Pawned Fields Medal

1936	Lars Valerian Ahlfors (Harvard University)

The first person in history to receive a Fields medal was a Finnish Ahlfors in 1936. At that time Finland was at war with England, no person could bring  more than 10 crowns out of Finland. Ahlfors was accepting a job offer from Harvard, so he pawned his Fields Medal for ticket to leave Finland, later got the medal back from the pawn shop.

[caption id="" align="alignright" width="300"] Lars Valerian Ahlfors (Photo credit: Wikipedia)[/caption]

Why French excel in math ?

Mathematics and quantitative finance, France

Since 1990, there have been 22 winners of the Fields Medal, widely regarded as the Nobel Prize of mathematics. Thirteen came from just two countries, Russia and France. Russia has more winners (seven), but more than twice the population, so the honours go to France, with six winners.

Cédric Villani, the 2010 Fields Medallist, cited national character. “Maths is an abstract way of looking at the world, which fits well with the French mentality. We apply algebra to everything.” Elite institutions help too. France’s brightest school leavers progress to the grandes écoles, which traditionally educate top scientists, administrators and presidents. For maths, you want Monsieur Villani’s alma mater, the École Normale Supérieure (ENS). All 10 French Fields Medallists learnt there. At ENS, no teacher can stay longer than 10 years. Instead of ancient dons, students get tutors at the forefront of mathematics. Many try, but only 40 mathematicians a year enter the ENS.

The French have applied their maths genius to the money markets too. The Financial Times business schools rankings suggest France leads the world in producing “financial engineering” experts, with six institutions in the top 10 masters courses in finance. France can thus claim to dominate quantitative finance, the highly mathematical specialism involved in about half of all financial trades.

They should thank Michel Crouhy. In 1986, at the École des Hautes Études Commerciales (EHESS) in Paris, he devised the world’s first masters course in financial engineering. “The business school students didn’t have good enough maths, so I said ‘Let’s take only maths graduates, engineers. I won’t have to spend forever explaining the equations.’ It worked; the EHESS still offers the world’s best finance masters course, according to the Financial Times.

“Americans told me they wanted to start a course like ours but they weren’t allowed,” says Crouhy. “Because US MBA programmes were so strong, the universities worried a finance masters would compete with their MBA and destroy the MBA’s franchise.” America’s hesitation seems to have cost them.
--

"Turn-off" School Math

"...There's a long history of high caliber mathematicians finding their experiences with school mathematics alienating or irrelevant. "
Read here:
http://lesswrong.com/r/discussion/lw/2uz/fields_medalists_on_school_mathematics/

In Récoltes et Semailles Fields Medalist Alexander Grothendieck describes an experience of the type that Alain Connes mentions:

I can still recall the first "mathematics essay" (math test, or Composition Mathématique) , and that the teacher gave it a bad mark. It was to be a proof of "three cases in which triangles were congruent." My proof wasn't the official one in the textbook he followed religiously. All the same, I already knew that my proof was neither more nor less convincing than the one in the book, and that it was in accord with the traditional spirit of "gliding this figure over that one." It was self-evident that this man was unable or unwilling to think for himself in judging the worth of a train of reasoning. He needed to lean on some authority, that of a book which he held in his hand. It must have made quite an impression on me that I can now recall it so clearly.

ST Yao丘成桐

丘成桐 (ST Yao 1949~) Fields Medal @1982 [33岁] proved Calabi Conjecture

1. 读私立 培正中学, 高中遇 好数学老师. @香港中文大学, 发觉 Math Beauty, '豁然开朗'.
2. Best Math student not necessary Mathematician, only sufficient!
3. 一名数学科学家 都应对 文学,哲学 这类 学科有基本的涉猎. 好的数学 使你体验到庄子讲的
"天地与我并生, 万物与我为一" 的境界
4. 成功 = 要有数学热情.
Strategy:
a. 深入思考
b. 在心中或纸上仔细研究
c. Find clues from book, till get answer.
d. 出题目给自己

Perelman rejected Fields Medal & $1m Clay Prize

1. Perelman first published his Poincaré Conjecture proof at this site: http://arxiv.org/

2. After the USA study trip where he was attracted by Prof Hamilton's attempted proof with 'Ricci Flow', Perelman rejected a Harvard Professor job offer, returned to Russia to prove the Conjecture in isolation for 8 yrs as a low-pay free researcher.

“Absorbing the problem in its entirety and then boiling it down to an essence that proved simpler than everyone had assumed.”

3. In 2006 he rejected both Fields medal and US$1 m Clay Prize!

4. He won 1982 IMO Gold at 16 with full mark (42/42).
Perelman explained to the Math Olympiad jury his solution, who gave him full mark. Before the jury walked away, Perelman said: "Wait, I have 3 more solutions to this question!"

International Math Awards

1. Abel Prize: each yr, 1 or few share US$1m.

2. Wolf Prize: US$100K.

3. Shaw Prize (by Hong Kong Run-Run Shaw): US$ 1m, from 2002, every yr.

4. Clay Prize: 7 x US$ 1 m conjectures.

5. Beal Prize: US$100K
Prove Beal Conjecture: x^n + y^n  = z^n   if x, y, z have a common factor for n>2.

6. Fields Medal (equivalent to Nobel Prize): US$13,500, every 4 yrs, < 40 yr-old.

Fields Medal Inscription

"Transire suum pectus mundoque potiri"
[To transcend human limitations & to master the universe]