那一剑的寂寞
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几个我比较崇拜的数学家
1， 以前在国内也很喜欢看数学译林。对当代一些顶尖的数学家的名字最初就是从数学译林上了
解到的。象ATIYAH， GROTHENDIECK
记得曾经看老译林上对90年fields奖得主一个苏联的代数几何学家的采访录。 提到Groth
endieck 时这位刚拿来FIELDS奖的主说： 在我成长为数学家的过程中，他对我就是神话里的
英雄。
82年的fileds 奖Faltings， 属於少年得志的天才类型。
可以想象的高傲。 不过在他 得奖以后，
当时已经从数学界退休的GROTHENDIECK给他写了一封勉励
有加的信。Faltings 高兴 的把这封信给很多朋友看， 得意之极不下与他拿FIELDS奖吧。
其实这也难怪。
我想Faltings 最佩服的数学家就是GROTHENDIECk了吧。
在他拿FIELDs后有记者问他：
谁是本世纪最伟大的数学家。 此公托口而出： Grothendieck 和上帝最伟大 ！
2 Riemann
3 Ramanujan
4 A.孔涅生于法国，1983年获奖，从事算子代数研究，引进了新的不变量，从根本上解决了J.
冯.诺伊曼留下的代数分类问题。
孔涅于1947年4月1日生于法国的德拉吉尼昂，1966—1970年在巴黎高等师范学校学习，其后
在国家科学研究中心做研究，1973年获国家博士学位，在博士论文中解决了Ⅲ型因子的分类
问题，引起广泛的注意。1976—1980年他在巴黎第6大学任教，1979年以后在高等科学研究中
心任教授，1984年起兼任法兰西学院教授。
一般认为，法国数学家孔涅（A.Connes）是分析专家，因为他在1982年获奖的主要依据是对
冯·诺伊曼代数的研究，而冯·诺伊曼代数来源于1929年冯·诺伊曼对希尔伯特空间的算子
理论的研究，这通常被认为是泛函分析的领域，但冯·诺伊曼一开始就从诺特（E.Noether）
的抽象代数找到灵感，而且把他的研究对象称为算子环。冯·诺伊曼和马瑞（F.Murray）在
1936一1943年合写的4篇论文奠定这个理论的基础。但3O多年过去了，这个孤立的理论进展甚
微，一直到孔涅的工作完全改变这个领域的面貌。
孔涅在197O年代系统地把冯·诺伊曼代数的结构理论推向完整，使算子代数产生革命性的变
化，但这只是一个学科的进展。孔涅的伟大之处，在于把算子代数同各个主流学科联系起来
，特别是微分几何、叶形理论、拓扑学、K理论等，并且统一成非交换几何理论。这个理论不
仅对量子理论给予全新的理解，而且同数论这种似乎全不相干的理论建立联系。这种几乎包
容一切的理论并非只是一套形式理论，而是解决大问题的工具。孔涅在20世纪末的论文的确
使人叹为观止，他把非交换几何与黎曼ζ函数、各种L函数联系在一起，从类域论到塞尔伯格
迹公式，从阿德尔（Ade1e）到代数几何到量子统计，样样都有。这就是新世纪的数学！孔涅
在20O1年独得瑞典科学院克拉福德奖，也许是新世纪大数学家的象征。
5，M.孔采维奇（Kontsevich）1964年生于俄罗斯，1998年获奖，对“线理 论”和理论物理学，代数几何与拓扑
学的研究作出了贡献。
2O世纪最后2O多年，代数几何学已不仅仅在数论方面显示威力了。它已经涉及所有数学领域
并进而推进到数学物理学。这在孔采维奇的工作中充分显示出来。
孔采维奇于1964年8月25日生于苏联西姆基，1980—1985年在莫斯科大学学习，毕业后在莫斯
科信息传输问题研究所任初级研究员。1990年后，他先后去哈佛大学、德国波恩的马克斯·
普朗克数学研究所以及普林斯顿高等研究院访问，并于1992年在波恩大学取得博士学位，同
年获得首届欧洲数学家大会颁发的青年数学家奖，1993—1996年他任美国加州大学伯克利分
校教授，1995年起任巴黎高等科学院教授。
孔采维奇对代数几何学的贡献主要是发展19世纪奠基的计数几何学，特别是定出各种代数簇
上各阶有理曲线的数目，这是长期以来一直毫无进展的难题。在此之前他证明威腾关于复曲
线参模空间的交截理论的猜想，它与著名的KdV方程有关。此外，他构造一般的纽结、环链和
3维流形不变量，与统计物理、量子场论、无穷维代数等密切相关。最新的工作则是泊松（P
oisson）流形的量子化，这是数学和数学物理的交会点。他的工作代表新世纪发展的方向。
6 1998 Fields Medalist Richard E. Borcherds
Richard E. Borcherds received a medal for his work in the fields of algebra and
geometry, in particular for his proof of the so-called Moonshine conjecture. Thi
s conjecture was formulated at the end of the '70s by the British mathematicians
John Conway and Simon Norton and presents two mathematical structures in such a
n unexpected relationship that the experts gave it the name "Moonshine." In 1989
, Borcherds was able to cast some more light on the mathematical background of t
his topic and to produce a proof for the conjecture.
