Pierre Bézier and Paul de Casteljau

Every smooth curve you've ever dragged in a drawing app comes from two French engineers who worked at rival car companies and, for years, had no idea they'd invented the same thing. Pierre Bézier (1910–1999) worked at Renault; Paul de Casteljau (1930–2022) worked at Citroën. The curves got Bézier's name; the elegant way to draw them got de Casteljau's.

The famous work

A Bézier curve is defined by a few "control points" you can grab and pull, bending the curve without ever touching it directly. The cubic version is the workhorse of every font, logo and animation path:

B(t) = (1-t)^3 P_0 + 3(1-t)^2 t\, P_1 + 3(1-t)\, t^2 P_2 + t^3 P_3.

And de Casteljau's algorithm is the gorgeous way to actually plot it: just keep taking midpoints of midpoints, again and again, and the curve appears out of pure repeated averaging. Fonts, vector art, spacecraft trajectories and game paths all ride on these curves.

De Casteljau actually got there first, around 1959 — but Citroën treated his work as a trade secret and forbade him from publishing it. So the mathematics sat locked in internal reports while Bézier, freer to talk about his own version at Renault, published and became the household name. De Casteljau received his due only decades later. It's a rare case where the person who invented something ended up with the algorithm named after them while their rival got the curve — a fittingly geometric way to split the credit.