[goldenkey]

I don't know if I can agree with that. I bought every book Serge Lang produced. He was a member of Bourbaki. His Linear Algebra book is far better at providing intuition and motivations than the rest. Yet it is also rigorous. Lang is #1 for Mathematics books in my world.

[soVeryTired]

Fair - I don't doubt that there are some great educators in the Bourbaki school. But as Arnold mentions in his lecture I do think mathematics lost something when it embraced formalism so fully.

For me, the definition "A group is a set of transformations on an object such that..." is so much more enlightening than "A group is a set G together with a binary operation * such that..."

Only yesterday I was trying to learn about differential forms. Most of the notes I found online introduce the wedge product in a deeply unhelpful way, by listing some axioms that it satisfies and deducing results from the axioms. It takes hours of work to understand why those specific axioms were chosen. For me - and maybe I'm wrong here - that's Bourbaki's formalist approach in a nutshell.

It was only when I found Terry Tao's notes [0] and Dan Piponi's notes [1] that I could actually see the use of differential forms. It's an unfortunate state of affairs for the discipline that in order to learn about X, you have to google "X intuition", since it's not given to you as a matter of course.

[0] https://terrytao.wordpress.com/2007/12/25/pcm-article-differ... [1] https://github.com/dpiponi/forms/raw/master/forms.pdf

[goldenkey]

I totally agree. A lot of times you have to search for intuition rather than it being provided. Rote memorization is useless because mathematical research requires the intuition to give your mind the right direction to go in.