The Moonshine conjecture provides an interrelationship between the so-called "mo
nster group" and elliptic functions. These functions are used in the constructio
n of wire-frame structures in two-dimensions, and can be helpful, for example, i
n chemistry for the description of molecular structures. The monster group, in c
ontrast, only seemed to be of importance in pure mathematics. Groups are mathema
tical objects which can be used to describe the symmetry of structures. Expresse
d technically, they are a set of objects for which certain arithmetic rules appl
y (for example all whole numbers and their sums form a group.) An important theo
rem of algebra says that all groups, however large and complicated they may seem
, all consist of the same components - in the same way as the material world is
made up of atomic particles. The "monster group" is the largest "sporadic, finit
e, simple" group - and one of the most bizarre objects in algebra. It has more e
lements than there are elementary particles in the universe (approx. 8 x 1053).
Hence the name "monster." In his proof, Borcherds uses many ideas of string theo
ry - a surprisingly fruitful way of making theoretical physics useful for mathem
atical theory. Although still the subject of dispute among physicists, strings o
ffer a way of explaining many of the puzzles surrounding the origins of the univ
erse. They were proposed in the search for a single consistent theory which brin
gs together various partial theories of cosmology. Strings have a length but no
other dimension and may be open strings or closed loops.
Richard Ewen Borcherds (born 29 November 1959) has been "Royal Society Research
Professor" at the Department of Pure Mathematics and Mathematical Statistics at
Cambridge University since 1996. Borcherds began his academic career at Trinity
College, Cambridge before going as assistant professor to the University of Cali
fornia in Berkeley. He has been made a Fellow of the Royal Society, and has also
held a professorship at Berkeley since 1993.
7，von Neumann, John
(1903 -- 1957)
Von Neumann studied chemistry at the University of Berlin and, at Technische Hoc
hschule in Zürich, received the diploma in chemical engineering in 1926. The sa
me year, he received the Ph.D. in mathematics from the University of Budapest, w
ith a dissertation about set theory. His axiomatization has left a permanent mar
k on the subject; and his definition of ordinal numbers, published when he was 2
0, has been universally adopted.
Von Neumann was privatdocent (lecturer) at Berlin in 1926-29 and at the Universi
ty of Hamburg in 1929-30. During this time he worked mainly on quantum physics a
nd operator theory. Largely because of his work, quantum physics and operator th
eory can be viewed as two aspects of the same subject.
In 1930 von Neumann was visiting lecturer at Princeton University; he was appoin
ted professor in 1931. In 1932 he gave a precise formulation and proof of the "e
rgodic hypothesis" of statistical mathematics. His book on quantum mechanics, Th
e Mathematical Foundations of Quantum Mechanics, published in 1932, remains a st
andard treatment of the subject. In 1933 he became a professor at the newly foun
ded Institute for Advanced Study, Princeton, keeping that position for the rest
of his life. Meanwhile, he turned his attention to the challenge made in 1900 by
a German mathematician, David Hilbert, who proposed 23 basic theoretical proble
ms for 20th-century mathematical research. Von Neumann solved a special case of
Hilbert's fifth problem, the case of compact groups.
