于理论演练,但是范剑青的工作却让理论变成了现实。由于他的工作,许多原先只能解决饱和、一元、正态、均匀、参数的统计学问题被扩展到非饱和、多元、非正态、非均匀、非参数。国际统计界对他的评价是“在理论和方法论上都开辟了很多新领域,为后续研究奠定了基础”。他独创的非参数建模法使他获得了2000年的考普斯总统奖,北卡罗来纳大学统计系教授Marron甚至用“文艺复兴”形容这项工作对统计学的影响。



在这项工作中,范剑青的贡献在于提出局部建模新理念。他说:“统计的最大问题在于模型误差,局部建模的优点在于可以大大降低误差。以地球为例,整体建模就是一个球体,但是局部看来就是有山有水、有平地有弧度,可以精确描述。当时,关于非参数的想法存在相互争论的两派,我进入这个领域的第一篇文章就是说两派都有其优缺点,但局部建模综合了它们的优点。”范剑青证明了他的方法是最有效的,从此结束了该领域的长期争论。局部建模法能广泛应用于许多复杂问题的解决,如医学、保险、经济等方面。2000年诺贝尔经济学奖得主赫克曼就是用类似模型分析经济问题而名扬世界。



范剑青认为,好的工作首先是知识创新,“我经常跟学生说,应该随时考虑自己的工作有没有创新,而不是多辛苦,仅仅辛苦是不够的”。



“我对统计很有自信,跟人合作时喜欢说两句话:'只要你觉得问题对你的领域充分重要、我听上去问题很复杂,肯定会有好结果。’因为如果问题不复杂,我能解决别人也可以,甚至说不定已经解决,那就没意思了。”



“统计学家要讲多种语言”



范剑青非常喜欢伽利略的一句名言“自然是用数学语言来编码的”。他说:“当我们用数学解决问题时,说明我们对这个问题非常了解,可以定量研究它,否则只是一种描述性的认识。统计就是用数学工具找出编码的规律,是解开密码的强有力的工具。”



用数学方法来解决社会问题,统计学注定是一门交叉学科。范剑青在普林斯顿大学的5个部门任职:运筹学与金融工程系、经济系、金融中心、应用数学以及生物工程。他常讲:“统计学家是讲多种语言的。要和物理、化学、工程、环境保护、金融、生物等领域打交道,这个范围要多广有多广。我自己将主要精力放在四个方向:金融学、生物信息、机器学习和生物统计,这四个方向已经够广了。”



怎样与不同领域的专家合作呢?范剑青有两种方法:读文章和自己动手做。他说:“首先是读文章,世界上的文章多得读不完,但重要的文章还是得读下来,尤其要读综述性的、大师的文章。这很重要,我要看看以前的问题是怎么解决的?拿到的数据是什么?他们做了怎样的统计假设?这些假设在要解决的问题中是否合理?站在这个角度就很容易找到新的有意思的题目。第二,进入一个领域最好的方法就是自己去做,对统计学家来说,只听是不行的,数据到眼前就一目了然了,就像听了对一幅画的介绍,但百闻不如一见,还是要去亲自了解一下数据是怎样收集的、要解决的真正问题是什么。”所以统计学家要学一些新的语言。



“我比15年前更喜欢统计”



当他被问及什么时候是学术生涯中最困难的时期,范剑青说是15年前刚毕业两三年的时候。“当时,我发表了三篇有创意的文章,但暂时找不到下一个好问题,对信心有一定的打击。而且当时对统计的理解还有些片面,整个统计学也没有太大进展。后来,随着社会和新技术的发展,出现了很多新问题,我做了很多原先不懂的问题,进入一些新的领域,慢慢走出来了。”



1997年,范剑青在香港中文大学做访问学者。在那里,范剑青的工作深得校方的大力支持。然而,2003年他还是被已有20多年没有聘请过统计学家的普林斯顿大学“硬拉过去了”。当时,香港中大校长李国璋对他说:“你要的东西我都给你了,这几年亏待过你吗?”范剑青说:“我也没有贪心多要。为什么要走?因为人要在工作中不断充实自己,我需要充电。”



