ABRAHAM DE MOIVRE

Abraham de Moivre is renowned for his eponymous formula, which links complex numbers and trigonometry, and for advancing the study of probability.

LIFE AND TIMES

Born in the Champagne province of France on May 26, 1667. De Moivre studied physics in Paris but due to his faith (he was a French Protestant) he was forced to flee persecution and settle in London. Here, he became friends with Sir Isaac Newton and the astronomer Edmond Halley.

DE MOIVRE’S FORMULA

For any real number x and integer n… (cos x + i sin x)ⁿ = cos(nx) + i sin(nx).

The theorem gives a formula for calculating the powers of complex numbers. These are numbers that can be written in the form a + bi, where i is the unit imaginary number (defined such that i² = –1).

De Moivre’s formula connects complex numbers and trigonometry. He was instrumental in bringing trigonometry out of the realm of geometry and into mathematical analysis.

PROBABILITY

Despite his brilliance, de Moivre couldn’t find a chair in mathematics at a university. He earned a living as a private mathematics tutor and a consultant on gambling and insurance. His 1718 work The Doctrine of Chances covered a wide range of problems in dice and other games. It greatly enhanced the study of probability theory.

DID YOU KNOW?

De Moivre is reputed to have predicted the date of his own death—successfully! He noticed that in old age he was sleeping an extra fifteen minutes each night and correctly calculated that his sleep time would be twenty-four hours a day on November 27, 1754, the date of his actual death.