**Abraham De Moivre** was a French-born mathematician who pioneered the development of analytic geometry and the theory of probability.

- De Moivre's parents were Protestants but he first attended the Catholic school of the Christian Brothers in Vitry which was a tolerant school, particularly so given the religious tensions in France at this time.
- When he was eleven years old his parents sent him to the Protestant Academy at Sedan where he spent four years studying Greek under Du Rondel.
- The Edict of Nantes had guaranteed freedom of worship in France since 1598 but, although it made any extension of Protestant worship in France legally possible, it was much resented by the Roman Catholic clergy and by the local French parliaments.
- Despite the Edict, the Protestant Academy at Sedan was suppressed in 1682 and de Moivre, forced to move, then studied logic at Saumur until 1684.
- Although mathematics was not a part of the course that he was studying, de Moivre read mathematics texts in his own time.
- In particular he read Huygens' treatise on games of chance De ratiociniis in ludo aleae Ⓣ(Reasoning in gambling games).
- By this time de Moivre's parents had gone to live in Paris so it was natural for him to go there.
- He continued his studies at the Collège de Harcourt where he took courses in physics and for the first time had formal mathematics training, taking private lessons from Ozanam.
- At this time de Moivre was imprisoned for his religious beliefs in the priory of St Martin.
- By the time he arrived in London de Moivre was a competent mathematician with a good knowledge of many of the standard texts.
- However after he made a visit to the Earl of Devonshire, carrying with him a letter of introduction, he was shown Newton's Principia.
- He realised instantly that this was a work far deeper than those which he had studied and decided that he would have to read and understand this masterpiece.
- Although this was not the ideal environment in which to study the Principia, it is a mark of de Moivre's abilities that he was quickly able to master the difficult work.
- De Moivre had hoped for a chair of mathematics, but foreigners were at a disadvantage in England so although he now was free from religious discrimination, he still suffered discrimination as a Frenchman in England.
- We describe below some attempts to procure a chair for him.
- By 1692 de Moivre had got to know Halley, who was at this time assistant secretary of the Royal Society, and soon after that he met Newton and became friendly with him.
- In 1710 de Moivre was appointed to the Commission set up by the Royal Society to review the rival claims of Newton and Leibniz to be the discovers of the calculus.
- The Royal Society knew the answer it wanted! It is also interesting that de Moivre should be given this important position despite finding it impossible to gain a university post.
- De Moivre pioneered the development of analytic geometry and the theory of probability.
- It was Francis Robartes, who later became the Earl of Radnor, who suggested to de Moivre that he present a broader picture of the principles of probability theory than those which had been presented by Montmort in Essay d'analyse sur les jeux de hazard Ⓣ(Essay on the analysis of games of chance) (1708).
- Clearly this work by Montmort and that by Huygens which de Moivre had read while at Saumur, contained the problems which de Moivre attacked in his work and this led Montmort to enter into a dispute with de Moivre concerning originality and priority.
- Unlike the Newton-Leibniz dispute which de Moivre had judged, the argument with Montmort appears to have been settled amicably.
- The definition of statistical independence appears in this book together with many problems with dice and other games.
- The Doctrine of Chance appeared in new expanded editions in 1718, 1738 and 1756.
- The 1756 edition of The Doctrine of Chance contained what is probably de Moivre's most significant contribution to this area, namely the approximation to the binomial distribution by the normal distribution in the case of a large number of trials.
- He even appears to have perceived, although he did not name, the parameter now called the standard deviation ...
- De Moivre also investigated mortality statistics and the foundation of the theory of annuities.
- It is almost certain that de Moivre's friendship with Halley led to his interest in annuities and he published Annuities on lives in 1724.
- derivation of formulas for annuities based on a postulated law of mortality and constant rates of interest on money.
- In Miscellanea Analytica (1730) appears Stirling's formula (wrongly attributed to Stirling) which de Moivre used in 1733 to derive the normal curve as an approximation to the binomial.
- In the second edition of the book in 1738 de Moivre gives credit to Stirling for an improvement to the formula.
- It appears in this form in a paper which de Moivre published in 1722, but a closely related formula had appeared in an earlier paper which de Moivre published in 1707.
- Despite de Moivre's scientific eminence his main income was as a private tutor of mathematics and he died in poverty.
- Desperate to get a chair in Cambridge he begged Johann Bernoulli to persuade Leibniz to write supporting him.
- He did so in 1710 explaining to Leibniz that de Moivre was living a miserable life of poverty.
- Indeed Leibniz had met de Moivre when he had been in London in 1673 and tried to obtain a professorship for de Moivre in Germany, but with no success.
- Indeed de Moivre revised the Latin translation of Newton's Optics and dedicated The Doctrine of Chance to him.
- Literature, ancient and modern, furnished his recreation; he once said that he would rather have been Molière than Newton; and he knew his works and those of Rabelais almost by heart.
- After sight and hearing had successively failed, he was still capable of rapturous delight at his election as a foreign associate of the Paris Academy of Sciences on 27 June 1754.
- De Moivre, like Cardan, is famed for predicting the day of his own death.

Born 26 May 1667, Vitry-le-François, Champagne, France. Died 27 November 1754, London, England.

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Analysis, Geometry, Number Theory, Puzzles And Problems, Special Numbers And Numerals

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive