Jacques Hadamard | |
|---|---|
 Jacques Salomon Hadamard | |
| Born | (1865-12-08)8 December 1865 Versailles, France |
| Died | 17 October 1963(1963-10-17) (aged 97) Paris, France |
| Alma mater | École Normale Supérieure |
| Known for | Hadamard product Proof of prime number theorem Hadamard matrices Hadamard's maximal determinant problem |
| Awards | Grand Prix des Sciences Mathématiques (1892) Prix Poncelet (1898) CNRS Gold medal (1956) |
| Scientific career | |
| Fields | Mathematics |
| Institutions | University of Bordeaux Sorbonne Collège de France École Polytechnique École Centrale Paris |
| Thesis | Essai sur l'étude des fonctions données par leur développement de Taylor (1892) |
| Doctoral advisor | C. Émile Picard[1] Jules Tannery |
| Doctoral students | Maurice René Fréchet Marc Krasner Paul Lévy Szolem Mandelbrojt André Weil |
| Signature | |
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Jacques Salomon HadamardForMemRS[2] (French:[adamaʁ]; 8 December 1865 – 17 October 1963) was a French mathematician who made major contributions innumber theory,complex analysis,differential geometry, andpartial differential equations.[3][4][5]
The son of a teacher, Amédée Hadamard, ofJewish descent, and Claire Marie Jeanne Picard, Hadamard was born inVersailles, France and attended theLycée Charlemagne andLycée Louis-le-Grand, where his father taught. In 1884 Hadamard entered theÉcole Normale Supérieure, having placed first in the entrance examinations both there and at theÉcole Polytechnique. His teachers includedTannery,Hermite,Darboux,Appell,Goursat, andPicard. He obtained his doctorate in 1892 and in the same year was awarded theGrand Prix des Sciences Mathématiques for his essay on theRiemann zeta function.
In 1892 Hadamard married Louise-Anna Trénel, also of Jewish descent, with whom he had three sons and two daughters. The following year he took up a lectureship in theUniversity of Bordeaux, where he proved hiscelebrated inequality ondeterminants, which led to the discovery ofHadamard matrices when equality holds. In 1896 he made two important contributions: he proved theprime number theorem, usingcomplex function theory (also proved independently byCharles Jean de la Vallée-Poussin); and he was awarded the Bordin Prize of theFrench Academy of Sciences for his work ongeodesics in thedifferential geometry of surfaces anddynamical systems. In the same year he was appointed Professor of Astronomy and Rational Mechanics in Bordeaux. His foundational work on geometry andsymbolic dynamics continued in 1898 with the study of geodesics on surfaces ofnegative curvature. For his cumulative work, he was awarded thePrix Poncelet in 1898.
After theDreyfus affair, which involved him personally because his second cousin Lucie was the wife of Dreyfus, Hadamard became politically active and a staunch supporter ofJewish causes[6] though he professed to be an atheist in his religion.[7][8]
In 1897 he moved back to Paris, holding positions in theSorbonne and theCollège de France, where he was appointed Professor of Mechanics in 1909. In addition to this post, he was appointed to chairs of analysis at theÉcole Polytechnique in 1912 and at theÉcole Centrale in 1920, succeedingJordan and Appell. In Paris Hadamard concentrated his interests on the problems of mathematical physics, in particularpartial differential equations, thecalculus of variations and the foundations offunctional analysis. He introduced the idea ofwell-posed problem and themethod of descent in the theory ofpartial differential equations, culminating in his seminal book on the subject, based on lectures given atYale University in 1922. Later in his life he wrote onprobability theory andmathematical education.
Hadamard was elected to theFrench Academy of Sciences in 1916, in succession toPoincaré, whose complete works he helped edit. He became foreign member of theRoyal Netherlands Academy of Arts and Sciences in 1920.[9] He was elected a foreign member of theAcademy of Sciences of the USSR in 1929. He visited theSoviet 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 theSecond World War and escaped to southern France in 1940. TheVichy government permitted him to leave for the United States in 1941 and he obtained a visiting position atColumbia 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.) byYale University in October 1901, during celebrations for the bicentenary of the university.[10] He was awarded theCNRS Gold medal for his lifetime achievements in 1956. He died in Paris in 1963, aged ninety-seven.
Hadamard's students includedMaurice Fréchet,Paul Lévy,Szolem Mandelbrojt, andAndré Weil.
In his bookPsychology of Invention in the Mathematical Field,[11] Hadamard uses the results of introspection to study mathematical thought processes,[11]: 2 and tries to report and interpret observations, personal or gathered from other scholars engaged in the work of invention.[11]: 133 In sharp contrast to authors who identifylanguage andcognition, he describes his own mathematical thinking as largely wordless, often accompanied bymental 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 physicistsCarl Friedrich Gauss,Hermann von Helmholtz,Henri Poincaré and others as viewing entire solutions with "sudden spontaneousness".[11]: 13–16
Hadamard described the process as having four steps of the five-stepGraham Wallascreative process model, with the first three also having been put forth by Helmholtz:[11]: 56 Preparation, Incubation, Illumination, and Verification (Wallas' five stages added "Intimation" prior to Illumination, a sudden feeling of being about to find the solution to a problem).[12]
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[.]
{{cite book}}:ISBN / Date incompatibility (help)The Wallas Stage Model of Creativity divides the process of creative thinking into 5 stages. These stages are Preparation, Incubation, Intimation, Illumination, and Verification.
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