Michel Rolle

Michel Rolle (1652–1719) was a largely self-taught French mathematician who left one small, perfect theorem that every calculus student meets. The idea is almost obvious once you hear it: if a smooth curve starts and ends at the same height, then somewhere in between it must level off flat.

The lasting legacy

That tidy observation is Rolle's theorem, and it's the seed from which one of the great results of calculus grows — the mean value theorem, which says that over any stretch a smooth curve must, at some instant, travel at exactly its average speed. Simple to picture, and quietly holding up huge parts of analysis.

Here's the twist: Rolle didn't trust calculus. For years he loudly attacked the new methods of Newton and Leibniz as a collection of "ingenious errors," arguing in front of the French Academy that the whole thing rested on shaky foundations. So the theorem now used to prove calculus works was written by one of its fiercest early critics. He was eventually talked round — but you have to admire a man who fought the very subject that made him famous.