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Jacques Hadamard
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Jacques Hadamard
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Biography
The son of a teacher, AmÃ©dÃ©e Hadamard, of Jewish descent, and Claire Marie Jeanne Picard, Hadamard was born in Versailles, France and attended the LycÃ©e Charlemagne and LycÃ©e Louis-le-Grand, where his father taught. In 1884 Hadamard entered the Ã‰cole Normale SupÃ©rieure, having placed first in the entrance examinations both there and at the Ã‰cole Polytechnique. His teachers included Tannery, Hermite, Darboux, Appell, Goursat and Picard. He obtained his doctorate in 1892 and in the same year was awarded the Grand Prix des Sciences MathÃ©matiques for his essay on the Riemann zeta function.In 1892 Hadamard married Louise-Anna TrÃ©nel, also of Jewish descent, with whom he had three sons and two daughters. The following year he took up a lectureship in the University of Bordeaux, where he proved his celebrated inequality on determinants, which led to the discovery of Hadamard matrices when equality holds. In 1896 he made two important contributions: he proved the prime number theorem, using complex function theory (also proved independently by Charles Jean de la VallÃ©e-Poussin); and he was awarded the Bordin Prize of the French Academy of Sciences for his work on geodesics in the differential geometry of surfaces and dynamical systems. In the same year he was appointed Professor of Astronomy and Rational Mechanics in Bordeaux. His foundational work on geometry and symbolic dynamics continued in 1898 with the study of geodesics on surfaces of negative curvature. For his cumulative work, he was awarded the Prix Poncelet in 1898.After the Dreyfus affair, which involved him personally because his second cousin Lucie was the wife of Dreyfus, Hadamard became politically active and a staunch supporter of Jewish causesBOOK, Hadamard, Jacques, An essay on the psychology of invention in the mathematical field / by Jacques Hadamard, Dover Publications, New York, 1954, 0-486-20107-4, though he professed to be an atheist in his religion.Hadamard on HermiteBOOK, Shaposhnikova, T. O., Jacques Hadamard: A Universal Mathematician, 1999, American Mathematical Soc., 978-0-8218-1923-4, 33â€“34, In 1924, Hadamard recounted his meetings with Hermite: "...When Hermite loved to direct to me remarks such as: "He who strays from the paths traced by Providence crashes." These were the words of a profoundly religious man, but an atheist like me understood them very well, especially when he added at other times: "In mathematics, our role is more that of servant than master."", In 1897 he moved back to Paris, holding positions in the Sorbonne and the CollÃ¨ge de France, where he was appointed Professor of Mechanics in 1909. In addition to this post, he was appointed to chairs of analysis at the Ã‰cole Polytechnique in 1912 and at the Ã‰cole Centrale in 1920, succeeding Jordan and Appell. In Paris Hadamard concentrated his interests on the problems of mathematical physics, in particular partial differential equations, the calculus of variations and the foundations of functional analysis. He introduced the idea of well-posed problem and the method of descent in the theory of partial differential equations, culminating in his seminal book on the subject, based on lectures given at Yale University in 1922. Later in his life he wrote on probability theory and mathematical education.Hadamard was elected to the French Academy of Sciences in 1916, in succession to PoincarÃ©, whose complete works he helped edit. He became foreign member of the Royal Netherlands Academy of Arts and Sciences in 1920.WEB,weblink Jacques S. Hadamard (1865â€“1963), Royal Netherlands Academy of Arts and Sciences, 19 July 2015, He was elected a foreign member of the Academy of Sciences of the USSR in 1929. He visited the Soviet Union in 1930 and 1934 and China in 1936 at the invitation of Soviet and Chinese mathematicians.Hadamard stayed in France at the beginning of the Second World War and escaped to southern France in 1940. The Vichy government permitted him to leave for the United States in 1941 and he obtained a visiting position at Columbia University in New York. He moved to London in 1944 and returned to France when the war ended in 1945.Hadamard was awarded an honorary doctorate (LL.D.) by Yale University in October 1901, during celebrations for the bicentenary of the university.NEWSPAPER THE TIMES, United States, Thursday, 24 October 1901, 3, 36594, He was awarded the CNRS Gold medal for his lifetime achievements in 1956. He died in Paris in 1963, aged ninety-seven.Hadamard's students included Maurice FrÃ©chet, Paul LÃ©vy, Szolem Mandelbrojt and AndrÃ© 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.Hadamard described the experiences of the mathematicians/theoretical physicists Carl Friedrich Gauss, Hermann von Helmholtz, Henri PoincarÃ© and others as viewing entire solutions with "sudden spontaneousness".Hadamard, 1954, pp. 13â€“16.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:Hadamard, 1954, p. 56. Preparation, Incubation, Illumination, and Verification.Publications
- An Essay on the Psychology of Invention in the Mathematical Field. Princeton University Press, 1945;JOURNAL, Barzun, Jacques, Jacques Barzun, Review: An essay on the psychology of invention in the mathemathical field by J. Hadamard, Bull. Amer. Math. Soc., 1946, 52, 3, 222â€“224,weblink 10.1090/s0002-9904-1946-08528-6, new edition under the title The Mathematician's Mind: The Psychology of Invention in the Mathematical Field, 1996; {{isbn|0-691-02931-8}}, Online
- Le problÃ¨me de Cauchy et les Ã©quations aux dÃ©rivÃ©es partielles linÃ©aires hyperboliques, Hermann 1932JOURNAL, Tamarkin, J. D., Jacob Tamarkin, Review: Le ProblÃ¨me de Cauchy et les Ã‰quations aux DÃ©rivÃ©es Partielles LinÃ©aires Hyperboliques by J. Hadamard, Bull. Amer. Math. Soc., 1934, 40, 3, 203â€“204,weblink 10.1090/s0002-9904-1934-05815-4, (Lectures given at Yale, Eng. trans. Lectures on Cauchy's problem in linear partial differential equations, Yale University Press, Oxford University Press 1923, Reprint Dover 2003)
- La sÃ©rie de Taylor et son prolongement analytique, 2nd edn., Gauthier-Villars 1926
- La thÃ©orie des Ã©quations aux dÃ©rivÃ©es partielles, Peking, Editions Scientifiques, 1964
- LeÃ§ons sur le calcul des variations, Vol. 1, Paris, Hermann 1910,JOURNAL, Hedrick, E. R., Earle Raymond Hedrick, Review: LeÃ§ons sur le Calcul des Variations, par J. Hadamard; recueillies par M. FrÃ©chet. Tome Premier., Bull. Amer. Math. Soc., 1914, 21, 1, 30â€“32,weblink 10.1090/s0002-9904-1914-02567-4, Online
- LeÃ§ons sur la propagation des ondes et les Ã©quations de l'hydrodynamique, Paris, Hermann 1903,JOURNAL, Wilson, Edwin Bidwell, Edwin Bidwell Wilson, Review: LeÃ§ons sur la Propagation des Ondes et les Equations de l'Hydrodynamique by Jacques Hadamard, Bull. Amer. Math. Soc., 1904, 10, 6, 305â€“317,weblink 10.1090/s0002-9904-1904-01115-5, Online
- Four lectures on Mathematics, delivered at Columbia University 1911, Columbia University Press 1915JOURNAL, Moore, C. N., Charles Napoleon Moore, Review: Four Lectures on Mathematics (Delivered at Columbia University in 1911) by J. Hadamard, Bull. Amer. Math. Soc., 1917, 23, 7, 317â€“319,weblink 10.1090/S0002-9904-1917-02949-7, (1. The definition of solutions of linear partial differential equations by boundary conditions, 2. Contemporary researches in differential equations, integral equations and integro-differential equations, 3. Analysis Situs in connection with correspondendes and differential equations, 4. Elementary solutions of partial differential equations and Greens functions), Online
