View source for Jacques Hadamard

{{Short description|French mathematician (1865–1963)}}
{{Redirect|Hadamard|other uses|Hadamard (disambiguation)}}
{{Use dmy dates|date=January 2018}}
{{Infobox scientist
| name              = Jacques Hadamard
| honorific_suffix  = {{postnom|country=GBR|ForMemRS|size=100%}}
| image             = Hadamard2 cropped.jpg
| signature         = Jacques Hadamard signature.png
| image_size        = 225px
| caption           = Jacques Salomon Hadamard
| birth_date        = {{birth date|df=y|1865|12|8}}
| birth_place       = [[Versailles (city)|Versailles]], France
| death_date        = {{death date and age|df=y|1963|10|17|1865|12|8}}
| death_place       = Paris, France
| nationality       = French
| alma_mater        = [[École Normale Supérieure]]
| thesis_title      = Essai sur l'étude des fonctions données par leur développement de Taylor
| thesis_url        = http://sites.mathdoc.fr/JMPA/PDF/JMPA_1892_4_8_A4_0.pdf
| thesis_year       = 1892
| doctoral_advisor  = [[Charles Émile Picard|C. Émile Picard]]<ref>{{Cite journal | last1 = Hadamard | first1 = J. | author-link = Jacques Hadamard| title = Emile Picard. 1856–1941 | doi = 10.1098/rsbm.1942.0012 | journal = [[Obituary Notices of Fellows of the Royal Society]] | volume = 4 | issue = 11 | pages = 129–150| year = 1942 | title-link = Émile Picard | s2cid = 162244074 }}</ref><br />[[Jules Tannery]]
| doctoral_students = [[Maurice René Fréchet]]<br />[[Marc Krasner]]<br />[[Paul Lévy (mathematician)|Paul Lévy]]<br />[[Szolem Mandelbrojt]]<br />[[André Weil]]
| known_for         = [[Hadamard product (matrices)|Hadamard product]]<br />[[prime number theorem|Proof of prime number theorem]]<br />[[Hadamard matrix|Hadamard matrices]]<br />[[Hadamard's maximal determinant problem]]
| footnotes         = 
| field             = [[Mathematics]]
| work_institution  = [[University of Bordeaux]]<br />[[University of Paris|Sorbonne]]<br />[[Collège de France]]<br />[[École Polytechnique]]<br />[[École Centrale Paris]]
| prizes            = [[Grand Prix des Sciences Mathématiques]] (1892)<br />[[Prix Poncelet]] (1898) <br /> [[CNRS Gold medal]] (1956)
}}

'''Jacques Salomon Hadamard''' {{postnom|country=GBR|ForMemRS}}<ref name="frs">{{Cite journal | last1 = Cartwright | first1 = M. L. | author-link = Mary Cartwright| doi = 10.1098/rsbm.1965.0005 | title = Jacques Hadamard. 1865-1963 | journal = [[Biographical Memoirs of Fellows of the Royal Society]] | volume = 11 | pages = 75–99| year = 1965 | doi-access = free }}</ref> ({{IPA|fr|adamaʁ|lang}}; 8 December 1865 – 17 October 1963) was a French mathematician who made major contributions in [[number theory]], [[complex analysis]], [[differential geometry]], and [[partial differential equations]].<ref>{{MacTutor Biography|id=Hadamard|mode=cs1}}</ref><ref>{{MathGenealogy |id=24555}}</ref><ref>{{cite journal|last1=Mandelbrojt|first1= Szolem|author-link1=Szolem Mandelbrojt|last2=Schwartz|first2=Laurent|author-link2=Laurent Schwartz|title=Jacques Hadamard (1865–1963)|journal=[[Bulletin of the American Mathematical Society|Bull. Amer. Math. Soc.]]|year=1965|volume=71|issue=1|pages=107–129|mr=0179049|doi=10.1090/s0002-9904-1965-11243-5|doi-access=free}}</ref>

