Probability and statistics in Italy during the First World War I: Cantelli and the laws of large numbers

Some of the most important Italian contributions to probability and statistics came to light in the WW1 years 1915-1918: the Cantelli’s theory of stochastic convergence together with the first correct and (rather) general version of the strong law of large numbers, and the Gini theory of statistical association. These studies were influential in determining the characteristics of the subsequent developments of the statistical and probabilistic research in Italy. The present paper is the first part of an article that aims at describing the spirit of these studies, and helping readers understand their connections both with pre-existent and contemporary literature. It is devoted to the contributions of Cantelli. The (future) second part will deal with statistics and, in particular, with Gini’s works on statistical association. Résumé Quelques unes des plus importantes contributions italiennes aux probabilités et statistiques apparurent pendant les années de guerre 1915-1918: la théorie de Cantelli sur la convergence stochastique et la première version correcte et assez générale de la loi forte des grands nombres, ainsi que la théorie de Gini d’association statistique. Ces études furent déterminantes pour caractériser les développements ultérieurs des recherches en probabilité et statistique en Italie. Cet article est la première partie d’un texte qui a pour but de décrire l’esprit de ces études, et d’aider les lecteurs à comprendre leurs connexions avec celles qui les ont précédées. Elle est consacrée aux contributions de Cantelli. La (future) deuxième partie traitera des statistiques, en particulier des travaux de Gini sur l’association statistique. 1 A few biographical notes As to probability and statistics, the Italian panorama during 1910-1930 was dominated by Francesco Paolo Cantelli and Corrado Gini. Cantelli was born in Palermo on December 20, 1875 and graduated from the town University in Pure Mathematics in the year 1899 after discussing a thesis on celestial mechanics. In his initial research, at the Astronomic Observatory in Palermo, he tried to verify if the position of the stars mentioned by Dante in the Divina Commedia corresponded either to the year 1300 or to the year ∗Università degli Studi di Pavia, Dipartimento di Matematica “F. Casorati”, Via Ferrata 1, 27100 Pavia (Italy). E-mail: [email protected]