The first time I heard of Bourbaki, no one knew who the members were. They were quite anonymous.
You couldn't claim it on your list of published works and anyone who cites Bourbaki is citing the group, not you individually. The tremendous energy that they put into an anonymous work seems contrary to the publish-or-perish mindset in academia of today.
According to Pr Gleik they "engineered" math so that not another Poincaré would appear again. A french mathematician that based his reasoning to geometry at the dislike of yet another academy that thought talent should not despise the recognition earned by the experts. And Poincaré made clear he despised the formalism fanatics and the french school of math.
So they pushed what Feynman called an hyperverbose reformed version of math that would rather focus on being objectively "scientifically correctly expressed" by being able to manipulate formalism instead of having intuition that could ridiculed the best.
They said that Mandelbrot owe them a lot, and Mandelbrot just fled these people without really caring because he thought geometry was important and these people were kind of pedantic.
The message of bourbaki in one "lemma" is never draw.
A drawing is always a special case and no drawings of schema will ever lead you to build strong abstractions. Formalize everything.
It kinds of looks like modern computer science fights between the craftsmen vs the tools/language/frameworks/methodology fanatics.
And for an extended understanding of the mechanism of how Bourbaki's 'new math' and other amazing formalism makes it to the top of the educational offer in California a little light on still standard practices is necessary: it is all about the best choice possible
