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### BIOGRAPHY 8.2 Abraham de Moivre (1667 -1754)

Abraham de Moivre was born at Vitry, France, where his father was a surgeon. De Moivre studied mathematics and physics in Paris, but in 1685, after the Edict of Nantes was revoked, he was imprisoned for being a Protestant. When released three years later, he emigrated to England to escape religious persecution. He never returned to France and never published anything in French.

By all accounts, he was a mathematical genius, and he was in constant touch (at the Royal Society) with the leading thinkers of his day, including Isaac Newton who became a close friend. Yet de Moivre never succeeded in obtaining a university appointment. He eked out a living by tutoring the sons of nobility and by advising gamblers and speculators. This unwelcome fate was posterity's gain, for his successful solution of the problems he met in his consulting practice led to his writing of two great books. His text on probability, The Doctrine of Chances, emanated from an article first published in Latin in 1711 and was published posthumously in its final and third edition in 1756. It is notable (among many other contributions) for the origin of the general laws of addition and multiplication of probabilities (discussed in text Chapter 8), for the origin of the binomial distribution law (discussed in Chapter 9), and for the origin of the formula for the normal curve (discussed in Chapter 10), which de Moivre discovered in 1733. De Moivre's other book, A Treatise of Annuities on Lives, was published in 1752. It was highly original and laid foundations for the mathematics of life insurance. De Moivre took great pains to free the science of probability from its connection with gambling and also to establish a connection between probability and theology. He says in The Doctrine of Chances:

And thus in all cases it will be found, that although Chance produces irregularities, still the Odds will be infinitely great, that in process of Time, those Irregularities will bear no proportion to the recurrency of that Order which naturally results from Original Design ... Again, as it is thus demonstrable that there are, in the constitution of things, certain Laws according to which Events happen, it is no less evident from Observation, that these Laws serve to wise, useful and beneficient purposes, to preserve the stedfast Order of the Universe, to propagate the several Species of Beings, and furnish to the sentient Kind such degrees of happiness as are suited to their State... Yet there are Writers, of a Class indeed very different from that of James Bernoulli, who insinuate as if the Doctrine of Probabilities could have no place in any serious Enquiry; and that studies of this kind, trivial and easy as they be, rather disqualify a man for reasoning on every other subject. Let the Reader chuse.

Source: Adapted from International Encyclopedia of Statistics, vol.1 (New York: Free Press, 1978), pp. 601-604. The quotation is taken from Abraham de Moivre, The Doctrine of Chances, 3rd ed. (London: 1756; reprinted New York: Chelsea, 1967), pp. 251-254.