A Journey from Undergrad Math in China to PhD Math in France

An autobiography of a Chinese PhD student  (France, University  Paris-11) in Number Theory and Algebraic  Geometry.
His journey from 武汉大学 4 years undergrad to Beijing, learn mostly from the French-educated Chinese Math professors (Ecole Normale  Superieure, Polytechniques).

来源:梁永祺的日志(转载请注明出处)2012-12-16 06:52

“趁着一丝冲动记下一些经历,也趁着现在还能想起来,写写路途中遇到的人和碰到的一些书。”
http://blog.sina.cn/dpool/blog/s/blog_4ee63ce90102ea2r.html

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Ecole Normale Supérieure (Paris) (E.N.S.): 巴黎高等师范大学 (Galois 的母校但他因参加法国革命被开除, 现在是法国/世界 Fields Medals 的摇篮, 出Bourbaki 学派的大师André Weil, Cartan, Dieudoné, …医学细菌发现者 Pasteur是排班上最后一名的劣等生)。E.N.S.训练未来的教授 (文, 数, 理), 每年只收全法国前50位精英学生, 培养成博士。后来演变成研究院, 出了不少 Nobel Prize (Science, Literature) 和Fields Medalists.

Paris University 11 = Paris Sud (Paris South). 欧洲最古老的巴黎大学(Sorbonne 索尔本), 继承十世纪阿拉伯人创办的大学制度 (Bachelor, Licencié, Baccalaureate, “Chair” of department…)。出科学家居里夫人 (Madame Curie)。现在有13分校, 其中第11分校是数学研究的重镇。

Ecole Polytechnique (aka X): 巴黎综合理工大学 (拿破仑建的工程军校, 出很多科学家, 数学家: Hertz, Ampere, Fourier, Cauchy, Poincaré, Louiville,…偏偏天才Galois 入学连续考2年Concours不及格, 学弟 Charles Hermite 入学考最后一名, 第二年又被踢出门)。
新加坡30年来至今有4位数学顶尖学生考进 “X”。最近一位(2012)林恩隆 (公教/南洋GEP小学/ RI 中学/ RJC 高中 / Lycée St. Geneviève @ Versailles )是全法(外国考生 ‘Concours’ 工校”科举”入考)第一名, 他同时也是 E.N.S.全法(纯法国人的Concours)第15名, 后生可畏!! (用法文考数理化和法国哲学, 不公平的竞争, 却难不倒华人学子)!

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What is “Motif” (Motive) ?

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Recommended Books:
1. Jean-Pierre Serre: 《Cours d’Arithmetique》
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“Arithmetic” Textbook for Ecole Normale Superieure (2nd Year) 1962-1964:
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2. Jean-Pierre Serre:《Finite Group》

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2. 冯克勤 : 《数论简史》
(His son is the USA IMO national team coach.)
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中英翻译数学名词:
数论: Number Theory
(微分)拓扑 : (Differential) Topology
(线性)代数: (Linear) Algebra
交换代数 : Commutative Algebra
代数几何: Algebraic Geometry
类域 (范畴): Category
(李)群: (Lie) Group
泛函分析 : Functional Analysis
实变(函数)分析 : Real (Functional) Analysis
复变(函数)分析: Complex (Functional) Analysis
调和分析 : Harmonic Analysis
朗兰兹纲领 : Langlands Programme
高斯: Gauss
志村: Shimura
模式: Modular Form

French Concours & 科举 (Chinese Imperial Exams)

French Concours (Entrance Exams for Grandes Écoles) was influenced by Chinese Imperial Exams (科举\ko-gu in ancient Chinese, today in Hokkien dialect) from 7th century (隋朝) till 1910 (清末).  The French Jesuits priests (天主教耶稣教会) in China during the 16th -18th centuries ‘imported’ them to France, and Napoléon adopted it for the newly established Grande École Concours (Entrance Exams), namely, “École Polytechnique” (a.k.a. X).

The “Bachelier” (or Baccalauréat from Latin-Arabic origin) is the Xiu-cai (秀才), only with this qualification can a person teach school kids.

With Licencié (Ju-ren 举人) a qualification to teach higher education.

Concours was admired in France as meritocratic and fair social system for poor peasants’ children to climb up the upper social strata — ” Just study hard to be the top Concours students”! As the old Chinese saying: “十年寒窗无人问, 一举成名天下知” (Unknown as a poor student in 10 years, overnight fame in whole China once top in Concours). Today,  even in France, the top Concours student in École Polytechnique has the honor to carry the Ensign (flag) and be the first person  to march-past at Champs-Elysées in the National Day Parade.

