Weierstrass Function
en.wikipedia.org> Henri Poincaré famously described them as "monsters" and called Weierstrass' work "an outrage against common sense", while Charles Hermite wrote that they were a "lamentable scourge"
For anyone here not aware, Poincaré and Hermite are some of the biggest names in maths ever.
If I was Weierstrass I would've taken it as a compliment that such big names were shocked. Note they're not saying the function doesn't exist or it fails to make the point.
Also known as an example for "if it pricks you when you touch it, it's not differentiable"