POINCARÉ, JULES-HENRY. - Mathematician and thinker, b. at Nancy (Meurthe-et-Moselle) on 29 Apr. 1854, d. in Paris on 17 July 1912. He taught (1881) in the Faculty of Sciences in Paris; he was (1887) a member of the Académie des Sciences. His works in pure and applied mathematics are collected in more than 30 volumes; he wrote nearly 500 memoirs and several works of a general character: *La science et l'hypothèse* (Paris 1902), *La valeur de la science* (ibid. 1905), *Science et méthode* (ibid. 1909), *Dernières pensées* (posthumous, 1913).
P. states that «the only objective reality is the relations between things from which universal harmony results»;
essays do not exist «outside of a mind that conceives them and feels them. Yet they are objective because they are, will be, and will remain common to all thinking beings» (*La valeur de la science*, p. 270). Science does not make things known but the relations between things: «Science is a system of relations» (loc. cit., p. 265). To E. Le Roy, who maintained that the scientist creates the scientific fact and that science is valuable only as a complex of rules of action, P. observes that science, in so far as it can predict facts, must also have a theoretical value, and the scientist does not create anything in the fact except the language with which he enunciates it (*La valeur de la science*, pp. 213 ff.). With regard to non-Euclidean geometries, P. admits that geometric 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 even in relation to religion: «There are men who forget their faith when entering the experimental laboratory... And that is all that can be asked of them» (*Dernières pensées*, p. 331). Morality cannot be founded either on metaphysics, or on religion, or on science, or on utilitarian motives, but only on sentiment (loc. cit., pp. 223 ff.).