Terence Tao, genius mathematician

Three Chinese Fields Medalists so far:

1. ST Yau (丘成桐): HK-USA, Harvard Dean of Maths.
2. Terence Tao (陶軒哲): Australia-USA (Parents immigrants from HK), UCLA Math Professor.
3. Ngo Bao Chau (吳宝珠): Vietnam-France, École Normale Supérieure (Paris) / Princeton University.

The other great Chinese Mathematician is S.S. Chern (陈省身), he was too old for Fields medal (only for below 40) but awarded Wolf Prize together with Paul Erdős. He was the thesis prof of ST Yau.

Hope Singapore, China and Taiwan will produce any new Chinese Fields medalist.

There is one rising star CHINA/USA YT Zhang 张益唐 (1955 -, 60 years old) who shocked the Math world last year from obscurity with the “Twin Primes 70-million Gap” Proof.

Terence Tao thinks highly of applying Math in engineering, medicine, science etc. He used Math to help reduce the harmful MRI Scan of patients from 10 mins to just 2 secs with the same quality of image.

Unfortunately today Math in primary schools to junior colleges are taught without explaining the theories behind, which makes Math subject rather dry and boring, until those who are fortunate taking university Math courses to find out the beauty of Math (Group Theory for Symmetry, etc).

费马大定理 Fermat’s Last Theorem

费马大定理 Fermat’s Last Theorem (FLT): 17世纪业余数学家法国大法官费马开的一个”玩笑”, 推动350年来近代数学(Modern Mathematics)的突飞猛进。

1977秋 ~1979秋 笔者在法国-图卢斯(Toulouse, Southern France, Airbus 产地)费马学院 (College Fermat, aka Lycée Pierre de Fermat: Classe Préparatoire, 178th Batch)读两年的大学近代数学 (Mathématiques Supérieures et Spéciales), 尝过一生读书的”地狱”生活, 严谨(Mathematical Rigor)的思考训练, 像地鼠般(法国人戏称taupe)不见天日, 废寝忘食的煎熬。 当年对数学的恐惧, 终生牢牢铭记在心; 30年后”由惧转爱”, 数学竟然成为半退休后的业余嗜好, 享受数学的美 — 也是造物者宇宙天地的美!

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FLT 350年数学长征英雄人物:
1. Fermat (费马 1601@ Toulouse, France)
2. Galois (伽罗瓦): Group Theory (群论)
3. Gauss (高斯)
4. Cauchy (柯西) Lamé (拉梅) Kummer (库马)
5. Solphie Germain
6. Euler (欧拉)
7. Taniyama (谷山丰), Shimura (志村五郎)

“数风流人物, 还看今朝”集大成者 :
8. Andrew Wiles (怀尔斯) 证明 (1994 -1995)”盒外思路” (Think Out of The Box): The Great Moment of 1994 Proof (YouTube)

\boxed {(1) = (2) = (3) }
(1). Elliptic Curve (椭圆曲线)
(2). Modular Form (模形式)
(3). Fermat’s Last Theorem (费马大定理)

费马大法官品尚清高, 讨厌政界官僚逢场作戏的应酬, 工余爱躲在家里玩数学, 然后写信和好友(巴斯卡 Pascal, 笛卡儿 Descartes,…)讨论, 无心中发明了物理(Optics)定律, 或然率 (Probability – 和Pascal合作), 解析几何 (Analytical Geometry – 和Descartes合作)…尤其他是近代数论(Number Theory)的开山鼻祖 (他的另一个Fermat’s Little Theorem今天用在电脑密码RSA Encryption)。
他偶然读到3,000年前希腊数学家Diaophantine的书 (10世纪阿拉伯人保存, 16世纪拉丁文翻译自阿拉伯文)。他心学来潮, 在书眉写道: “我找到一个漂亮的证明这题Diaophantine Equation, 但此书旁地方太小, 不能写下”。 他死后, 儿子整理遗作而发现此书, 就成为350年来的数学疑案。

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Excellent MITOpenCourseware

Strongly recommended the free excellent MIT Math for high school, undergrads/grads and any self-study Math learners.

Thanks Prof. Gilbert Strang for the unselfish sharing.

http://ocw.mit.edu/faculty/gilbert-strang/

I find extreme pleasure when I discovered his brilliant lecture notes in “Generating Function” – a Discrete Math technique for computing Sequence using function, and the application in complex Combinatorics. Download PDF here.

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Example:
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