Leçons sur la propagation des ondes et les équations de l'hydrodynamique

cours du Collège de Franc

On the alleged simplicity of impure proof

Roughly, a proof of a theorem, is “pure” if it draws only on what is “close” or “intrinsic” to that theorem. Mathematicians employ a variety of terms to identify pure proofs, saying that a pure proof is one that avoids what is “extrinsic,” “extraneous,” “distant,” “remote,” “alien,” or “foreign” to the problem or theorem under investigation. In the background of these attributions is the view that there is a distance measure (or a variety of such measures) between mathematical statements and proofs. Mathematicians have paid little attention to specifying such distance measures precisely because in practice certain methods of proof have seemed self- evidently impure by design: think for instance of analytic geometry and analytic number theory. By contrast, mathematicians have paid considerable attention to whether such impurities are a good thing or to be avoided, and some have claimed that they are valuable because generally impure proofs are simpler than pure proofs. This article is an investigation of this claim, formulated more precisely by proof- theoretic means. After assembling evidence from proof theory that may be thought to support this claim, we will argue that on the contrary this evidence does not support the claim

Einstein en France

Hadamard Jacques. Einstein en France. In: Revue internationale de l'enseignement, tome 76,1922. pp. 129-137

The mathematician's mind: the psychology of invention in the mathematical field

Fifty years ago when Jacques Hadamard set out to explore how mathematicians invent new ideas, he considered the creative experiences of some of the greatest thinkers of his generation, such as George Polya, Claude Lévi-Strauss, and Albert Einstein. It appeared that inspiration could strike anytime, particularly after an individual had worked hard on a problem for days and then turned attention to another activity. In exploring this phenomenon, Hadamard produced one of the most famous and cogent cases for the existence of unconscious mental processes in mathematical invention and other forms of creativity. Written before the explosion of research in computers and cognitive science, his book, originally titled The Psychology of Invention in the Mathematical Field, remains an important tool for exploring the increasingly complex problem of mental life. The roots of creativity for Hadamard lie not in consciousness, but in the long unconscious work of incubation, and in the unconscious aesthetic selection of ideas that thereby pass into consciousness. His discussion of this process comprises a wide range of topics, including the use of mental images or symbols, visualized or auditory words, "meaningless" words, logic, and intuition. Among the important documents collected is a letter from Albert Einstein analyzing his own mechanism of thought

Carta de Jacques Hadamard al cosí de Ferran Sunyer , 11 maig 1939

Carta de J. Hadamard (Institut de France, Académie des Sciences - Paris), on li comunica que la nota de F. Sunyer "Sur une classe de transformation des formules de sommabilité" s'ha publicat als "Comptes Rendus" del 6 de febrer de 1939

A propos d’enseignement secondaire

Hadamard Jacques. A propos d’enseignement secondaire. In: Revue internationale de l'enseignement, tome 75,1921. pp. 289-294

Les méthodes d’enseignement des sciences expérimentales

Hadamard Jacques. Les méthodes d’enseignement des sciences expérimentales. In: Revue internationale de l'enseignement, tome 81,1927. pp. 355-356

A propos d’enseignement secondaire

Hadamard Jacques. A propos d’enseignement secondaire. In: Revue internationale de l'enseignement, tome 75,1921. pp. 289-294