Henri Poincaré began teaching the calculus of probabilities in 1886 at the Faculty of Sciences at the University of Paris. In 1896, he published Calcul des probabilités, written up by Albert Quiquet (1862–1934), a former student of the École normale supérieure. A second edition appeared in 1912, revised and expanded by the author, with a particularly important Chapter XVI, "Miscellaneous questions."
In 1902, La Science et l’Hypothèse was published, including a Chapter XI entitled "The calculus of probabilities," in which the mathematician and physicist set out his ideas in simple terms. This popular-science book was hugely successful and was translated into several languages.
Even so, Poincaré is not regarded as a founder of probability theory, despite his pioneering work in so many areas of mathematics and physics. Let's take a closer look at Chapter XI of La Science et l’Hypothèse, a work of popularization remarkable for its depth, and at the second, 1912 edition of Calcul des probabilités.
Chapter XI
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For Poincaré, the probability of an event is defined as "the ratio of the number of outcomes favorable to that event to the number of possible outcomes." But he immediately qualifies this definition: "[to the number of possible outcomes], provided that these outcomes are equally probable." The definition is a strange one, since the word "probable" is used to define probability itself.