范剑青记得刚毕业时问前辈:未来是什么?前辈说不好讲。后来前辈遇到他问:你现在已经成熟了,你说未来是什么?他回答说:“我现在做统计比我15年前有兴趣得多,因为我真不知道现在许多问题中的数学问题是什么、它的答案是什么、自然的奥秘是什么。计算技术的发展为统计学的发展提供了新的能量,信息和技术革命又给统计学带来了很多新问题,只要用统计去解决实际问题,永远做不完,我现在比当年还用功。”



从大学开始接触统计学到今天,统计对范剑青意味着什么?他说:“一是强有力的工具,我做研究、与人打交道,十八般武艺最强的就是统计学;二是我的数学修养还可以,不是统计的问题也敢碰,能帮助别人解决实际问题。”



2004年,已是普林斯顿大学教授的范剑青放弃了再回香港中文大学兼职的机会,希望利用假期回来帮助大陆学术界。2004年,范剑青被评为中国科学院海外评审专家,2005年出任中国科学院数学与系统科学研究院统计科学研究中心主任,2006年获得国家杰出海外青年基金。虽然拥有了一系列头衔,但陈敏说:“这些头衔更多的是一种荣誉,范剑青回来工作付出的远远比荣誉多得多,甚至每次国际旅费都是他自己承担。”



“在华尔街做顾问,经常和百万富翁打交道,你有没有受到'诱惑’?”“人生如果有第二次选择,你会选什么?”面对这样的问题,范剑青都用“快乐”来回答。他说:“人生快乐很重要,成功了就会快乐。人最重要的是快乐、是对社会有用,现在做科学我很快乐,每天有做不完的工作。有人问我会不会沮丧,我想说连沮丧的时间都没有,没事做才沮丧,这么忙才不会呢。你问我的梦想是什么,我的梦想就是明天能比今天更好,能够做更多对社会有实际影响的工作。”
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ffer 发表于 2007-3-3 10:59:36 | 显示全部楼层
 
