A Group Form

On December 10,1934, a handful of young mathematicians gathered in a cafe in the Lat

Quarter of Paris. Their goal: to write a textbook on analysis. This is the beginning of

legendary enterprise that would change mathematics forever.

a

The University of Strasbourg,

where Andre Weil and Henri

Cartan taught at the beginning of

their careers.

£ A ndre Weil and I were both at the University of Strasbou

f^L in 1934.1 often talked with him about the course on d

JL JLferential and integral calculus that I was teaching. At th

time, a degree in mathematics was composed of certificates in ge

eral physics, differential and integral calculus, and classical mecha

ics. In other words, there was only one certificate in mathematic

[...] Therefore, I had to put as much as possible into what there wa

I often wondered about the best way to teach this course because t

existing textbooks were not satisfactory, especially when it came

multiple integrals and Stokes' Theorem. I discussed my concerns se

eral times with Andre Weil. One beautiful day he told me, 'I've had

we need to fix this for good. We need to write a good textbook

analysis. Then you'll stop complaining!'" This is how Henri Cart

described the origins of Bourbaki to Marian Schmidt in 1982, an

Andre Weil confirms it in his Souvenirs d'apprentissage (translated

The Apprenticeship of a Mathematician), published in 1991: "O

winter's day, in late 1934,1 came up with a terrific idea for putting

end to my friend's persistent interrogation. I told him [Henri Cartan

'There are five or six of us teaching the same course in various un

versities. Let's get together, fix the problems, and after that I'll final

be free from your questions.' I didn't realize that Bourbaki was bo

at this moment."

It's impossible to guarantee that human memory accurate

recalls events from more than fifty years in the past. Yet even thoug

this conversation from 1934 only gives a hint of the profound re

sons for forming the group and of what would happen later, the

two quotations do summarize the birth of the Bourbaki group.