[neel_k]

It's worth understanding the context Bourbaki arose in.

An entire generation of French mathematicians was turned to bits of blood and gristle in the trenches of World War I, and so French mathematicians in the 1920s and early 1930s faced an acute shortage of teachers who were current with modern mathematics.

The premise of the Bourbaki effort was to write everything down in enough detail that a sufficiently motivated reader could learn it without having to learn it master-apprentice style -- because too many potential masters were dead.

[woolion]

In that case, that means they have entirely failed. The very few people I've met who actually bothered with the books only made fun of how horrible they were to read and understand. I never even did open one myself! I always admired the principle though, because you can reduce everything to pure logic (and even in some cases you can "brute-force" formalism to obtain new results). Which makes me think category theory kind of fills this role in a better way?

[n4r9]

Even without the context, there's something to be said for a formalised approach. When I was in undergrad there was a lecture course given by a notoriously aloof and formal lecturer. One of the other - more popular - lecturers decided to give an "understandable" alternative to the course at the same time of the day. Myself and a few others were in the 5% that continued with the official schedule. Those notes were hard as hell to work through, but once you understood something, you REALLY understood it.

One of the exam questions was conveniently targeted at one of the lectures from the more difficult course. I think it was proving that A5 is simple by considering the rotations of a dodecahedron.

[jacobolus]

I disagree. An overly dry and formal style (definition, definition, lemma, theorem, corollary, definition, lemma, lemma, theorem, ...) does not make students “really understand” the material. It just focuses students on low level details of formal definitions and symbolic manipulation and gives a lot of practice regurgitating/performing those, often at the expense of knowing the purpose or meaning of the subject. Low-level details are certainly essential, but the only way to really understand is to figure out what the formalism is for (what problems does it solve), grapple with the possibility space of definitions and theorems (if we picked this alternate definition, would that also get us where we want?), figure out how topics and structures relate to each-other, spend some time doing personal explorations, and build up mental models of what the definitions mean, not just their formal content.

A too-dry mathematics course/book is like a screenwriting course where you focus on snappy dialog and details of the setting but never talk about the plot or themes of the story.

[bsedlm]

> a sufficiently motivated reader could learn it without having to learn it master-apprentice style

if that's the case, I would say they failed.

however, what they accomplished would certainly help jog the memory of somebody who knew the material once upon a time.

maybe it's a bit like looking at a zip file directly and uncompressing the contents on the fly in your head? (something about 'understanding' as a compression scheme)