Colin Maclaurin

Colin Maclaurin (1698–1746) was a Scottish prodigy who went to university at eleven and became a professor at nineteen. A devoted follower of Newton, he spent his life making calculus rigorous at a time when many people still weren't sure it was allowed.

The headline achievement

His name lives on in the Taylor and Maclaurin series — the special, tidy case where you build a function's power series right at zero. He never claimed to have invented it (he cheerfully credited Taylor), but he used it so effectively in his textbooks that his name stuck to the zero-centred version forever.

Maclaurin wasn't just a chalkboard mathematician. When a Jacobite army marched on Edinburgh in 1745, he threw himself into organising the city's defences, designing trenches and barricades. The effort — including a hard escape from the city — wrecked his health, and he died a few months later, still only in his forties. He also once won a share of a prize from the French Academy for working out the shape a spinning fluid planet would settle into. A rare mathematician who did maths, engineering and civic heroism all at once.