The Jagged, Monstrous Function That Broke Calculus

Calculus, invented in the 17th century, lacked a solid foundation until the 19th century. In 1872, Karl Weierstrass introduced a function that was continuous everywhere but differentiable nowhere, challenging existing calculus concepts. This discovery forced mathematicians to redefine key concepts more rigorously, leading to the development of mathematical analysis. Weierstrass' work revealed the existence of "mathematical monsters" and found practical applications in modeling various phenomena, including financial markets.