Abraham de Moivre

Abraham de Moivre (1667–1754) was a French-born mathematician who fled religious persecution to London, became close friends with Isaac Newton, and then spent his life brilliant but broke — tutoring students and answering gambling questions in coffee houses because no university would give a foreigner a proper job.

An idea for the ages

De Moivre's most elegant gift is the formula linking powers of complex numbers to trigonometry, (\cos\theta + i\sin\theta)^n = \cos(n\theta) + i\sin(n\theta), which we now call De Moivre's theorem. It turns fiddly angle calculations into simple multiplication. He was also a probability pioneer: he was among the first to spot the bell-shaped "normal" curve emerging from games of chance, decades before it was named.

There's a famous legend that in old age de Moivre noticed he was sleeping about fifteen minutes longer each night, worked out an arithmetic progression, and calculated the date he'd sleep forever — dying, the story goes, on exactly that day. It's a wonderful tale and probably too neat to be literally true, but it captures the man perfectly: someone who saw patterns and probabilities in absolutely everything, right to the end.