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 new type of fractal measures Ks, 1 ≤ s ≤ 2, defined on the subsets of the graph of a continuous function is introduced. The K-dimension defined by this measure is `closer' to the Hausdorff dimension ...

Abstract Given an o-minimal structure expanding the field of reals, we show a piecewise Weierstrass preparation theorem and a piecewise Weierstrass division theorem for definable holomorphic functions ...