John Forbes Nash

Born: 13 June 1928 in Bluefield, West Virginia, USA

     John F Nash's father, also called John Forbes Nash so we shall refer to him
as John Nash Senior, was a native of Texas. John Nash Senior was born in 18
92 and had an unhappy childhood from which he escaped when he studied electr
ical engineering at Texas Agricultural and Mechanical. After military servic
e in France during World War I, John Nash Senior lectured on electrical engi
neering for a year at the University of Texas before joining the Appalacian
Power Company in Bluefield, West Virginia. John F Nash's mother, Margaret Vi
rginia Martin, was known as Virginia. She had a university education, studyi
ng languages at the Martha Washington College and then at West Virginia Univ
ersity. She was a school teacher for ten years before meeting John Nash Seni
or, and the two were married on 6 September 1924.
Johnny Nash, as he was called by his family, was born in Bluefield Sanatoriu
m and baptised into the Episcopal Church. He was [2]:-
... a singular little boy, solitary and introverted ...
but he was brought up in a loving family surrounded by close relations who s
howed him much affection. After a couple of years Johnny had a sister when M
artha was born. He seems to have shown a lot of interest in books when he wa
s young but little interest in playing with other children. It was not becau
se of lack of children that Johnny was
behaved in this way for Martha and her cousins played the usual childhood ga
mes cutting patterns out of books, playing hide-and-seek in the attic, playi
ng football. However while the others played together Johnny played by himse
lf with toy airplanes and matchbox cars.
His mother responded by enthusiastically encouraging Johnny's education, bot
h by seeing that he got good schooling and also by teaching him herself. Joh
nny's father responded by treating him like an adult, giving him science boo
ks when other parents might give their children colouring books.
Johnny's teachers at school certainly did not recognise his genius, and it w
ould appear that he gave them little reason to realise that he had extraordi
nary talents. They were more conscious of his lack of social skills and, bec
ause of this, labelled him as backward. Although it is easy to be wise after
the event, it now would appear that he was extremely bored at school. By th
e time he was about twelve years old he was showing great interest in carryi
ng out scientific experiments in his room at home. It is fairly clear that h
e learnt more at home than he did at school.
Martha seems to have been a remarkably normal child while Johnny seemed diff
erent from other children. She wrote later in life (see [2]):-
Johnny was always different. [My parents] knew he was different. And they kn
ew he was bright. He always wanted to do thinks his way. Mother insisted I d
o things for him, that I include him in my friendships. ... but I wasn't too
keen on showing off my somewhat odd brother.
His parents encouraged him to take part in social activities and he did not
refuse, but sports, dances, visits to relatives and similar events he treate
d as tedious distractions from his books and experiments.
Nash first showed an interest in mathematics when he was about 14 years old.
Quite how he came to read E T Bell's Men of mathematics is unclear but cert
ainly this book inspired him. He tried, and succeeded, in proving for himsel
f results due to Fermat which Bell stated in his book. The excitement that N
ash found here was in contrast to the mathematics that he studied at school
which failed to interest him.
He entered Bluefield College in 1941 and there he took mathematics courses a
s well as science courses, in particular studying chemistry which was a favo
urite topic. He began to show abilities in mathematics, particularly in prob
lem solving, but still with hardly any friends and behaving in a somewhat ec
centric manner, this only added to his fellow pupils view of him as peculiar
. He did not considered a career in mathematics at this time, however, which
is not surprising since it was an unusual profession. Rather he assumed tha
t he would study electrical engineering and follow his father but he continu
ed to conduct his own chemistry experiments and was involved in making explo
sives which led to the death of one of his fellow pupils. [2]:-
Boredom and simmering adolescent aggression led him to play pranks, occasion
ally ones with a nasty edge.
He caricatured classmates he disliked with weird cartoons, enjoyed torturing
animals, and once tried to get his sister to sit in a chair he had wired up
with batteries.
Nash won a scholarship in the George Westinghouse Competition and was accept
ed by the Carnegie Institute of Technology (now Carnegie-Mellon University)
which he entered in June 1945 with the intention of taking a degree in chemi
cal engineering. Soon, however, his growing interest in mathematics had him
take courses on tensor calculus and relativity. There he came in contact wit
h John Synge who had recently been appointed as Head of the Mathematics Depa
rtment and taught the relativity course. Synge and the other mathematics pro
fessors quickly recognised Nash's remarkable mathematical talents and persua
ded him to become a mathematics specialist. They realised that he had the ta
lent to become a professional mathematician and strongly encouraged him.
Nash quickly aspired to great things in mathematics. He took the William Low
ell Putnam Mathematics Competition twice but, although he did well, he did n
ot make the top five. It was a failure in Nash's eyes and one which he took
badly. The Putnam Mathematics Competition was not the only thing going badly
for Nash. Although his mathematics professors heaped praise on him, his fel
