Day 41 · Feb 10

Death of Karl Weierstrass (1897) — The Father of Rigour

Karl Weierstrass died in Berlin on February 10, 1897, having spent his career dismantling the comfortable intuitions of calculus and replacing them with iron-clad logic. He gave the famous ε-δ definition of a limit that students still learn today, making rigorous what Newton and Leibniz had left intuitive. More shockingly, he exhibited a function that is continuous everywhere but differentiable nowhere — a curve with no tangent at any point: W(x) = Σ bⁿ cos(aⁿπx). It violated every geometric instinct. Poincaré called such functions 'monsters.' But Weierstrass showed that the monsters are real, and that geometry cannot be trusted without algebra to back it up.

A function can be continuous everywhere (no gaps or jumps) yet have no derivative anywhere (no tangent at any point). Can you draw what a small piece of such a curve might look like?

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