In the late 19th century, Karl Weierstrass invented a fractal-like function that was decried as nothing less than a “deplorable evil.” In time, it would transform the foundations of mathematics.

Charles Hermite called it a “deplorable evil.” To understand why Weierstrass’ result was so unnerving, it helps to first understand two of the most fundamental concepts in calculus: continuity and ...

In the space of continuous functions of a real variable, the set of nowhere differentiable functions has long been known to be topologically "generic". In this paper it is shown further that in a ...