low students found him a very strange person. Physically he was strong and t
his saved him from being bullied, but his fellow students took delight in ma
king fun of Nash who they saw as an awkward immature person displaying child
ish tantrums. One of his fellow students wrote:-
He was a country boy unsophisticated even by our standards. He behaved oddly
, playing a single chord on a piano over and over, leaving a melting ice cre
am cone melting on top of his castoff clothing, walking on his roommate's sl
eeping body to turn off the light.
Another wrote:-
He was extremely lonely.
And a third fellow student wrote:-
We tormented poor John. We were very unkind. We were obnoxious. We sensed he
had a mental problem.
He showed homosexual tendencies, climbing into bed with the other boys who r
eacted by making fun of the fact that he was attracted to boys and humiliate
d him. They played cruel pranks on him and he reacted by asking his fellow s
tudents to challenge him with mathematics problems. He ended up doing the ho
mework of many of the students.
Nash received a BA and an MA in mathematics in 1948. By this time he had bee
n accepted into the mathematics programme at Harvard, Princeton, Chicago and
Michigan. Now he felt that Harvard was the leading university and so he wan
ted to go there, but on the other hand their offer to him was less generous
than that of Princeton. Nash felt that Princeton were keen that he went ther
e while he felt that his lack of success in the Putnam Mathematics Competiti
on meant that Harvard were less enthusiastic. He took a while to make his de
cision, while he was encouraged by Synge and his other professors to accept
Princeton. When Lefschetz offered him the most prestigious Fellowship that P
rinceton had, Nash made his decision to study there.
In September 1948 Nash entered Princeton where he showed an interest in a br
oad range of pure mathematics: topology, algebraic geometry, game theory and
logic were among his interests but he seems to have avoided attending lectu
res. Usually those who decide not to learn through lectures turn to books bu
t this appears not to be so for Nash who decided not to learn mathematics "s
econd-hand" but rather to develop topics himself. In many ways this approach
was successful for it did contribute to him developing into one of the most
original of mathematicians who would attack a problem in a totally novel wa
y.
In 1949, while studying for his doctorate, he wrote a paper which 45 years l
ater was to win a Nobel prize for economics. During this period Nash establi
shed the mathematical principles of game theory. P Ordeshook wrote:-
The concept of a Nash equilibrium n-tuple is perhaps the most important idea
in noncooperative game theory. ... Whether we are analysing candidates' ele
ction strategies, the causes of war, agenda manipulation in legislatures, or
the actions of interest groups, predictions about events reduce to a search
for and description of equilibria. Put simply, equilibrium strategies are t
he things that we predict about people.
Milnor, who was a fellow student, describes Nash during his years at Princet
on in [6]:-
He was always full of mathematical ideas, not only on game theory, but in ge
ometry and topology as well. However, my most vivid memory of this time is o
f the many games which were played in the common room. I was introduced to G
o and Kriegspiel, and also to an ingenious topological game which we called
Nash in honor of the inventor.
In fact the game "Nash" was almost identical to Hex which had been invented
independently by Piet Hein in Denmark.
Here are three comments from fellow students:-
Nash was out of the ordinary. If he was in a room with twenty people, and th
ey were talking, if you asked an observer who struck you as odd it would hav
e been Nash. It wasn't anything he consciously did. It was his bearing. His
aloofness.
Nash was totally spooky. He wouldn't look at you. he'd take a lot of time an
swering a question. If he thought the question was foolish he wouldn't answe
r at all. He had no effect. It was a mixture of pride and something else. He
was so isolated but there really was underneath it all a warmth and appreci
ation of people.
A lot of us would discount what Nash said. ... I wouldn't want to listen. Yo
u didn't feel comfortable with the person.
He had ideas and was very sure they were important. He went to see Einstein
not long after he arrived in Princeton and told him about an idea he had reg
arding gravity. After explaining complicated mathematics to Einstein for abo
ut an hour, Einstein advised him to go and learn more physics. Apparently a
physicist did publish a similar idea some years later.
In 1950 Nash received his doctorate from Princeton with a thesis entitled No
n-cooperative Games. In the summer of that year he worked for the RAND Corpo
ration where his work on game theory made him a leading expert on the Cold W
ar conflict which dominated RAND's work. He worked there from time to time o
ver the next few years as the Corporation tried to apply game theory to mili
tary and diplomatic strategy. Back at Princeton in the autumn of 1950 he beg
an to work seriously on pure mathematical problems. It might seem that someo
ne who had just introduced ideas which would, one day, be considered worthy
of a Nobel Prize would have no problems finding an academic post. However, N
ash's work was not seen at the time to be of outstanding importance and he s
aw that he needed to make his mark in other ways. We should also note that i
t was not really a move towards pure mathematics for he had always considere
d himself a pure mathematician. He had already obtained results on manifolds
and algebraic varieties before writing his thesis on game theory. His famou
s theorem, that any compact real manifold is diffeomorphic to a component of
