What is the legacy of Bourbaki?

Question

As I was preparing a short lecture (for amateurs) on the mathematics of the '900, I realized that this year marks the 70-th anniversary of the founding of the Bourbaki group.

I remember that Bourbaki has been important in my formation (in the years 1970-80), when it was considered as a "school" of math. So I'm interesting to know how much this "school" is influential also today.

I know that we can find the legacy of Bourbaki in many notations (the most important being the symbol $\emptyset$, as far as I know about the use of this symbol), and also in the definition of modern mathematical branches as commutative algebra. But my curiosity is about the influence as a "way of thinking" about mathematics.

To be not too vague I can articulate it in two questions:

The first (for mathematician): has Bourbaki been important in your formation? And his "style" is it important in your work today?
The second (for students): do you know Bourbaki? Have you used in someway his books in your learning?

Any other consideration about the legacy of Bourbaki is welcome.

Bourbaki books are unreadable. I usually get lost after the first page. if u wanna punish someone makin him read any of the bourbaki books — ILoveMath, Feb 12 '15 at 10:16
I agree. But they are a source to find proofs of many results. Or only they was for me? — Emilio Novati, Feb 12 '15 at 10:21
@Muaro : thankyou. But... this is the history. What about the contemporary influence of Bourbaki? — Emilio Novati, Feb 12 '15 at 11:01
From the quotation in the other post : "Mathematics should be seen, Dieudonné added, as a hierarchy of structures"; we can say that the central role played by the concept of structure in "modern" (I mean post II World War) math is due to B. — Mauro ALLEGRANZA, Feb 12 '15 at 17:06
I am in no position to judge the possible indirect influence on me, but Bourbaki has had no direct influence on me whatsoever. In particular, I’ve never even looked at any of the books. — Brian M. Scott, Feb 12 '15 at 21:01
Maybe that the influence of B. in US was much lesser than in Europe? — Emilio Novati, Feb 12 '15 at 21:05
You can see also Leo Corry, Writing the Ultimate Mathematical Textbook Nicolas Bourbaki’s Éléments de mathématique. — Mauro ALLEGRANZA, Feb 12 '15 at 21:22
Lastly, you can see : Maurice Mashaal, Bourbaki : une société secréte de mathématiciens (2006). — Mauro ALLEGRANZA, Feb 12 '15 at 21:26
Thanks @Mauro, I've many things to read now. Given the poor interest to this post it seems that B. has not many followers today.. — Emilio Novati, Feb 12 '15 at 21:32
I'm not sure if it's a direct result of Bourbakists, but you could say that those ideas basically burned the bridge between physicists and mathemathicians which are only recently starting to recover. As a physicist, I think it's a shame. Insistence on rigor and formalism at every step of the way (which, I believe, is at least partially Bourbaki's legacy) unnecessarily stifles understanding and, therefore, progress. Jusy my opinion, make of it what you will. — lel, Jan 08 '19 at 16:47

score 3 · Accepted Answer · edited Apr 13 '17 at 12:20

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The said legacy is mixed. The volumes dealing with algebra and particularly Lie theory are thought to be excellent. The volume Theory of Sets is not merely out of date but contains serious errors analyzed by a professional logician named Adrian Mathias (see my answer here).

edited Apr 13 '17 at 12:20

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answered Apr 07 '16 at 13:43

Mikhail Katz

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What is the legacy of Bourbaki?

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