Jacques Hadamard
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Jacques Solomon Hadamard (December 8, 1865 – October 17, 1963) was a French mathematician best known for his proof of the prime number theorem in 1896.
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[edit] Biography
He 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), he became politically active and became a staunch supporter of Jewish causes.
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.
In his book Psychology of Invention in the Mathematical Field, Hadamard uses introspection to describe mathematical thought processes. In sharp opposition to authors who identify language and cognition, he describes his own mathematical thinking as largely wordless, often accompanied by mental images that condense the overall idea of a proof. He surveyed 100 of the leading physicists of the day (approx. 1900), asking them how they did their work. Many of the responses mirrored his; some reported seeing mathematical concepts as colors. Einstein reported feeling sensations in his forearms. Alan Kay, in his "Alan Kay: Doing with Images Makes Symbols Pt 1 (1987)[1]", maps this as Piaget's stages of learning.
His students included Maurice Fréchet, Paul Lévy, Szolem Mandelbrojt and André Weil.
[edit] Writings
- Hadamard, Jacques, "Psychology of Invention in the Mathematical Field". Dover Pubns; November 1990. ISBN 0-486-20107-4
[edit] See also
[edit] External links
- O'Connor, John J., and Edmund F. Robertson. "Jacques Hadamard". MacTutor History of Mathematics archive.
- Jacques Hadamard at the Mathematics Genealogy Project
[edit] Further reading
- Life and Work of Jacques Hadamard, Vladimir Maz'ya & T. O. Shaposhnikova, American Mathematical Society, February 1998, hardcover, 574 pages, ISBN 0-8218-0841-9
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