Journ @ l Electronique d ’ Histoire des Probabilités et de la Statistique Electronic Journ @ l for History of Probability and Statistics

We examine Poisson’s personal contribution to the probability calculus, placing it in the mathematical and social context of the beginning of the 19th century (§1). Then we look briefly at Poisson’s administrative work in the Royal Council for Public Education from 1820 to 1840 (§2). 1. The Probability Calculus At first glance, Poisson appears to have come to probability relatively late. It was at the age of 38, on March 13, 1820, that he read his first memoir on a question in probability to the Academy of Sciences, and the question seemed as anodyne as could be: how to calculate the house’s advantage in the game of thirty and forty [71]. The decree of June 24, 1806, tolerated public games under certain conditions in the spa towns and in Paris. The ordinance of August 5, 1812, even conceded to the city of Paris the right to establish casinos and to derive from them proceeds that provided special funds for the police during the entire period of the Restoration. The most popular game at the time was thirty and forty, also known as “Red and Black.” Gamblers spent more than 230 million in 1820 francs on this game alone each year. So we can understand that the problem of calculating the house’s advantage in advance came up. Because we have to start somewhere and we are talking about probability and Poisson, we will start by briefly reviewing Poisson’s calculation of the house’s probability of winning in thirty and forty. He presented a simplified version of the problem as follows: An urn contains x1 balls marked 1, x2 balls marked 2, . . . finally xi balls marked i, the largest number on any of the balls. We successively draw one, two, three, . . . balls, without putting them back in the urn after taking them out. This sequence of draws continues until the sum of the numbers on the balls drawn out equals or exceeds a given number x. What is the probability this sum will equal x? [71, pp. 176–177] We set x1 + x2 + · · ·+ xi = s. If the balls were put back into the urn after they were drawn, the solution of the problem would be simple. Indeed, it was known since the beginning of the 18th century that the This article originally appeared in French as “Poisson, le calcul des probabilités et l’instruction publique,” on pp. 51–94 of Siméon Denis Poisson et la science de son temps, Michel Métivier, Pierre Costabel, and Pierre Dugac, eds., Editions de l’Ecole Polytechnique, Palaiseau, 1981. The author uses quotations marks freely, and the passages and terms quoted are usually in French. We translate what is quoted into English but usually retain the quotation marks. We also translate names of institutions into English; occasionally we add the French name in parentheses. We leave names of books and periodicals in French. It is also interesting to mention that the subject of the present paper has also been extensively discussed in [39] and [87].