A brief history of Ars Conjectandi [Reseña]

This is a review submitted to Mathematical Reviews/MathSciNet. Reviewer Name: de Paz, Mar´ıa Mathematical Reviews/MathSciNet Reviewer Number: 127139 Address: Dep. de Filo., Log. y Filo. de la Cien. Fac. de Filosof´ıa, Univ. of Sevilla C/Camilo Jos´e Cela S/N 41018 Seville SPAIN [email protected] Author: Mart´ınez-Adame, Carmen Title: A brief history of Ars Conjectandi. MR Number: MR3587407 Primary classification: 01A45 Secondary classification(s): Review text: This paper is about the history of Ars Conjectandi, a posthumous work by Jacob Bernoulli, and one of the first publications in which, according to the author, probability is taken as a serious mathematical theory and not only a technique to understand gambling. The paper is divided in five sections. In the first one the author analyzes the state of the art on the concepts of probability previous to Bernoullis contribution. So, special attention is paid to Pascal, Fermat, Huygens, and Leibniz. In the second section she stresses Huygens influence on Bernoullis work on probability and the correspondence between Leibniz and Bernoulli. The analysis of the correspondence is the most interesting part of the paper where the author shows the controversy between Leibniz and Bernoulli. The third section is dedicated to analyze properly the four parts of the Ars Conjectandi, where emphasis is put on the application of probability to civil, moral and economical topics, the true important contribution made by Bernoulli on the subject. Forth section is about the reception of Ars Conjectandi after Bernoullis death and fifth is a final comment about the long life of this text, which now is three hundred years old. Comments to the MR Editors (not part of the Review Text): Whenever in the text is written ’Ars Conjectandi’, it should be published in italics. 1