Irénée-Jules Bienaymé

Irénée-Jules Bienaymé (b. Paris 28 August 1796 d. Paris 19 October 1878), was a French statistician. He built on the legacy of Laplace generalizing his least squares method. He contributed to the fields and probability, and statistics and to their application to finance, demography and social sciences. In particular, he formulated the Bienaymé-Chebyshev inequality concerning the law of large numbers and the Bienaymé formula for the variance of a sum of uncorrelated random variables.

Irénée-Jules Bienaymé
Biography

With Irénée-Jules Bienaymé ends the line of great French probability thinkers that began with Pascal and Fermat, then continued with Laplace and Poisson. After Bienaymé, progress in statistics took place in the UK and Russia.

His personal life was marked by bad fortune. He studied at the Lycée de Bruges and then at the Lycée Louis-le-Grand in Paris. After participating in the defense of Paris in 1814, he attended the École Polytechnique in 1815. Unfortunately that year's class was excluded in the following year by Louis XVIII because of their sympathy for Bonapartists.

In 1818, he lectured on mathematics at the Académie militaire de Saint-Cyr but, two years later, he entered the Finance Ministry. He was rapidly promoted, first to inspector, then to inspector general. But the new Republican administration removed him in 1848 for his lack of support for the Republican regime.

He became professor of probability at the Sorbonne, but he lost his position in 1851. He then became a consultant as an expert statistician for the government of Napoléon III.

In 1852 he was admitted to the Académie des sciences. After 23 years, Bienaymé became the examiner for the attribution of the academy's prize in statistics. He was also a founding member of the Société Mathématique de France, holding its presidency in 1875.
Contributions to mathematics

Bienaymé published only 23 articles, half of which appeared in obscure conditions. His first works concerned demographics and actuarial tables. In particular he studied the extinction of closed families (aristocratic families for instance) which declined even as the general population was growing.

As a disciple of Laplace and under the influence of Laplace's Théorie analytique des probabilités (1812), he defended the latter's conceptions in a debate with Poisson on the size of juries and on the necessary majority for obtaining a conviction.

He translated into French the works of his friend the Russian mathematician Pafnuty Chebychev, and published the Bienaymé-Chebyshev inequality which gives a simple demonstration of the law of large numbers. He corresponded with Quételet, and also had links with Lamé.

Bienaymé criticized Poisson's "law of large numbers" and was involved in a controversy with Cauchy.
References

« Actes de la journée du 21 juin 1996 consacrée à Irénée-Jules Bienaymé », 'Cahiers du Centre d'Analyse et de Mathématiques Sociales', n° 138, Série Histoire du Calcul des Probabilités et de la Statistique, n° 28, Paris, E.H.E.S.S.-C.N.R.S