https://www.quantamagazine.org/inside-the-secret-math-society-known-as-nicolas-bourbaki-20201109/

# Tag Archives: Bourbaki

# 【数学科普】：函数概念的四重境界 Bourbaki Definition of “Function”

# Why Math is so Sexy?

Cédric Villani (**Field Medal 2010**) the French mathematician becomes a ** deputé** (equivalent to Member of Parliament) in President Emmanuel Macron’s new party “En Marche” consisting of 90% non politicians.

His new revolution in French Primary School Math Education is introducing “**Singapore Math**” : the 1960s Chinese Secondary School One Math (算术 Arithmetic) modified by the ex-Nantah (南大, now Nanyang Technological University) Prof Lee Peng Yee (李秉彝) with the **Polya** Problem Solving Method aided by visual **Model** diagrams.

France excels in Abstract (aka New / Modern / Bourbaki) Math but poor in Applied Math, while Asian countries (China, Singapore, Korea, Japan etc) are opposite. This demonstrates clearly in the Asian 15-year-old students scoring Top PISA Math Tests & **Math Olympiad** Championships (even in the USA teams), while the French young Mathematicians (< 40 years old) take 1/3 of the world’s **Field Medals – ***“the Nobel Prize of Math”.*

It is ideal to combine the Asian (applied) Math pedagogy for Primary school (from 7 to 13 years old) math and the French (abstract) Math (eg. Set, Group, Ring, Field, Vector Space, epsilon-delta Analysis…) in high-school math (from 15 to 18 years old).

The wise Cédric Villani is just doing this

for French Primary School Math Education .Ideal Combination of “East and West”

Note: In the video (12:12 mins) Villani described his “**Eureka discovery”** inspiration at 4 am in Princeton Institute of Advanced Math. The same experience found by many mathematicians eg. Poincaré, Zhang Yitang, etc. Read Villani’s book where he called this “Strange Head Voice” (*definitely not hallucination!!*) experience as “**The direct phone call from God **“.

# Edward Frenkel’s Lecture at Séminaire Bourbaki

“Gauge Theory and Langrands Duality”

**Number Theory ** | ** Curves over Finite Fields ** | **Riemann Surfaces ** | ** Quantum Physics**

# Our Daily Story #11: The Anonymous Mathematician “Nicolas Bourbaki”

The romantic gallic Frenchmen like to joke and played pranks. We have already seen the Number 1 Mathematical ‘prank’ in Our Daily Story #1 (The Fermat’s Last Theorem), here is another 20th century Math prank “Nicolas Bourbaki” – the anonymous French mathematician who did not exist, but like Fermat, changed the scene of Modern Math after WW II.

http://en.m.wikipedia.org/wiki/Nicolas_Bourbaki

André Weil (not to confuse with Andrew Wiles of FLT in Story #2 ) and his university classmates from the Ecole Normale Supérieure (Évariste Galois‘s alma mater which expelled him for involvement in the French Revolution), wanting to do something on the outdated French university Math textbooks, formed an underground ‘clan’ in a Parisian Café near Jardin du Luxembourg. They met often to brainstorm and debate on the most advanced Math topics *du jour*. Finally they decided to totally re-write the foundation of Math based on Set Theory. Inspired by the rigorous **axiomatic** approach of Euclid’s “The Elements”, they named their books **“Élements de Mathématique **” (The Elements of Mathematic) (Note: Math in singular). Collectively they picked a pseudonym “**Nicolas Bourbaki**” as the author of this series of Modern Math books. The Bourbakian **extremely abstract and rigorous ** approach to Math pedagogy influenced the French Math and the world ‘s Modern Math in post-WW II till today. The founding students in the Bourbaki group, led by André Weil (who migrated to the USA), almost all won the prestigious Fields medals. The Bourbakian baton passed on to the next generation of French mathematicians, including the hermit mathematician Alexander Grothendieck and the Chinese mathematician Wu Wenjun 吴文俊.

Notes:

1. The Bourbakians’ idea was to rewrite the foundations of math using a new standard of rigor based on the set theory initiated by Cantor in the late 19th century. They succeeded only **partially,** but their influence on math has been enormous.

2.The Bourbaki Seminar, one of the longest running math seminars in the world, held at the Henri Poincaré Institute in Paris, takes up a weekend 3 times a year.

Ref:

# Contemporary Math

Bourbaki started as rebels against the established modes of thought in French mathematics in the early 20th century.

But with new discoveries and the increasing important interaction between physics and math, their exclusionist (from Physics etc) approach lost its effectiveness.

Contemporary math is more multifaceted, it includes more varied **theoretical** and **applied** approaches.