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.

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    $\begingroup$ 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 $\endgroup$ – ILoveMath Feb 12 '15 at 10:16
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    $\begingroup$ You can see this post. $\endgroup$ – Mauro ALLEGRANZA Feb 12 '15 at 10:41
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    $\begingroup$ Maybe that the influence of B. in US was much lesser than in Europe? $\endgroup$ – Emilio Novati Feb 12 '15 at 21:05
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    $\begingroup$ Lastly, you can see : Maurice Mashaal, Bourbaki : une société secréte de mathématiciens (2006). $\endgroup$ – Mauro ALLEGRANZA Feb 12 '15 at 21:26
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    $\begingroup$ 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.. $\endgroup$ – Emilio Novati Feb 12 '15 at 21:32

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 The volume Theory of Sets is not merely out of date but contains serious errors analyzed by a professional logician named Adrian Mathias (see my answer here).


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