Bourbaki – A Secret Society of Mathematicians

ultimately they failed because they wrote such that it didn't matter if other people understood. it's a style that is only intelligible if you already know (from some other experience) what they are describing.

I also heard that part of the bad reputation that Bourbaki got was due to their being used in graduate education, despite warnings that they weren't suitable. In the 1950s/60s, there was a lack of good graduate texts. Of course, then Serge Lang came along...

Bourbaki is known for their "definition-theorem-proof" style, which for a while influenced a lot of mathematical writing. It makes the logic of the presentation easy to follow. The proofs are complete and fairly clear. The logical order within books and in the series of books as a whole is also pretty good - if you read pages 1 through n in the books, you have the prerequisites to read a proof on page n + 1. There is a good index, a table of notation, exercises (at the back, not by section), and a table of contents (at the back, since the books are in French).

They probably originated the "dangerous bend" symbol (a Z-shaped curve in the margin) to indicate a tricky or subtle point.

They're pretty good as references (to look up the proof of a result, or read about single topic).

On the negative side:

There is little exposition in the sense of motivation for what is presented, or applications.

I'm looking at "Algèbre - Chapitre 10 - Algèbre homologique" (the only Bourbaki I own). In the introduction, they say:

"Le mode d'exposition suivi est axiomatique et procède le plus souvent du général au particulier."

"L'utilité de certaines considérations n'apparaitra donc au lecteur qu'à la lecture de chapitres ultérieurs, à moins qu'il ne possède déjà des connaissances assez èntendues."

Thus, you won't find applications, or many examples - just definition-theorem-proof.

It's assumed you know why you're reading the material, and so don't need to be told.

This particular volume is a little unusual for the series in that it has lots of pictures, but that's only because this is homological algebra, so there are many commutative diagrams. Most of the volumes are just walls of text (though the formatting and the production tend to be very clear).

(I believe they actually wrote some historical remarks in some of the books which were collected in a separate volume - I don't see any historical material in the volume I'm looking at, however. The members were not unmindful of things like history: Dieudonne wrote an excellent history of algebraic and differential topology, and Andre Weil wrote a book on the history of numbers.)

The fact that it took a while for many of the volumes to be translated from French to English may have deterred some English readers (though mathematical French is not too hard to understand even if you don't know French [like me]).

On the whole, (in my opinion) the presentation is too relentlessly formal for most people to try learning a subject (as opposed to a small topic) by reading Bourbaki. They did produce a "definitive exposition" of the subjects they covered, in the sense that the results and proofs are there. It's just that most people would have a hard time learning any of the subjects by reading through the books.

yes, this is the original link I submitted. not sure why it was modified.