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數學 Mathematics

1. 頒獎之後,(數學家) 陳省身開始他的學術演講,演講中幾次提到「物理學和幾何」的關係,引起聽眾的轟動的笑聲,氣氛異常熱烈。我們在此摘錄幾段:

「我旁邊坐了兩位偉大的物理學家 (指楊振寧和謝希德)。接下去我想班門弄斧一下,談一下物理與幾何的關係。我覺得物理學裡有很多重要的工作,是物理學家要証明說物理就是幾何。比方說,你從牛頓的第二運動定律開始。

牛頓的第二定律說:F=ma

F是力,m是質量,a是加速度。加速度我們現在叫曲率。所以右邊這一項是幾何量。而力當然是物理量。所以牛頓費了半天勁,他只是說「物理就是幾何。」(大笑,鼓掌)

不但如此,愛因斯坦的廣義相對論也是這樣。愛因斯坦的廣義相對論的方程說: Rik – (1/2) gikR = 8πKTik

Rik 是里奇曲率,R是 scalar curvature,即標量曲率,K是常數,Tik是energy-stress tensor,即能量 – 應力張量。你仔細想想,它的左邊是幾何量,是從黎曼度量得出來的一些曲率。所以愛因斯坦的重要方程式也就是說,幾何量等於物理量。(掌聲)… 「

進入20世紀,數學的重要性已成為人們的共識,兩個最高水平的數學獎也相繼誕生:一個是菲爾茲獎,另一個是沃爾夫獎。在華人中,陳省身和他的學生丘成桐,分別是這兩項獎的獲得者。到今天為止,獲此殊榮的華人也只有他們兩位。

《陳省身傳》P.173-175

2. Princeton in 1948 was to mathematicians what Paris once was to painters and novelists, Vienna to psychoanalysts and architects , and ancient Athens to philosophers and playwrights . Harald Bohur brother of Niels Bohr, the physicist, had declared it “the mathematical center of the universe” in1936.

When the deans of mathematics held their first worldwide meeting after World War II, it was in Princeton. Fine Hall housed the world’s most competitive. Up-to-the minute mathematics department. Next door connected, In face – was the nation’s leading physics department, whose members, including Eugene Wigner, had driven off to Illinois, California, and New Mexico during the war, lugging bits of laboratory equipment, to help build the atomic bomb. A mile or so away , on what had been Olden Farm, was the Institute for Advanced Study, the modern equivalent of Plato’s Academy, where Einstein, Godel, Oppenheimer, and von Neumann scribbled on their blackboards and held their learned discourses. Visitors and students from the four comers of the world streamed to this polyglot mathematical oasis, fifty miles south of New York. What was proposed in a Princeton seminar one week was sure to be debated in Paris and Berkeley the week after, and in Moscow and Tokyo the week after that.

“A Beautiful mind  P60-61”

3. 2012年諾貝爾經濟學?頒給兩位研究「博奕論」(Game Theory)的學者。自1970至2007年間已有十二位諾貝爾得獎者是因博奕論而獲殊榮,其中又以電影《有你終生美麗》 (A Beautiful Mind) 的主角約翰・納什 (John Nash,數學家,1994年獲諾貝爾經濟學獎) 最廣為人知。

“2013年1月24日信報C2”

 

數學世界大學排名

  1. 麻省理工學院 Massachusetts Institute of Technology (MIT)
  2. 哈佛大學 Harvard University
  3. 史丹佛大學 Stanford University
  4. 牛津大學 University of Oxford
  5. 劍橋大學 University of Cambridge
  6. 普林斯頓大學 Princeton University
  7. 加州大學,伯克利分校 University of California, Berkeley (UCB)
  8. 蘇黎世聯邦理工學院 ETH Zurich – Swiss Federal Institute of Technology
  9. 加州大學洛杉磯分校 University of California, Los Angeles (UCLA)
  10. 帝國理工學院 Imperial College London
  11. 紐約大學 New York University (NYU)
  12. 加州理工學院 California Institute of Technology (Caltech)
  13. 新加坡國立大學 National University of Singapore (NUS)
  14. 哥倫比亞大學 Columbia University
  15. 耶魯大學 Yale University 

 

更多資訊: https://zh.wikipedia.org/wiki/Wikipedia:%E5%88%86%E9%A1%9E%E7%B4%A2%E5%BC%95