Bertrand's work on probability
In 1856 Joseph Louis François Bertrand (1822-1900) was appointed professor at the École Polytechnique, 1862 as professor at the College de France. In 1855 he translated Gauss' writings on the theory of errors and method of least squares into French. During 1887-1888 he published 25 notes on probability and combination of observations. His treatise Calcul des probabilités appeared in 1888 (and 1889), his last note on probability in 1892. In the author opinion this treatise is ``not a masterpiece. He was mistaken in denying the Bayesian inference and even statistical probability, he considered the estimation of the precision of observations without possessing astronomical know-how, and superficially criticized the Gaussian formula; his discussion of the application of probability to jurisprudence and his recommendations about rejecting outlying observations were contradictory. \dots his treatise is badly organised and written carelessly (obviously in great haste).'' On the other hand Bertrand initiated the revival of probability in France, he stimulated Jules-Henri Poincaré (1854-1912), Louis Bachelier (1870-1946), Emile Borel (1881-1956), and others. His work contains important material in probability as the ballot problem, an interesting use of a generation function, the determination of the normal approximation of the hypergeometric distribution, some theorems on order statistics, a critical note on Gauss' second justification of the method of least squares, an approach to the theorem on the independence of the mean and the mean square error for a normal sample and an elegant demonstration that the term at random is not precise (Bertand's paradox). 36 references by Bertrand, 92 by other authors.
scientific article; zbMATH DE number 714704