The Saw-Toothed Function That Broke Calculus

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The Saw-Toothed Function That Broke Calculus - Wired

Quick Summary:

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.

Mathematicians were forced to follow in Weierstrass’ footsteps, further sharpening their definition of functions, their understanding of the relationship between continuity and differentiability, and their methods for computing derivatives and integrals.

But Weierstrass had proved beyond doubt that, though his function had no discontinuities, it was never differentiable.