How a destructive idea paved the way for modern math
The monster in question is the Weierstraß function [0], noteworthy for being  continuous everywhere yet differentiable nowhere.<p>I don't if the article talks about other "monsters" too. I didn't look further than to this one.<p>[0] <a href="https://en.wikipedia.org/wiki/Weierstrass_function" rel="nofollow">https://en.wikipedia.org/wiki/Weierstrass_function</a>