Jacques Salomon Hadamard ForMemRS^{[2]} (French: [adamaʁ]; 8 December 1865 – 17 October 1963) was a French mathematician who made major contributions in number theory, complex function theory, differential geometry and partial differential equations.^{[3]}^{[4]}^{[5]}
Jacques Hadamard  

Jacques Salomon Hadamard


Born  8 December 1865 Versailles, France 
Died  17 October 1963 (aged 97) Paris, France 
Residence  France 
Nationality  French 
Alma mater  École Normale Supérieure 
Known for  Hadamard product Proof of prime number theorem Hadamard matrices 
Awards  Grand Prix des Sciences Mathématiques (1892) Prix Poncelet (1898) CNRS Gold medal (1956) 
Scientific career  
Fields  Mathematician 
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 
The son of a teacher, Amédée Hadamard, of Jewish descent, and Claire Marie Jeanne Picard, Hadamard was born in Versailles, France and attended the Lycée Charlemagne and Lycée LouisleGrand, where his father taught. In 1884 Hadamard entered the École Normale Supérieure, having placed first in the entrance examinations both there and at the École 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 Mathématiques for his essay on the Riemann zeta function.
In 1892 Hadamard married LouiseAnna Trénel, 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 ValléePoussin); 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 causes^{[6]} though he professed to be an atheist in his religion.^{[7]}^{[8]}
In 1897 he moved back to Paris, holding positions in the Sorbonne and the Collège 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 École Polytechnique in 1912 and at the École 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 wellposed 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 Poincaré, whose complete works he helped edit. He became foreign member of the Royal Netherlands Academy of Arts and Sciences in 1920.^{[9]} 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.^{[10]} He was awarded the CNRS Gold medal for his lifetime achievements in 1956. He died in Paris in 1963, aged ninetyseven.
Hadamard's students included Maurice Fréchet, Paul Lévy, Szolem Mandelbrojt and André Weil.
In his book Psychology of Invention in the Mathematical Field,^{[6]} 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 Poincaré and others as viewing entire solutions with "sudden spontaneousness".^{[11]}
Hadamard described the process as having four steps of the fivestep Graham Wallas creative process model, with the first three also having been put forth by Helmholtz:^{[12]} Preparation, Incubation, Illumination, and Verification.
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.""
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