Mathematics
The Weierstrass Function and the Concept of Nowhere Differentiability
Quick fact
In 1872, Karl Weierstrass presented a function that is continuous everywhere but differentiable nowhere, shattering the long-held belief that every continuous function must be differentiable at most points. His function is defined as an infinite sum of cosine waves with carefully chosen amplitudes and frequencies.
Why this is interesting
You've probably been taught that a continuous curve has a tangent line at almost every point. But what if a curve were so jagged that it had no tangent anywhere—not even at a single point?