Maty’s Biography of Abraham De Moivre, Translated, Annotated and Augmented

Abstract

November 27, 2004, marked the 250th anniversary of the death of Abraham De Moivre, best known in statistical circles for his famous large-sample approximation to the binomial distribution, whose generalization is now referred to as the Central Limit Theorem. De Moivre was one of the great pioneers of classical probability theory. He also made seminal contributions in analytic geometry, complex analysis and the theory of annuities. The first biography of De Moivre, on which almost all subsequent ones have since relied, was written in French by Matthew Maty. It was published in 1755 in the Journal britannique. The authors provide here, for the first time, a complete translation into English of Maty's biography of De Moivre. New material, much of it taken from modern sources, is given in footnotes, along with numerous annotations designed to provide additional clarity to Maty's biography for contemporary readers.

The Resistible Rise of Bayesian Thinking in Management

“…So ANT scholars aim to follow how scientific facts, concepts and theories emerge from a construction process that consists of the 'assembling' and 'disassembling' a set of heterogeneous elements referred to as an 'actornetwork' (Alcadipani & Hassard, 2010;Callon & Latour, 1981;Latour, 2005). For instance, an ANT account of the construction of probability theory would show how such a theory came to exist in the 17 th century thanks to material devices such as 'honest' six-faced dices (David, 1955), the social practice of gambling in the French court society and in England, and the epistolary relationships between mathematicians (Fermat, Laplace, Pascal) and noblemen (the Chevalier de Moivre, the 2 nd Earl Stanhope) interested in solving problems of chance (Bellhouse & Genest, 2007). Building on these elements, ANT scholars would explain that a complex set of relations between human beings interested in games of chance, material artifacts (e.g., dices, playing cards) and a set of socially situated practices (e.g., gambling)…”

The normal distribution, an epistemological view

“…Or to put it in a more general or modern language, what is the probability of certain numbers of outcomes in fixed number of trials, given that outcomes have fixed probability of appearing in each trial. De Moivre elegantly addressed the problem by applying the binomial distribution, however, calculating those probabilities for large number of trials based on binomial distribution proved to be very tedious [17]. In search of simplification, he discovered that as number of trials increases the binomial distribution approximates and becomes almost indistinguishable from a bell shaped curve that we know today as the normal curve (Figure 6) [17].…”

“…De Moivre elegantly addressed the problem by applying the binomial distribution, however, calculating those probabilities for large number of trials based on binomial distribution proved to be very tedious [17]. In search of simplification, he discovered that as number of trials increases the binomial distribution approximates and becomes almost indistinguishable from a bell shaped curve that we know today as the normal curve (Figure 6) [17]. Shortly after Gauss, Laplace published his derivation of the normal curve, which will have far more reaching consequences on quantitative science as a whole [2].…”

A case of mathematical eponymy: the Vandermonde determinant

“…One may think that writing down (LIP) would have seemed useless and even misleading to Newton: he must have been aware that his method was both faster and numerically more stable than the direct application of (LIP). The first one to explicitly write (LIP) is Newton's friend Abraham de Moivre (1667-1754, in 1730 (on de Moivre's relationship with Newton, see [Bellhouse & Genest 2007]). Instead of interpolation, de Moivre's motivation was to calculate the coefficients in a linear combination of geometric series, when that linear combination is supposed equal to another series.…”