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For all that Bourbaki has been highly influential (and equally contentious) in maths, I don't actually know anyone who owns a copy of "Éléments". Is that just because I'm not French and it's actually huge among French mathematicians or perhaps because I'm just not "there" yet in my study of maths, having not got on to analysis in particular?

Obviously some ex-members of the group (Grothendieck and Serge Lang in particular) have published books that are more widely read.



Given that you're talking about your "study of maths", I presume that you're a student. Well, Bourbaki books aren't textbooks. They're reference books. They're great when you need a theorem and you know you can just pickup your copy of "Lie algebras" and find it exactly where you expect it to be. And you know the proof will be there, and you know the proof of every single lemma used will be there. But it's not a learning tool. Think more about a dictionary/encyclopedia than a school book. You wouldn't learn to speak English by reading an English dictionary.


Sounds awesome. It's worth saying that the Serge Lang textbooks I have are awesome for learning maths from. I really love them - they don't treat me like an idiot and they have lots of problems to practise on - from basic to pretty hard, so I'm not negative about the group as a whole. I was genuinely curious.


> Well, Bourbaki books aren't textbooks. They're reference books.

The Bourbaki group has repeatedly emphasized that point and explained their goal and rationale with the Elements; and yet, people still blame them for all sorts of developments in post-graduate mathematics education. I find it rather unbecoming.


Having met current and past members of the Bourbaki group, I can say with certainty that the group in general is very much opposed to the whole "new math" trend that (thankfully) fell out of grace. But I guess it's easier to find bogeyman for all of society's problems.


Could you elaborate more? What is the new trend? How it fell out of grace? Who were the members that voiced the view?


I guess there is a trend to consider, in which algebra and statistics tend to be picked and studied more in the last decade compared to e.g. analysis. Thus why we don't see all that many people studying advanced analysis books.

I would also argue that each country / culture teaches mathematics in a different way, which may not suit well with an outsider. From my experience US/UK tend to emphasize intuition first and rigor later, while French mainly focus on rigorous reasoning and proofs, leaving intuition as a by-product of experience that will be eventually picked up by the student on his own. That may discourage non-French students to further read such books.


I actually own most of elements, in the original French and first edition! Found them on a used bookstore warehouse outside of DC for $5 each. They sell on eBay pretty regularly for >$100 (you have to search the French title). I don't speak French but it's cool to have them as a collectors item




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