- LeÃ§ons de gÃ©omÃ©trie Ã©lÃ©mentaire, 2 vols., Paris, Colin, 1898,JOURNAL, Morley, Frank, Frank Morley, Review: LeÃ§ons de GÃ©omÃ©trie Ã©lÃ©mentaire (vol. 1), par Jacques Hadamard, Bull. Amer. Math. Soc., 1898, 4, 10, 550â€“551,weblink 10.1090/s0002-9904-1898-00547-5, 1906 (Eng. trans: Lessons in Geometry, American Mathematical Society 2008), Vol. 1, Vol. 2
- Cours d'analyse professÃ© Ã l'Ã‰cole polytechnique, 2 vols., Paris, Hermann 1925/27, 1930 (Vol. 1:JOURNAL, Hildebrandt, T. H., Theophil Henry Hildebrandt, Review: Cours d'Analyse, vol. 1, by J. Hadamard, Bull. Amer. Math. Soc., 1928, 34, 6, 781â€“782,weblink 10.1090/s0002-9904-1928-04650-5, ComplÃ©ments de calcul diffÃ©rentiel, intÃ©grales simples et multiples, applications analytiques et gÃ©omÃ©triques, Ã©quations diffÃ©rentielles Ã©lÃ©mentaires, Vol. 2:JOURNAL, Moore, C. N., Review: Cours d'Analyse, vol. 2, by J. Hadamard, Bull. Amer. Math. Soc., 1933, 39, 3, 185â€“186,weblink 10.1090/s0002-9904-1933-05568-4, Potentiel, calcul des variations, fonctions analytiques, Ã©quations diffÃ©rentielles et aux dÃ©rivÃ©es partielles, calcul des probabilitÃ©s)
- Essai sur l'Ã©tude des fonctions donnÃ©es par leur dÃ©veloppement de Taylor. Ã‰tude sur les propriÃ©tÃ©s des fonctions entiÃ¨res et en particulier d'une fonction considÃ©rÃ©e par Riemann, 1893, Online
- Sur la distribution des zÃ©ros de la fonction zeta(s) et ses consÃ©quences arithmÃ©tiques, Bulletin de la SociÃ©tÃ© MathÃ©matique de France, Vol. 24, 1896, pp. 199â€“220 weblink" title="web.archive.org/web/20120717195014weblink">Online
- {{Citation | last1=Hadamard | first1=Jacques | title=Lectures on Cauchy's problem in linear partial differential equations | origyear=1923 | url=https://books.google.com/books?id=B25O-x21uqkC | publisher=Dover Publications, New York | series=Dover Phoenix editions | isbn=978-0-486-49549-1 | year=2003 | mr=0051411 | jfm=49.0725.04}}
- {{Citation | last1=Hadamard | first1=Jacques | title=Non-Euclidean geometry in the theory of automorphic functions | origyear=1951 | url=https://books.google.com/books?isbn=0821820303 | publisher=American Mathematical Society | location=Providence, R.I. | series=History of Mathematics | isbn=978-0-8218-2030-8 | year=1999 | volume=17 | mr=1723250}}
- {{Citation | last1=Hadamard | first1=Jacques | title=Lessons in geometry. I | origyear=1947 | url=https://books.google.com/books?id=fLwydFiM7zMC | publisher=American Mathematical Society | location=Providence, R.I. | isbn=978-0-8218-4367-3 | year=2008 | mr=2463454 | doi=10.1090/mbk/057}}
- {{Citation | last1=Hadamard | first1=Jacques | editor1-last=FrÃ©chet | editor1-first=M. | editor2-last=LÃ©vy | editor2-first=P. | editor3-last=Mandelbrojt | editor3-first=S. |display-editors = 3 | editor4-last=Schwartz | editor4-first=Laurent | title=Å’uvres de Jacques Hadamard. Tomes I, II, III, IV | url=https://books.google.com/books?id=XOTuAAAAMAAJ | publisher=Ã‰ditions du Centre National de la Recherche Scientifique, Paris | year=1968 | mr=0230598}}
See also
References
{{Reflist|30em}}Further reading
- {{DSB |first=S. |last=Mandelbrojt |title=Hadamard, Jacques |volume=6 |pages=3â€“5}}
- {{citation|title=Life and Work of Jacques Hadamard|first1=Vladimir|last1=Maz'ya|author1-link=Vladimir Gilelevich Maz'ya|first2=T. O.|last2=Shaposhnikova|publisher=American Mathematical Society|year=1998|isbn=0-8218-0841-9}}.
- {{citation|title=Jacques Hadamard: a universal mathematician|first=V. G.|last= Maz'ya|first2= T. O.|last2= Shaposhnikova|authorlink1=Vladimir Gilelevich Maz'ya|publisher=American Mathematical Society/London Mathematical Society|series=History of Mathematics|volume=14|year=1998|isbn=0821819232}}
External links
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- {{Gutenberg author | id=Hadamard,+Jacques | name=Jacques Hadamard}}
- {{Internet Archive author |sname=Jacques Salomon Hadamard}}
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