In the second half of the 1930s the main part of von Neumann's publications, wri
tten partly in collaboration with F.J. Murray, was on "rings of operators" (now
called Neumann algebras). Of all his work, these concepts will quite probably be
remembered the longest. Currently it is one of the most powerful tools in the s
tudy of quantum physics. An important outgrowth of rings of operators is "contin
uous geometry." Von Neumann saw that what really determines the character of the
dimensional structure of a space is the group of rotations that the structure a
llows. The groups of rotations associated with rings of operators make possible
the description of space with continuously varying dimensions.
About 20 of von Neumann's 150 papers are in physics; the rest are distributed mo
re or less evenly among pure mathematics (mainly set theory, logic, topological
group, measure theory, ergodic theory, operator theory, and continuous geometry)
and applied mathematics (statistics, numerical analysis, shock waves, flow prob
lems, hydrodynamics, aerodynamics, ballistics, problems of detonation, meteorolo
gy, and two nonclassical aspects of applied mathematics, games and computers). H
is publications show a break from pure to applied research around 1940.
During World War II, he was much in demand as a consultant to the armed forces a
nd to civilian agencies. His two main contributions were his espousal of the imp
losion method for bringing nuclear fuel to explosion and his participation in th
e development of the hydrogen bomb.
The mathematical cornerstone of von Neumann's theory of games is the "minimax th
eorem," which he stated in 1928; its elaboration and applications are in the boo
k he wrote jointly with Oskar Morgenstern in 1944, Theory of Games and Economic
Behavior. The minimax theorem says that for a large class of two-person games, t
here is no point in playing. Either player may consider, for each possible strat
egy of play, the maximum loss that he can expect to sustain with that strategy a
nd then choose as his "optimal" strategy the one that minimizes the maximum loss
. If a player follows this reasoning, then he can be statistically sure of not l
osing more than that value called the minimax value. Since (this is the assertio
n of the theorem) that minimax value is the negative of the one, similarly defin
ed, that his opponent can guarantee for himself, the long-run outcome is complet
ely determined by the rules.
In computer theory, von Neumann did much of the pioneering work in logical desig
n, in the problem of obtaining reliable answers from a machine with unreliable c
omponents, the function of "memory," machine imitation of "randomness," and the
problem of constructing automata that can reproduce their own kind. One of the m
ost striking ideas, to the study of which he proposed to apply computer techniqu
es, was to dye the polar ice caps so as to decrease the amount of energy they wo
uld reflect--the result could warm the Earth enough to make the climate of Icela
nd approximate that of Hawaii.
The "axiomatic method" is sometimes mentioned as the secret of von Neumann's suc
cess. In his hands it was not pedantry but perception; he got to the root of the
matter by concentrating on the basic properties (axioms) from which all else fo
llows. His insights were illuminating and his statements precise.
8，William Paul Thurston
Born: 30 Oct 1946 in Washington, D.C., USA（一个神秘的人物）
9，Atle Selberg
Born: 14 June 1917 in Langesund, Norway
10， Henri Poincaré（以一个伟大人物结尾）
| 发表时间：2005-10-18, 23:23:34 |
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萍踪浪迹
发表文章数: 1983
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Re: 几个我比较崇拜的数学家
Gauss，Riemann，Poincare，Abel，Galois，Hilbert，Weyl，Weil，Siegel，Cartan，Chern，Kelmogrove，Hua。。。。。。。。。。。。。。。。。
漫漫长夜不知晓 日落云寒苦终宵
痴心未悟拈花笑 梦魂飞度同心桥
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红叶晚萧萧，长亭酒一瓢
残云归太华，疏雨过中条
树色随山迥，河声入海遥
帝乡明日到，犹自梦渔樵
| 发表时间：2005-10-20, 01:26:46 |
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追忆
发表文章数: 693
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Re: 几个我比较崇拜的数学家
飞兄以前贴过一个贴子，尽管有些不太准确，不过人物算是比较齐全的。
青山隐隐水迢迢，秋尽江南草木凋；
二十四桥明月夜，玉人何处教吹萧？
| 发表时间：2005-10-20, 11:15:53 |
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