==Biography==
The son of a teacher, Amédée Hadamard, of [[Jewish]] descent, and Claire Marie Jeanne Picard, Hadamard was born in [[Versailles (city)|Versailles, France]] and attended the [[Lycée Charlemagne]] and [[Lycée Louis-le-Grand]], 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 [[Paul Tannery|Tannery]], [[Hermite]], [[Jean Gaston Darboux|Darboux]], [[Paul Émile Appell|Appell]], [[Édouard Goursat|Goursat]], and [[Charles Émile Picard|Picard]]. He obtained his doctorate in 1892 and in the same year was awarded the {{lang|fr|Grand Prix des Sciences Mathématiques}} for his essay on the [[Riemann 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 the [[University of Bordeaux]], where he proved his [[Hadamard's inequality|celebrated inequality]] on [[determinant]]s, which led to the discovery of [[Hadamard matrix|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 Vallée-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 [[Jew]]ish causes<ref>{{harvtxt|Cartwright|1965}}, p. 731: "Hadamard recognised the danger of Hitlerism very early and, although a free thinker and anti-zionist, he was against all racial discrimination and worked to help the Jews in Germany in a more enlightened way than the Israelite Consistory and Zionist circles. With Paul Langevin he schemed to get a chair created for Einstein in France."</ref> though he professed to be an atheist in his religion.<ref name="atheist">{{cite journal |last1=Hadamard |first1=Jacques |editor1-last=Mandelbrot |editor1-first=Benoit B. |editor1-link=Benoit Mandelbrot |translator=I. H. Rose |title=How I did not discover relativity |journal=[[The Mathematical Intelligencer]] |date=March 1988 |volume=10 |issue=2 |pages=65–67 |doi=10.1007/BF03028360 |publisher=Springer |s2cid=122781052 |quote=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[.] |quote-page=66}}
*{{cite web |date=March 2006 |title=Hadamard on Hermite |website=MacTutor |url=https://mathshistory.st-andrews.ac.uk/Extras/Hadamard_Hermite/}}</ref><ref>{{cite book|last=Shaposhnikova|first=T. O.|title=Jacques Hadamard: A Universal Mathematician|year=1999|publisher=American Mathematical Soc.|isbn=978-0-8218-1923-4|pages=33–34}}</ref>

In 1897 he moved back to Paris, holding positions in the [[University of Paris|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 [[Camille Jordan|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 equation]]s, 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 [[Henri Poincaré|Poincaré]], whose complete works he helped edit. He became foreign member of the [[Royal Netherlands Academy of Arts and Sciences]] in 1920.<ref>{{cite web|url=http://www.dwc.knaw.nl/biografie/pmknaw/?pagetype=authorDetail&aId=PE00000612 |title=Jacques S. Hadamard (1865–1963) |publisher=Royal Netherlands Academy of Arts and Sciences |access-date=19 July 2015}}</ref> 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 France|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 ([[Legum Doctor|LL.D.]]) by [[Yale University]] in October 1901, during celebrations for the bicentenary of the university.<ref>{{Cite newspaper The Times |title=United States|date=24 October 1901 |page=3 |issue=36594}}</ref> 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 René Fréchet|Maurice Fréchet]], [[Paul Lévy (mathematician)|Paul Lévy]], [[Szolem Mandelbrojt]], and [[André Weil]].

==On creativity==
In his book ''Psychology of Invention in the Mathematical Field'',<ref name=psy-math-54>{{cite book |author=Hadamard, Jacques |title=An essay on the psychology of invention in the mathematical field |publisher=[[Dover Publications]] |location=New York |year=1954 |isbn=0-486-20107-4 |url-access=registration |url=https://archive.org/details/essayonpsycholog00hada }}</ref> Hadamard uses the results of introspection to study mathematical thought processes,{{r|psy-math-54|p=2}} and tries to report and interpret observations, personal or gathered from other scholars engaged in the work of invention.{{r|psy-math-54|p=133}} 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".{{r|psy-math-54|pp=13–16}}

Hadamard described the process as having four steps of the five-step [[Graham Wallas]] [[creativity|creative]] process model, with the first three also having been put forth by Helmholtz:{{r|psy-math-54|p=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).<ref>{{cite web |url=https://creativeagni.com/ezine/2012/01/creativity-techniques-creative-process-the-graham-wallas-5-stage-model-illustration-of-instructional-designer-elearning-course-developer-in-delhi-india/ |title=The Wallas Stage Model of Creativity |last=Anand |first=Shafali R. |date=3 January 2012 | access-date=2024-01-24 |quote=The Wallas Stage Model of Creativity divides the process of creative thinking into 5 stages. These stages are Preparation, Incubation, Intimation, Illumination, and Verification.}}</ref>

