Moivre, Abraham de (1667-1754)

French mathematician who pioneered the development of analytical trigonometry, for which he formulated his theorem regarding complex numbers. He also devised a means of research into the theory of probability.

Life De Moivre was born in Vitry-le-François, Champagne, and studied in Paris. With the revocation of the Edict of Nantes in 1685, he was imprisoned as a Protestant for 12 months; on his release he went immediately to England. In London he became a close friend of the English scientists Isaac Newton and Edmond Halley, but he never obtained a permanent position; he eked out a precarious living by tutoring and acting as a consultant for gambling syndicates and insurance companies.

Probability theory His The Doctrine of Chances was published first in Latin and then in expanded English versions in 1718, 1738, and 1756. It was one of the first books on probability, and made an approximation to the normal or Gaussian distribution, which was incorporated into statistical studies for the next 200 years. De Moivre was the first to derive an exact formulation of how ‘chances’ and stable frequency are related.

Theory of annuities Analysing mortality statistics, De Moivre laid the mathematical foundations of the theory of annuities, for which he devised formulae based on a postulated law of mortality and constant rates of interest on money. First published in 1725, his work became standard in textbooks of all subsequent commercial applications.

Analytical trigonometry In analytical trigonometry he discovered an equation that is now named after him:

(cos z + i sin z)n = cos nz + i sin nz

First stated in 1722, it had been anticipated by related forms in 1707. Although it was to become one of the most useful steps in the early development of complex number theory, much of De Moivre's work was appreciated only after his death.