Everything about Jacques Hadamard totally explained
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.
Biography
Hadamard 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 though he professed to be an atheist in his religion.
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.
On creativity
In 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.” The same has been reported in literature by many others, such as Denis Brian,
G. H. Hardy,,
B. L. van der Waerden,, Harold Ruegg.,
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:
- Preparation
- Incubation
- Illumination
- Verification
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.” As cited by von Franz, according to Jung: “Archetypes … manifest themselves only through their ability to
organize images and ideas, and this is always an unconscious process which can't be detected until afterwards.”
Writings
Jacques Hadamard The Psychology of Invention in the Mathematical Field (Dover, 1954) ISBN 0-486-20107-4 (Princeton University Press, 1945)
Jacques Hadamard The Mathematician's Mind: The Psychology of Invention in the Mathematical Field (Princeton, 1996) ISBN 0-691-02931-8Further Information
Get more info on 'Jacques Hadamard'.
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