The original version of this story appeared in Quanta Magazine. Calculus is a powerful mathematical tool. But for hundreds of years after its invention in the 17th century, it stood on a shaky ...

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.

Real and complex functions form the backbone of modern mathematical analysis, uniting the study of continuity, differentiability, and integrability on the real line with the rich structure of analytic ...