Statistical Science 2007, Vol. 22, No. 1, 109–136 DOI: 10.1214/088342306000000268 c Institute of Mathematical Statistics, 2007 Maty’s Biography of Abraham De Moivre, Translated, Annotated and Augmented David R. Bellhouse and Christian Genest 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 the- ory. 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 mate- rial, 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. INTRODUCTION ´emigr´es that both of them are known to have fre- Matthew Maty (1718–1776) was born of Huguenot quented. In the weeks prior to De Moivre’s death, parentage in the city of Utrecht, in Holland. He stud- Maty began to interview him in order to write his ied medicine and philosophy at the University of biography. De Moivre died shortly after giving his Leiden before immigrating to England in 1740. Af- reminiscences up to the late 1680s and Maty com- ter a decade in London, he edited for six years the pleted the task using only his own knowledge of the Journal britannique, a French-language publication man and De Moivre’s published work. The biogra- out of the Netherlands that was meant to promote phy, written in French, appeared in the 1755 edition British science and literature throughout continen- of the Journal britannique. tal Europe. Surviving copies of Maty (1755) are available in arXiv:0708.3965v1 [stat.ME] 29 Aug 2007 Some time after his arrival in London, Maty be- only a few locations and are relatively difficult for came acquainted with Abraham De Moivre. It is many to access.1 More readily available, via Gallica possible that their first encounter occurred at Slaugh- on the Internet, is Grandjean de Fouchy’s eulogy of ter’s Coffee-house, a favorite meeting place of French De Moivre (Fouchy, 1754). Also written in French, it is based largely on the work of Maty (1755), as David R. Bellhouse is Professor, Department of Fouchy acknowledges near the end of his text. In Statistical and Actuarial Sciences, University of fact, his eulogy is for the most part a transcription Western Ontario, London, Ontario, Canada N6A 5B7 of excerpts of Maty’s biography, with the latter’s e-mail: [email protected]. Christian Genest is scientific and personal biases replaced by his own Professeur titulaire, D´epartement de math´ematiques et de statistique, Universit´eLaval, Qu´ebec, Canada G1K 7P4 e-mail: [email protected]. 1De Morgan (1846) was possibly the first to refer to Maty (1755) in print. Some 90 years after its publication, Maty’s This is an electronic reprint of the original article biography of De Moivre was already regarded as obscure by published by the Institute of Mathematical Statistics in De Morgan, who states: “I can hardly find any notice of this Statistical Science, 2007, Vol. 22, No. 1, 109–136. This little tract of Dr. Maty.” A transcript of Maty (1755) is now reprint differs from the original in pagination and available in PDF format on the second author’s webpage, at typographic detail. archimede.mat.ulaval.ca/pages/genest. 1 2 D. R. BELLHOUSE AND C. GENEST in some places. In spite of appearances, the biogra- phy of Maty (1755) predates the eulogy of Fouchy (1754) considerably, since the 1754 volume of the Histoire de l’Acad´emie royale des sciences which carried Fouchy’s article was actually published in 1759. Since De Moivre’s times, concise descriptions of his life and works have been published in several bio- graphical dictionaries, the most recent being Schnei- der (2004). Maty’s article is the major source for almost all of them and remains, to this date, the best and most complete description of this great Abraham De Moivre 1667–1754 mathematician’s life (Schneider, 2001). On the occa- sion of the 250th anniversary of De Moivre’s death, therefore, it seems fitting to revisit Maty’s biogra- publishing what I have been able to gather pertain- phy and to provide it in a language that is accessible ing to his life and writings. Drawing upon materi- to a large number of readers. Much additional source als that I have collected at pains to myself as well material is readily accessible today so that Maty’s as discoveries that only experts in such matters are biographical information has been substantially an- competent to appraise, I shall attempt to portray a notated and augmented. These complements appear mathematician who took pride in his own rectitude in the form of numbered footnotes. Maty’s own let- and who imposed no condition to me other than I tered footnotes to his biography of De Moivre are speak the language of the truth. given as endnotes to the article. Abraham De Moivre was born at Vitry3 in Cham- A thorough description and evaluation of pagne on May 26, 1667. His father was a surgeon De Moivre’s mathematical work may be found in and although he was not wealthy, he spared no ex- Schneider (1968, 2005). Hald (1990) also gives a de- pense to educate his children.4 His son was sent to tailed account of De Moivre’s work in probability. school at an early age, and this son, who retained Consequently, attention is restricted here mostly to the fondest memory of his parents throughout his biographical rather than technical detail; the excep- life, recalled with pleasure a letter that he wrote to tions are when some mathematical commentary en- them on New Year’s Day, 1673. hances Maty’s text. Religious zeal, which was not as keen in this city as in the rest of France, did not preclude Catholic MEMOIR ON THE LIFE AND WRITINGS and Protestant families from entrusting their chil- OF MR. DE MOIVRE dren to the same tutors. Young De Moivre began By Matthew Maty his studies in Latin with a priest, and after one I hereby pay tribute to the memory of Mr. De Moivre2 on behalf of a Journal britannique and dis- a further 20 or more had “de la” (Huguenot Society, 1914). charge the duty invested in me through his trust, by If the person was of noble origin, it was noted in the register; for example, Louis de Saint-Delis, Marquis de Heucourt, and 2Walker (1934) has given an extensive discussion of the Jean de Meslin, Seigneur de Campagny. The vast majority of spelling of De Moivre’s surname. French sources almost in- the 120 entries were not from the nobility. variably refer to the name as Moivre, since the particle “de” 3Modern-day Vitry-le-Fran¸cois, a rebuilding of “Vitry en would normally be associated with nobility. However, En- Perthois,” is located in the Department of Marne, about glish sources, including De Moivre himself, use De Moivre, de halfway between Paris and Nancy in North-Eastern France. Moivre and Demoivre. De Moivre is used here, since it is the 4In a petition for English citizenship (naturalization), form of his signature on most of his manuscript writings that Abraham De Moivre states that his parents were named the authors have been able to see. Schneider (2004) speculates Daniel and Anne (Huguenot Society, 1923). De Moivre had that De Moivre added the particle “de” to his name on arrival at least one brother, also named Daniel, who was a musician in England in order to gain prestige in dealing with English and composer in London; see Lasocki (1989). Schneider (2004) clients, especially among the nobility. This seems doubtful. states that this brother became a merchant. However, it was Among the nearly 1600 Huguenot refugees presenting them- more likely Daniel’s son, another Daniel, who was the mer- selves to the Savoy Church, a French Huguenot church in Lon- chant. The latter Daniel made a business trip to Mexico to don, approximately 120 had “de” prefixing their surnames and buy jewelry in the early 1730s (PRO C104/266 Bundle 38). MATY’S BIOGRAPHY OF ABRAHAM DE MOIVRE 3 year, continued his education with the Fathers of grade, also known as Rhetoric. He remained there the Christian Doctrine. He studied with the latter until he reached the age of thirteen, that is, until until the age of eleven and reached third grade. At the year 1680, famed for its comet.9 It had been in- the time, he was also being taught arithmetic by a tended that he enter the Academy under Mr. Bayle tutor of writing. However, one day, when he asked after the summer holidays the following year, but his teacher to clarify an operation on aliquot parts,5 his plans were thrown into confusion by the sup- the latter replied by boxing his ears. This answer pression of the Academy and, for lack of a tutor, he was neither to the taste of the young student nor was forced to return to Champagne. to that of his father; and as the latter was already The progress he had made in arithmetic was me- displeased with the school, he then enrolled his son teoric.