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.

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 ...

A very elementary proof is given of the theorem that on a set of measure zero on $T$, any continuous function is equal to a continuous function of analytic type. The ...

Ricardo Martinez does not work for, consult, own shares in or receive funding from any company or organization that would benefit from this article, and has disclosed no relevant affiliations beyond ...

This monthly journal, begun in 1950, is devoted entirely to research in pure and applied mathematics, principally to the publication of original papers of moderate length. A section called Shorter ...