==Publications==
{{refbegin}}
* ''An Essay on the Psychology of Invention in the Mathematical Field.'' Princeton University Press, 1945;<ref>{{cite journal|author=Barzun, Jacques|author-link=Jacques Barzun|title=Review: ''An essay on the psychology of invention in the mathemathical field'' by J. Hadamard|journal=Bull. Amer. Math. Soc.|year=1946|volume=52|issue=3|pages=222–224|url=https://www.ams.org/journals/bull/1946-52-03/S0002-9904-1946-08528-6/S0002-9904-1946-08528-6.pdf|doi=10.1090/s0002-9904-1946-08528-6|doi-access=free}}</ref> new edition under the title ''The Mathematician's Mind: The Psychology of Invention in the Mathematical Field'',  1996; {{isbn|0-691-02931-8}}, [https://archive.org/details/eassayonthepsych006281mbp Online]
*''Le problème de Cauchy et les équations aux dérivées partielles linéaires hyperboliques'', Hermann 1932<ref>{{cite journal|author=Tamarkin, J. D.|author-link=Jacob Tamarkin|title=Review: ''Le Problème de Cauchy et les Équations aux Dérivées Partielles Linéaires Hyperboliques'' by J. Hadamard|journal=Bull. Amer. Math. Soc.|year=1934|volume=40|issue=3|pages=203–204|url=https://www.ams.org/journals/bull/1934-40-03/S0002-9904-1934-05815-4/S0002-9904-1934-05815-4.pdf|doi=10.1090/s0002-9904-1934-05815-4|doi-access=free}}</ref> (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 série de Taylor et son prolongement analytique'', 2nd edn., Gauthier-Villars 1926
*''La théorie des équations aux dérivées partielles'', Peking, Editions Scientifiques, 1964
*''Leçons sur le calcul des variations'', Vol. 1, Paris, Hermann 1910,<ref>{{cite journal|author=Hedrick, E. R.|author-link=Earle Raymond Hedrick|title=Review: ''Leçons sur le Calcul des Variations'', par J. Hadamard; recueillies par M. Fréchet. Tome Premier.|journal=Bull. Amer. Math. Soc.|year=1914|volume=21|issue=1|pages=30–32|url=https://www.ams.org/journals/bull/1914-21-01/S0002-9904-1914-02567-4/S0002-9904-1914-02567-4.pdf|doi=10.1090/s0002-9904-1914-02567-4|doi-access=free}}</ref> [https://archive.org/details/leonssurlecalc00hadauoft Online]
*''Leçons sur la propagation des ondes et les équations de l'hydrodynamique'', Paris, Hermann 1903,<ref>{{cite journal|author=Wilson, Edwin Bidwell|author-link=Edwin Bidwell Wilson|title=Review: ''Leçons sur la Propagation des Ondes et les Equations de l'Hydrodynamique'' by Jacques Hadamard|journal=Bull. Amer. Math. Soc.|year=1904|volume=10|issue=6|pages=305–317|url=https://www.ams.org/journals/bull/1904-10-06/S0002-9904-1904-01115-5/S0002-9904-1904-01115-5.pdf|doi=10.1090/s0002-9904-1904-01115-5|doi-access=free}}</ref> [https://archive.org/details/leconssurlaprop00hadagoog Online]
*[http://catalog.hathitrust.org/Record/009789898 ''Four lectures on Mathematics, delivered at Columbia University 1911''], Columbia University Press 1915<ref>{{cite journal|author=Moore, C. N.|author-link=Charles Napoleon Moore|title=Review: ''Four Lectures on Mathematics'' (Delivered at Columbia University in 1911) by J. Hadamard|journal=Bull. Amer. Math. Soc.|year=1917|volume=23|issue=7|pages=317–319|url=https://www.ams.org/journals/bull/1917-23-07/S0002-9904-1917-02949-7/S0002-9904-1917-02949-7.pdf|doi=10.1090/S0002-9904-1917-02949-7|doi-access=free}}</ref> (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 correspondences and differential equations, 4. Elementary solutions of partial differential equations and Greens functions), [https://archive.org/details/fourlecturesonma29788gut Online]
*''Leçons de géométrie élémentaire'', 2 vols., Paris, Colin, 1898,<ref>{{cite journal|author=Morley, Frank|author-link=Frank Morley|title=Review: ''Leçons de Géométrie élémentaire'' (vol. 1), par Jacques Hadamard|journal=Bull. Amer. Math. Soc.|year=1898|volume=4|issue=10|pages=550–551|url=https://www.ams.org/journals/bull/1898-04-10/S0002-9904-1898-00547-5/S0002-9904-1898-00547-5.pdf|doi=10.1090/s0002-9904-1898-00547-5|doi-access=free}}</ref> 1906 (Eng. trans: ''Lessons in Geometry'', American Mathematical Society 2008), Vol. 1, [https://archive.org/details/leonsdegomtriel04hadagoog Vol. 2]