a real-algebraic variety, was thought of by Nash as a possible result to fa
ll back on if his work on game theory was not considered suitable for a doct
oral thesis. He said in a recent interview:-
I developed a very good idea in pure mathematics. I got what became Real Alg
ebraic Manifolds. I could have published that earlier, but it wasn't rushed
to publication. I took some time in writing it up. Somebody suggested that I
was a prodigy. Another time it was suggested that I should be called "bug b
rains", because I had ideas, but they were sort of buggy or not perfectly so
und. So that might have been an anticipation of mental problems. I mean, tak
ing it at face value.
In 1952 Nash published Real Algebraic Manifolds in the Annals of Mathematics
. The most important result in this paper is that two real algebraic manifol
ds are equivalent if and only if they are analytically homeomorphic. Althoug
h publication of this paper on manifolds established him as a leading mathem
atician, not everyone at Princeton was prepared to see him join the Faculty
there. This was nothing to do with his mathematical ability which everyone a
ccepted as outstanding, but rather some mathematicians such as Artin felt th
at they could not have Nash as a colleague due to his aggressive personality
.
Halmos received the following letter in early 1953 from Warren Ambrose relat
ing to Nash (see for example [2]):-
There's no significant news from here, as always. Martin is appointing John
Nash to an Assistant Professorship (not the Nash at Illinois, the one out of
Princeton by Steenrod) and I'm pretty annoyed at that. Nash is a childish b
right guy who wants to be "basically original," which I suppose is fine for
those who have some basic originality in them. He also makes a damned fool o
f himself in various ways contrary to this philosophy. He recently heard of
the unsolved problem about imbedding a Riemannian manifold isometrically in
Euclidean space, felt that this was his sort of thing, provided the problem
were sufficiently worthwhile to justify his efforts; so he proceeded to writ
e to everyone in the math society to cheek on that, was told that it probabl
y was, and proceeded to announce that he had solved it, module details, and
told Mackey he would like to talk about it at the Harvard colloquium. Meanwh
ile he went to Levinson to inquire about a differential equation that interv
ened and Levinson says it is a system of partial differential equations and
if he could only [get] to the essentially simpler analog of a single ordinar
y differential equation it would be a damned good paper - and Nash had only
the vaguest notions about the whole thing. So it is generally conceded he is
getting nowhere and making an even bigger ass of himself than he has been p
reviously supposed by those with less insight than myself. But we've got him
and saved ourselves the possibility of having gotten a real mathematician.
He's a bright guy but conceited as Hell, childish as Wiener, hasty as X, obs
treperous as Y, for arbitrary X and Y.
Ambrose, the author of this letter, and Nash had rubbed each other the wrong
way for a while. They had played silly pranks on each other and Ambrose see
ms not to have been able to ignore Nash's digs in the way others had learned
to do. It had been Ambrose who had said to Nash:-
If you're so good, why don't you solve the embedding theorem for manifolds.
From 1952 Nash had taught at the Massachusetts Institute of Technology but h
is teaching was unusual (and unpopular with students) and his examining meth
ods were highly unorthodox. His research on the theory of real algebraic var
ieties, Riemannian geometry, parabolic and elliptic equations was, however,
extremely deep and significant in the development of all these topics. His p
aper C1 isometric imbeddings was published in 1954 and Chern, in a review, n
oted that it:-
... contains some surprising results on the C1-isometric imbedding into an E
uclidean space of a Riemannian manifold with a positive definite C0-metric.
Nash continued to develop this work in the paper The imbedding problem for R
iemannian manifolds published in 1956. This paper contains his famous deep i
mplicit function theorem. After this Nash worked on ideas that would appear
in his paper Continuity of solutions of parabolic and elliptic equations whi
ch was published in the American Journal of Mathematics in 1958. Nash, howev
er, was very disappointed when he discovered that E De Giorgi has proved sim
ilar results by completely different methods.
The outstanding results which Nash had obtained in the course of a few years
put him into contention for a 1958 Fields' Medal but with his work on parab
olic and elliptic equations was still unpublished when the Committee made th
eir decisions he did not make it. One imagines that the Committee would have
expected him to be a leading contender, perhaps even a virtual certainty, f
or a 1962 Fields' Medal but mental illness destroyed his career long before
those decisions were made.
During his time at MIT Nash began to have personal problems with his life wh
ich were in addition to the social difficulties he had always suffered. Coll
eagues said:-
Nash was always forming intense friendships with men that had a romantic qua
lity. He was very adolescent, always with the boys. He was very experimental
- mostly he just kissed.
He met Eleanor Stier and they had a son, John David Stier, who was born on 1
9 June 1953. Eleanor was a shy girl, lacking confidence, a little afraid of
men, didn't want to be involved. She found in Nash someone who was even less
experienced than she was and found that attractive. [2]:-
Nash was looking for emotional partners who were more interested in giving t
han receiving, and Eleanor, was very much that sort.
