There's a wonderful book on Mathematical counterexamples in French[0], meant for undergrad/engineering school hopefuls.
So many of the continuity counter-examples are throwing Weierstrass at the wall and getting something to stick. It's fun but also feels a bit like cheating.
I do recommend this book for any french-speaking mathematician-adjacent person though. Real great dictionary for remembering why certain things only work in one direction.
It is interesting how France became so focused on analysis and properly proving theorems and stuff, while the applications don't have the same highlight in prépa.
One professor of mine commented that most French engineers are better mathematicians than most mathematicians in Brazil.
It is the opposite of what the linked article mentions that was happening in Weierstrass' time.
So many of the continuity counter-examples are throwing Weierstrass at the wall and getting something to stick. It's fun but also feels a bit like cheating.
I do recommend this book for any french-speaking mathematician-adjacent person though. Real great dictionary for remembering why certain things only work in one direction.
[0] Les contre-exemples en mathématiques: https://www.editions-ellipses.fr/accueil/5328-les-contre-exe...