為什麼法國能誕生11位菲爾茲獎獲得者？

01-30

http://zh.m.wikipedia.org/wiki/%E8%8F%B2%E5%B0%94%E5%85%B9%E5%A5%96

法國長期都是數學大國。

笛卡兒、費馬、柯西、劉維爾、傅立葉、泊松、勒讓德、勒貝格、拉普拉斯、拉格朗日、埃爾米特、哈達馬、韋達、雅各比、約當、韋伊、布爾巴基學派……

布爾巴基學派崇尚抽象典雅的風格對當代法國的數學教育影響巨大。

從內容上看，法國數學教學不注重心算口算，注重邏輯演練。數學的教學大綱很合理。

從組織上看，法國一向是精英教育，注重對天才的培養，不管天才是什麼樣的人。比如巴黎高等師範學校的入學考試非常難，完全是在選天才。

從經費上看，數學對經費要求很小，使得法國俄羅斯這種經常沒錢搞實驗物理的國家去鑽研數學。因為數學和理論物理是緊密相關的。

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P.S.

說什麼法語數字邏輯混亂導致法國數學好的，估計沒學過什麼數學。

數學遠大於算數的範圍。很多數學家不會心算除法，但人家會群論。

曾經碰到過習題課問老師為什麼x^a * x^b = x^(a+b)的法國人。

但是碰到的那些prepa數學出來的法國人真的是數學理論學得異常紮實，讓人敬佩不已自嘆不如，即使是去了高商的同學，照樣能在工程師學校的quantitative課程裡面展現出優秀的邏輯、理論概念認知。

法國優秀的學生會讀prepa, prepa里有非常嚴酷數學訓練，而且法國的數學不同於中國的數學教學那麼死板，更側重於邏輯和推理，考試經常都是各種推理證明題，計算之類的倒是很少，這種的教學，更加接近數學的本質。

此外，數學專業就不說了，工程師學校的學生也需要學不少數學，尤其側重概論統計之類的知識

這種問題英語世界的答案已經很豐富了,搬運一下：

As a French engineer who lived a lot in other countries, I might be well placed to answer this question:

- Teaching advanced mathematical concept early in school. Students are introduced to the vector calculus in the second year of "College", when they are 12, pretty much at the same time as percentages and simplest systems of equations. This part is mandatory for everyone, and there is no way to avoid it, even for those who will be attending vocational high schools. Until recently, the bases of Matrix theory, combinatorics and group theory (!) were also taught starting from 14 years of age.

- All natural sciences are taught through mathematics. In most countries in the world, the understanding of other natural sciences come from the intuition first, then some simple equations are written to formalize it. In France, it is completely different: first you write a pretty complex system of (differential) equations that fully describes all the variables of your system, then you spend a couple of hours solving it and finally get what you was initially interested in. It is not necessarily the best approach, but it has an advantage to still be working in case you have no intuition for what is going on (cf. Foucault pendulum or de BrogliesMatter waves).T

- Preparatory Classes and Grandes Ecoles system. In France, most prestigious business and engineering schools recruit based on a competitive exam that takes place after two years of "Preparatory Classes", roughly equivalent to the first three years of university. Since it is a competition and not an exam, a minimal passing grade doesnt mean success but failure. You have to get the best grade among all. This leads to an arms race between teachers and students of different "Preparatory Classes", which in turn leads to an upkeep of the level of problems encountered in the competitive exams. Most Prestigious "Grandes Ecoles", such as ENS would even include currently opened problems in fields of mathematics and theoretical physics in order to see how students react to problems that have no known solution, and just in case one of them comes up with an idea how to solve one.

- Tradition of mathematics and encouragement of a critical approach. A large part of 19th century mathematics underlying most of our modern technologies today were coined by French mathematicians ( Poisson,Fourier, Laplace, Galois...) just as some of more recent foundation concepts in mathematics ( Mandelbrot ). Knowing them personally as students or colleagues before they achieved their fame led mathematics professors of most of French higher education institutions to consider that any of their students could become the next mathematician of century and thus to be extremely precise and detailed in their teaching and to encourage a critical approach of existing theories.

Now, about porting it to developing countries:

- A high-quality introduction to mathematics at the middle and high school level is definitively a thing to do. However it requires a large corpus of good mathematics and natural science majors who are ready to stay as teachers in their home country rather then working abroad.

- Conversion to the "Cartesian" approach of natural sciences can be debatable, since it will drive off a large portion of students from sciences because of a too abstract approach.

- Competitive entrance exams is also a debatable approach, since a harsh competition is believed to reject way too many underprivileged students and lead to a creation of elite detached from the rest of society ( see Guardians article that explains it pretty well)

- Tradition of mathematics is hard to reproduce, but having a couple of world-renowned professors and the best of the alumni in the universities is definitely a plus. Encouraging a critical approach of current theories could definitively help too. Once again, it requires that the best alumni are more interested in staying within the country rather then leaving working abroad, which is more of a political / organizational problem.

地址：The reasons the french are so good at mathematics?

實際上法國沒拿菲爾茲獎的數學家更是牛逼的不行

首先，現代數學這種公理化、嚴格定義、根本上靠高度抽象的概念和縝密的邏輯推理支撐的範式就是拜布爾巴基學派所賜。換言之，人家是這一套的開山鼻祖。

其次，從小就被布爾巴基這種教法長期洗腦的孩子們，如果沒被玩殘，那……還要我說嘛？