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For other uses, see Hadamard (disambiguation).
Jacques Salomon Hadamard (December 8, 1865 – October 17, 1963) was a French mathematician best known for his proof of the prime number theorem in 1896.
[edit] BiographyHadamard studied at the École Normale Supérieure under the direction of Charles Émile Picard. After the Dreyfus affair, which involved him personally (Dreyfus was his brother-in-law), Hadamard, Jewish himself in his historical identity, became politically active and became a staunch supporter of Jewish causes[1] though he professed to be an atheist in his religion.[2] He introduced the idea of well-posed problem in the theory of partial differential equations. He also gave his name to the Hadamard inequality on volumes, and the Hadamard matrix, on which the Hadamard transform is based. The Hadamard gate in quantum computing uses this matrix. His students included Maurice Fréchet, Paul Lévy, Szolem Mandelbrojt and André Weil. [edit] On creativityIn his book Psychology of Invention in the Mathematical Field, Hadamard uses introspection to describe mathematical thought processes. In sharp contrast to authors who identify language and cognition, he describes his own mathematical thinking as largely wordless, often accompanied by mental images that represent the entire solution to a problem. He surveyed 100 of the leading physicists of the day (approximately 1900), asking them how they did their work. Many of the responses mirrored his; some reported seeing mathematical concepts as colors. Hadamard described the experiences of the mathematicians/theoretical physicists Carl Friedrich Gauss, Hermann von Helmholtz, Henri Poincaré and others as viewing entire solutions with “sudden spontaneousness.”[3] The same has been reported in literature by many others, such as Denis Brian,[4] G. H. Hardy,[5], B. L. van der Waerden,[6], Harold Ruegg.[7], Friedrich Kekulé (dreamed of benzene ring) and Tesla. Hadamard described the process as having four steps of the five-step Graham Wallas creative process model, with the first three also having been put forth by Helmholtz:[8]
Marie-Louise von Franz, a colleague of the eminent psychiatrist Carl Jung, noted that in these unconscious scientific discoveries the “always recurring and important factor … is the simultaneity with which the complete solution is intuitively perceived and which can be checked later by discursive reasoning.” She attributes the solution presented “as an archetypal pattern or image.”[9] As cited by von Franz,[10] according to Jung: “Archetypes … manifest themselves only through their ability to organize images and ideas, and this is always an unconscious process which cannot be detected until afterwards.”[11] [edit] Writings
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