Joseph Fourier

Joseph Fourier (1768–1830) was a French mathematician, physicist and — genuinely — a revolutionary, who had one gloriously stubborn idea: any wiggle you like, however jagged, can be built by stacking up enough plain sine and cosine waves. People told him it couldn't possibly be true. He was mostly right, and the whole modern world of signals runs on it.

The famous discovery

Fourier's big claim is that a repeating shape can be written as a sum of simple waves — his Fourier series. Stretch that idea to shapes that never repeat and you get the Fourier transform, the tool that lets a phone split music into its notes or a scanner rebuild an image. He didn't chase this for fun, either: he was trying to describe how warmth spreads through a solid bar, and cracked it by inventing the maths of the heat equation.

Fourier lived dangerously. He spoke up during the French Revolution, was arrested, and came uncomfortably close to the guillotine before the political winds shifted. Later he sailed to Egypt with Napoleon's expedition and helped run the scientific side of things. He came back convinced that heat was practically medicine — the story goes that he kept his rooms swelteringly hot and wrapped himself in blankets even in summer, certain that warmth was good for the body. A man who wrote the equations of heat and then tried to live inside them.