Science and MethodHenri PoincaréTranslated by George Bruce HalstedJules Henri Poincaré 29 April 1854 - 17 July 1912, was a French mathematician, theoretical physicist, engineer, and a philosopher of science. He is often described as a polymath, and in mathematics as The Last Universalist by Eric Temple Bell, since he excelled in all fields of the discipline as it existed during his lifetime.I bring together here different studies relating more or less directly to questions of scientific methodology. The scientific method consists in observing and experimenting; if the scientist had at his disposal infinite time, it would only be necessary to say to him: 'Look and notice well'; but, as there is not time to see everything, and as it is better not to see than to see wrongly, it is necessary for him to make choice. The first question, therefore, is how he should make this choice. This question presents itself as well to the physicist as to the historian; it presents itself equally to the mathematician, and the principles which should guide each are not without analogy. The scientist conforms to them instinctively, and one can, reflecting on these principles, foretell the future of mathematics.We shall understand them better yet if we observe the scientist at work, and first of all it is necessary to know the psychologic mechanism of invention and, in particular, that of mathematical creation. Observation of the processes of the work of the mathematician is particularly instructive for the psychologist.IntroductionBook I. Science and the Scientist The Choice of FactsThe Future of MathematicsMathematical CreationChanceBook II. Mathematical Reasoning The Relativity of SpaceMathematical Definitions and TeachingMathematics and LogicThe New LogicsThe Latest Efforts of the LogisticiansBook III. The New Mechanics Mechanics and RadiumMechanics and OpticsThe New Mechanics and AstronomyBook IV. Astronomic Science The Milky Way and the Theory of GasesFrench GeodesyGeneral Conclusions