Abraham de Moivre Biography

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World of Mathematics on Abraham de Moivre

Abraham de Moivre, a French mathematician chiefly remembered for the theorem in trigonometry that now bears his name, was born in Champagne, France on may 26, 1667. He died in London on November 27, 1754.

De Moivre was the son of a surgeon. Being a Huguenot, he chose to leave France when the Edict of Nantes was revoked in 1685. In London, he supported himself as a lecturer and private teacher in mathematics and natural science, while he continued his studies in mathematics. There he became a close friend of Newton, and is said to have torn the latter's Principia into sheets that he could carry with him and study in his spare time.

Although de Moivre aspired to a university position in mathematics, he never succeeded in securing one. Most of de Moivre's life was spent in poverty, and he managed to outlive most of his friends. He did achieve recognition for his work during his lifetime, which include a demonstration of the process of finding a root of an infinite series, and was admitted to the Royal Society (1697), and to the Berlin and Paris Academies.

In 1711, de Moivre published a long memoir about the laws of chance in the Philosophical Transactions. His first book, entitled Doctrine of Chances, dealt with questions about games of chance (such as dice) and was published in 1718. The book, which described methods for approximating function of large numbers, later gave him the idea of the normal distribution curve.

In 1725, he published Annuities on Lives, which was perhaps the first important mathematical treatment of that subject. In the book he adopted as the rule the idea that annuities can be computed on the assumption that that the number of persons in a given group that die will be the same during each year.

In 1730, De Moivre published in Miscellanea Analytica the formula for the factorials of large numbers that is now ironically known as Stirling's approximation.

De Moivre was one of the first mathematicians to make use of complex numbers in trigonometry. The theorem that he is most remembered (de Moivre's Theorem) for is as follows:

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

Twenty years after de Moivre derived this formula, Euler enlarged upon it to shift trigonometry from the domain of geometry into mathematical analysis.

Newton, impressed with the significance of this result, is said to have referred those who came to him with questions about mathematics to de Moivre, with the statement "He knows these things better than I."

When de Moivre was elected to the Royal Society in 1712, it was at the proposal of Jean Bernoulli, with whom de Moivre had been in extensive correspondence since 1704. In the same year, the Royal Society appointed de Moivre a partisan commissioner to evaluate the claims of Newton and Leibniz concerning the invention of the calculus.