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Well, I apologize if this "soft-question" (related to the "Arnold-Serre" debate) is considered as irrelevant for MO, and for possible misunderstandings in the two earlier versions of this post (which was not provocative).

I certainly do not want to stir a useless debate. As a french math teacher, I know that Henri Cartan, Claude Chevalley, Jean Dieudonné, Charles Ehresmann, Jean-Pierre Serre, André Weil ... were all great mathematicians. Obviously, N. Bourbaki had a huge impact on the mathematics of the last century. I'm also well aware of his predominance on french mathematics, but I know virtually nothing about his influence on others mathematical schools.

So I do believe that the following question is not really "opinion-based" (question which is not about the present production of the very much alive Bourbaki seminar) :

Question : Is it now possible to give a fair assessment of the influence of Bourbaki's "Eléments de mathématique" ?

(I'm ready to accept the answer : "No, it's impossible").

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closed as primarily opinion-based by Federico Poloni, Bill Johnson, YCor, abx, Andy Putman Apr 5 at 19:27

Many good questions generate some degree of opinion based on expert experience, but answers to this question will tend to be almost entirely based on opinions, rather than facts, references, or specific expertise.If this question can be reworded to fit the rules in the help center, please edit the question.

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Bourbaki did not die in 1968. They published a book recently and organize a seminar. –  quid Apr 5 at 17:32
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The problem with the way you formulate the question is that Bourbaki never published a research paper or book. So the question is a little bit like: what the mathematical importance of wikipedia ? If the question is to be understood "how useful are Bourbaki's books for a research mathematician, as compared say, with wikipedia?", then it may make some sense... Also, what happened in 1968 regarding to Bourbaki? –  Joël Apr 5 at 17:32
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@Joël I'm sorry for the bad editing. Of course, I'm well aware the the Bourbaki seminar (amphi Hermite, IHP, Paris) is still going on, and that at least Serre, Cartier and Grothendieck are still living, but I thought that the Bourbakist prank math.univ-angers.fr/~darniere/bourbaki.html#deces was more widely known, so my feeble attempt at humour failed miserably. Yes, my question is broad, and no, it is not subjective. I have a strong personal opinion, and I would like to read a truly unbiaised assessment, but you can close my question immediately –  user45639 Apr 5 at 19:35
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On my opinion their influence was enormous, and I do not see why this question was closed. It is no more "subjective" then other soft questions. –  Alexandre Eremenko Apr 5 at 20:19
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There is a serious attempt to assess the influence of what Bourbaki proposed as the central concept of the entire Elements corpus, namely that of Structure, by Leo Corry: tau.ac.il/~corry/publications/articles/bourbaki-structures.html. It can be argued, for various reasons, that this concept did not "take". On the other hand, we have the masterly Lie Groups and Lie Algebras which really set a standard for generations. So it seems to me an assessment of the influence of the Elements might best proceed on a book-by-book basis. –  Todd Trimble Apr 7 at 2:15