- Jacques Hadamard
name = Jacques Hadamard
image_width = 300px
caption = Jacques Salomon Hadamard
birth_date = birth date|1865|12|8|mf=y
death_date = death date and age|1963|10|17|1865|12|8|mf=y
nationality = French
University of Bordeaux Sorbonne Collège de France
École Normale Supérieure
doctoral_advisor = C. Émile Picard
Maurice René Fréchet Paul Lévy Szolem Mandelbrojt André Weil Xinmou Wu
known_for = Hadamard productProof of prime number theorem
Grand Prix des Sciences Mathématiques(1892) Prix Poncelet(1898)
Jacques Salomon Hadamard (
December 8, 1865– October 17, 1963) was a French mathematicianbest known for his proof of the prime number theoremin 1896.
Hadamard studied at the
École Normale Supérieureunder the direction of Charles Émile Picard. After the Dreyfus affair, which involved him personally (Dreyfus was his brother-in-law), Hadamard, Jewishhimself in his historical identity, became politically active and became a staunch supporter of Jewish causes [ [http://press.princeton.edu/einstein/book/2dHadamard.pdf The Psychology of Invention in the Mathematical Field] ] though he professed to be an atheist in his religion. [ [http://www-groups.dcs.st-and.ac.uk/~history/Extras/Hadamard_Hermite.html Hadamard on Hermite ] ]
He introduced the idea of "
well-posed problem" in the theory of partial differential equations. He also gave his name to the Hadamard inequalityon volumes, and the Hadamard matrix, on which the Hadamard transformis based. The Hadamard gatein quantum computinguses this matrix.
In his book "Psychology of Invention in the Mathematical Field", Hadamard uses
introspectionto describe mathematical thought processes. In sharp contrast to authors who identify languageand cognition, he describes his own mathematical thinking as largely wordless, often accompanied by mental imagesthat 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 Poincaréand others as viewing entire solutions with “sudden spontaneousness.” [ Hadamard, 1954, pp. 13-16.] The same has been reported in literature by many others, such as Denis Brian, [ Einstein, after years of fruitless calculations, suddenly had the solution of the general theory of relativityrevealed in a dream “like a giant die making an indelible impress, a huge map of the universe outlined itself in one clear vision.” See Brian, 1996, p. 159.] G. H. Hardy, [G. H. Hardy cited how the mathematician Srinivasa Ramanujanhad “moments of sudden illumination.” See Kanigel, 1992, pp. 285-286.] , B. L. van der Waerden, [von Franz, 1992, p. 297 and 314. Cited work: B. L. van der Waerden, "Einfall und Überlegung: Drei kleine Beiträge zur Psychologie des mathematischen Denkens" (Gasel & Stuttgart, 1954).] , Harold Ruegg. [von Franz, 1992, p. 297 and 314. Cited work: Harold Ruegg, "Imagination: An Inquiry into the Sources and Conditions That Stimulate Creativity" (New York: Harper, 1954)] , Friedrich Kekulé (dreamed of benzene ring) and Tesla.
Hadamard described the process as having four steps of the five-step
Graham Wallascreative process model, with the first three also having been put forth by Helmholtz: [ Hadamard, 1954, p. 56.]
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 archetypalpattern or image.” [ von Franz, 1992, pp. 297-298.] As cited by von Franz, [von Franz, 1992 297-298 and 314.] 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.” [Jung, 1981, paragraph 440, p. 231.]
* 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 0-691-02931-8
* Hadamard product
Hadamard's dynamical system
Hadamard three-circle theorem
Ostrowski-Hadamard gap theorem
Hadamard finite part integral
* "Life and Work of Jacques Hadamard", Vladimir Maz'ya [http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Mazya.html] & T. O. Shaposhnikova, American Mathematical Society, February 1998, hardcover, 574 pages, ISBN 0-8218-0841-9
* Denis Brian "Einstein: A Life" (John Wiley and Sons, 1996) ISBN 0-471-11459-6
* Jacques Hadamard "The Psychology of Invention in the Mathematical Field" (Dover, 1954) ISBN 0-486-20107-4
* C. G. Jung "The Collected Works of C. G. Jung. Volume 8. The Structure and Dynamics of the Psyche. " (Princeton, 1981) ISBN 0-691-09774-7
*Robert Kanigel "The Man Who Knew Infinity: A Life of the Genius Ramanujan " (Washington Square Press, 1992) ISBN 0-671-75061-5
* Marie-Louise von Franz, "Psyche and Matter" (Shambhala, 1992) ISBN 0-87773-902-1
NAME= Hadamard, Jacques
SHORT DESCRIPTION= French
DATE OF BIRTH=
December 8, 1865
PLACE OF BIRTH= Versailles, France
DATE OF DEATH=
October 17, 1963
PLACE OF DEATH=
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