“Gauge Theory and Langrands Duality”

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

“Gauge Theory and Langrands Duality”

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

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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Galois‘s alma mater which expelled him for involvement in the French Revolution), wanting to do something on the outdated French university Math textbooks, formed an underground ‘clan’ in a Parisian Café near Jardin du Luxembourg.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:

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.