Concours has its drawback which, albeit having produced top scholars and mandarins, also created a different class of elites to oppress the people. It is blamed for rapidly bringing down the Chinese Civilization post-Industrial Age in the last 200 years. 5 years before the 1911 Revolution, the 2nd last Emperor (光绪) abolished the 1,300- year-old Concours but was too late. Chinese people overthrew the young boy Emperor Puyi (溥仪) to become a Republic from 1911.

A strange phenomenon in the1,300-year Concours in which only few of the thousands top scorers — especially the top 3 : 状元, 榜眼, 探花 e.g. (唐)王维, (北宋)苏东坡, 奸相(南宋)秦桧,贪污内阁首輔(明)严嵩… — left their names known in history, while those who failed the Concours were ‘eternally’ famous in Literatures (the top poets LiBai 李白 and DuFu 杜甫), Great writers (吴承恩, 曹雪芹, 蒲松龄, 罗贯中, 施耐庵), Medicine (《本草綱目》李时珍, 发明”银翹散”的吳鞠通), Taipeng Revolution leader (洪秀全)….

Same for France, not many top Concours students in X are as famous in history (except Henri Poincaré) as Evariste Galois who failed tragically in 2 consecutive years.

The French “grandiose ” in Science – led by Pascal, Fermat, Descartes, Fourier, Laplace, Galois, etc. — has been declining after the 19th century, relative to the USA and UK,  the Concours system could be the “culprit” to blame, because it has produced  a new class of French “Mandarins”  who lead France now in both private and government sectors. This Concours system opens door to the rich and their children, for the key to the door lies in the Prépas (Classes Préparatoires, 2-year post-high school preparatory classes for grandes écoles like X), where the best Prépas are mostly in Paris and big cities (Lyon, Toulouse…), admit only the top Baccalauréat (A-level) students. It is impossible for poor provinces to have good Prépas, let alone compete in Concours for the grandes écoles. The new elites are not necessary the best French talents, but are the privilegés of the Concours system who are now made leaders of the country.

Note: Similar education & social problem in Japan, the new Japanese ‘mandarins’ produced by the competitive University Entrance Exams (Todai 东大) are responsible for the Japanese post-Bubble depression for 3 decades till now.

These ‘Mandarins’ (官僚) of the past and modern days (Chinese, French, Korean “Yangban 양반 両班 “, Japanese) are made of the same ‘mould’ who think likewise in problem solving, protect their priviledged social class for themselves and their children, form a ‘club mafia’ to recruit and promote within their alumni, all at the expense of meritocracy and well-being of the corporations or government agencies. The victim organisation would not take long to rot at the roots, it is a matter of time to collapse by a sudden storm overnight — as seen by the demise of the Chinese Qing dynasty, the Korean Joseon dynasty (朝鲜李氏王朝), and the malaise of present French and Japanese economies.

Reference:
1.
http://fr.m.wikipedia.org/wiki/Examens_impériaux#Influence_.C3.A0_l.E2.80.99.C3.A9tranger

2.
https://chinoiseries2014.wordpress.com/2014/12/16/科举-chinese-imperial-examinations/

PISA 2012: Singapore 2nd in Math

http://www.straitstimes.com/breaking-news/singapore/story/pisa-study-try-some-questions-yourself-20131203

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China, Singapore, Hong Kong and Taiwan are 4 predominantly Chinese population being ranked 1st, 2nd, 3rd and 4th, respectively, in the PISA 2012 Math Test for 15-year-old students.

While this is something to be proud of our Secondary School Math Education, it does not hide the fact that  beyond this age (15) these countries do not produce any high-level mathematicians like Fields Medalists or Nobel Prize Scientists.

What goes wrong ?

Reason: Asian education emphasizes on computation-driven Math drills, a long tradition of ‘abacus’ mindset, or ‘algorithmic‘ approach.
By doing plenty of Math assessments : in China “Sea of Math Questions” (题海), or in Singapore popular Math Tuition Class doing Past Years Math Papers, students are drilled in solving standard ‘sure-have-answer’ test questions with memorized or déjà-vu (of similar patterns) problem solving techniques.
Once they enter university where the Math is more of Proofing and “no-solution” type, most students are not trained in thinking and solving such questions, they will get stuck.

What Asian Math Education should improve is in the “Solving Unknown” Math skills – something worth to learn from the French Lycée (Secondary /High School) Math Education since they incubate 1/3 of Fields Medalists,  yet France’s PISA is average. (Why ? – another blog to discuss the French’s weakness in Applied Math.)

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.