POINGARÉ, JULES-HENRY. – Mathematician and thinker, born in Nancy (Meurthe-et-Moselle) on 29 April 1854, died in Paris on 17 July 1912. He taught (1881) in the Faculty of Sciences in Paris; in 1887 he became a member of the Académie des Sciences. His works on pure and applied mathematics are collected in more than 30 volumes; he wrote nearly 500 memoirs and several works of a general nature: La science et l'hypothèse (Paris 1902), La valeur de la science (there 1905), Science et méthode (there 1909), Dernières pensées (posthumously, there 1913).
P. maintains that “the sole objective reality is the relations among things from which universal harmony results”;
they do not exist “outside a mind that conceives and feels them. Yet they are objective because they are, will become, and will remain common to all thinking beings” (La valeur de la science, p. 270). Science does not make us know things but the relations among things: “Science is a system of relations” (op. cit., p. 265). To E. Le Roy, who maintained that the scientist creates the scientific fact and that science is valid only as a set of rules for action, P. observes that science, insofar as it can predict facts, must also possess theoretical value, and that the scientist creates nothing in the fact except the language with which he states it (La valeur de la science, p. 213 ff.). With regard to non-Euclidean geometries, P. admits that geometrical axioms are conventions whose choice “is guided by experimental facts, but remains free and is limited only by the necessity of avoiding contradiction” (La science et l'hypothèse, p. 66).
In scientific research P. demands absolute freedom, including with respect to religion: “There are men who forget their faith upon entering the experimental laboratory... And this is all that can be asked of them” (Dernières pensées, p. 331). Morality can be founded neither on metaphysics, nor on religion, nor on science, nor on utilitarian motives, but only on feeling (op. cit., p. 223 ff.).