Nash did not want to marry Eleanor although she tried hard to persuade him.
In the summer of 1954, while working for RAND, Nash was arrested in a police
operation to trap homosexuals. He was dismissed from RAND.
One of Nash's students at MIT, Alicia Larde, became friendly with him and by
the summer of 1955 they were seeing each other regularly. He also had a spe
cial friendship with a male graduate student at this time Jack Bricker. Elea
nor found out about Alicia in the spring of 1956 when she came to Nash's hou
se and found him in bed with Alicia. Nash said to a friend:-
My perfect little world is ruined, my perfect little world is ruined.
Alicia didn't seem too upset at discovering that Nash had a child with Elean
or and deduced that since the affair had been going on for three years, Nash
was probably not serious about her. In 1956 Nash's parents found out about
his continuing affair with Eleanor and about his son John David Stier. The s
hock may have contributed to the death of Nash's father soon after but even
if it did not Nash may have blamed himself. In February of 1957 Nash married
Alicia; by the autumn of 1958 she was pregnant but, a couple of months late
r near the end of 1958, Nash's mental state became very disturbed.
At a New Year's Party Nash appeared at midnight dressed only with a nappy an
d a sash with "1959" written on it. He spent most of the evening curled up,
like the baby he was dressed as, on his wife's lap. Some described his behav
iour as stranger than usual. On 4 January he was back at the university and
started to teach his game theory course. His opening comments to the class w
ere:-
The question occurs to me. Why are you here?
One student immediately dropped the course! Nash asked a graduate student to
take over his course and vanished for a couple of weeks. When he returned h
e walked into the common room with a copy of the New York Times saying that
it contained encrypted messages from outer space that were meant only for hi
m. For a few days people thought he was playing an elaborate private joke.
Norbert Wiener was one of the first to recognize that Nash's extreme eccentr
icities and personality problems were actually symptoms of a medical disorde
r. After months of bizarre behaviour, Alicia had her husband involuntarily h
ospitalised at McLean Hospital, a private psychiatric hospital outside of Bo
ston. Upon his release, Nash abruptly resigned from M.I.T., withdrew his pen
sion, and went to Europe, where he intended to renounce his U.S. citizenship
. Alicia left her newborn son with her mother, and followed the ill Nash. Sh
e then had Nash deported - back to the United States.
After their return, the two settled in Princeton where Alicia took a job. Na
sh's illness continued, transforming him into a frightening figure. He spent
most of his time hanging around on the Princeton campus, talking about hims
elf in the third person as Johann von Nassau, writing nonsensical postcards
and making phone calls to former colleagues. They stoically listened to his
endless discussions of numerology and world political affairs. Her husband's
worsening condition depressed Alicia more and more.
In January 1961 the despondent Alicia, John's mother, and his sister Martha
made the difficult decision to commit him to Trenton State Hospital in New J
ersey where he endured insulin-coma therapy, an aggressive and risky treatme
nt, five days a week for a month and a half. A long sad episode followed whi
ch included periods of hospital treatment, temporary recovery, then further
treatment. Alicia divorced Nash in 1962. Nash spent a while with Eleanor and
John David. In 1970 Alicia tried to help him taking him in as a boarder, bu
t he appeared to be lost to the world, removed from ordinary society, althou
gh he spent much of his time in the Mathematics Department at Princeton. The
book [2] is highly recommended for its moving account of Nash's mental suff
erings.
Slowly over many years Nash recovered. He delivered a paper at the tenth Wor
ld Congress of Psychiatry in 1996 describing his illness; it is reported in
[3]. He was described in 1958 as the:-
... most promising young mathematician in the world ...
but he soon began to feel that:-
... the staff at my university, the Massachusetts Institute of Technology, a
nd later all of Boston were behaving strangely towards me. ... I started to
see crypto-communists everywhere ... I started to think I was a man of great
religious importance, and to hear voices all the time. I began to hear some
thing like telephone calls in my head, from people opposed to my ideas. ...T
he delirium was like a dream from which I seemed never to awake.
Despite spending periods in hospital because of his mental condition, his ma
thematical work continued to have success after success. He said:-
I would not dare to say that there is a direct relation between mathematics
and madness, but there is no doubt that great mathematicians suffer from man
iacal characteristics, delirium and symptoms of schizophrenia.
In the 1990s Nash made a recovery from the schizophrenia from which he had s
uffered since 1959. His ability to produce mathematics of the highest qualit
y did not totally leave him. He said:-
I would not treat myself as recovered if I could not produce good things in
my work.
Nash was awarded (jointly with Harsanyi and Selten) the 1994 Nobel Prize in
Economic Science for his work on game theory. In 1999 he was awarded the Ler
oy P Steele Prize by the American Mathematical Society.
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wander1st 发表于 2007-3-8 09:12:39 | 显示全部楼层
 
太精彩了 谢谢拉 [s:47]  [s:46]  [s:48]
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l393981724 发表于 2007-3-12 10:06:56 | 显示全部楼层
 
说一则轶事吧 关于我们以前的系主任 不说名字了
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