de Moivre, Abraham

[duh mwah vruh] (1667–1754) French–British mathematician: founded analytical trigonometry and stated de Moivre’s theorem.

De Moivre had the misfortune to be a Huguenot (Protestant) at the time that Roman Catholic France revoked the Edict of Nantes and began to persecute them (1685). He was imprisoned in Paris for a year and moved to England on his release. Friendship with aided his election to the Royal Society (1697). However, de Moivre remained poor, working as a tutor or consultant to gambling or insurance syndicates, and never obtained a university post. He died blind and disillusioned, with his work unrecognized.

His book The Doctrine of Chances (1718) is a masterpiece, and sets out the binomial probability or Gaussian distribution, the concept of statistical independence and the use of analytical techniques in probability. Deriving an expansion for n ! = n ( n – 1) ( n – 2) … 3.2.1, de Moivre summed terms of the binomial form. He established many of the elements of actuarial calculations. Above all he discovered the trigonometric relation called de Moivre’s theorem (1722), which is a powerful step in developing complex number theory.