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.

Diego Fonseca looked at the computer and took a breath. It was his final attempt at the math placement test for his first year of college. His first three tries put him in pre-calculus, a blow for a ...