*''Cours d'analyse professé à l'École polytechnique'', 2 vols., Paris, Hermann 1925/27, 1930 (Vol. 1:<ref>{{cite journal|author=Hildebrandt, T. H.|author-link=Theophil Henry Hildebrandt|title=Review: ''Cours d'Analyse'', vol. 1, by J. Hadamard|journal=Bull. Amer. Math. Soc.|year=1928|volume=34|issue=6|pages=781–782|url=https://www.ams.org/journals/bull/1928-34-06/S0002-9904-1928-04650-5/S0002-9904-1928-04650-5.pdf|doi=10.1090/s0002-9904-1928-04650-5|doi-access=free}}</ref> ''Compléments de calcul différentiel, intégrales simples et multiples, applications analytiques et géométriques, équations différentielles élémentaires'', Vol. 2:<ref>{{cite journal|author=Moore, C. N.|title=Review: ''Cours d'Analyse'', vol. 2, by J. Hadamard|journal=Bull. Amer. Math. Soc.|year=1933|volume=39|issue=3|pages=185–186|url=https://www.ams.org/journals/bull/1933-39-03/S0002-9904-1933-05568-4/S0002-9904-1933-05568-4.pdf|doi=10.1090/s0002-9904-1933-05568-4|doi-access=free}}</ref> ''Potentiel, calcul des variations, fonctions analytiques, équations différentielles et aux dérivées partielles, calcul des probabilités'')
*''Essai sur l'étude des fonctions données par leur développement de Taylor. Étude sur les propriétés des fonctions entières et en particulier d'une fonction considérée par Riemann'', 1893, [https://archive.org/details/essaisurltuded00hadauoft Online]
*{{cite journal|title=Étude sur les propriétés des fonctions entières et en particulier d'une fonction considérée par Riemann|journal=Journal de mathématiques pures et appliquées|year=1893|pages=171–216|url=https://babel.hathitrust.org/cgi/pt?id=hvd.32044102908969&view=1up&seq=185&q1=hadamard}}
*''Sur la distribution des zéros de la fonction <math>\zeta(s)</math> et ses conséquences arithmétiques'', Bulletin de la Société Mathématique de France, Vol. 24, 1896, pp.&nbsp;199–220 [https://web.archive.org/web/20120717195014/http://www.numdam.org/numdam-bin/fitem?id=BSMF_1896__24__199_1 Online]
*{{cite book | last1=Hadamard | first1=Jacques | title=Lectures on Cauchy's problem in linear partial differential equations | orig-date=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}}
*{{cite book | last1=Hadamard | first1=Jacques | title=Non-Euclidean geometry in the theory of automorphic functions | orig-date=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}}
*{{cite book | last1=Hadamard | first1=Jacques | title=Lessons in geometry. I | orig-date=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}}
*{{cite book | last1=Hadamard | first1=Jacques | editor1-last=Fréchet | editor1-first=M. | editor2-last=Lévy | editor2-first=P. | editor3-last=Mandelbrojt | editor3-first=S. |display-editors = 3 | editor4-last=Schwartz | editor4-first=Laurent | title=Œuvres de Jacques Hadamard. Tomes I, II, III, IV | url=https://books.google.com/books?id=XOTuAAAAMAAJ | publisher=Éditions du Centre National de la Recherche Scientifique, Paris | year=1968 | mr=0230598}}
{{refend}}

==See also==
*[[List of things named after Jacques Hadamard]]

==References==
{{Reflist|30em}}

==Further reading==
* {{DSB |first=S. |last=Mandelbrojt |title=Hadamard, Jacques |volume=6 |pages=3–5}}
*{{cite book|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|url-access=registration|url=https://archive.org/details/jacqueshadamardu0000mazi}}.
*{{cite book|title=Jacques Hadamard: a universal mathematician|first1=V. G.|last1= Maz'ya|first2=  T. O.|last2= Shaposhnikova|author-link1=Vladimir Gilelevich Maz'ya|publisher=American Mathematical Society/London Mathematical Society|series=History of Mathematics|volume=14|year=1998|isbn=0821819232}}

==External links==
{{wikiquote}}
*{{Commons category-inline}}
*{{wikisourcelang-inline|fr}}
* {{Gutenberg author | id=34172| name=Jacques Hadamard}}
* {{Internet Archive author |sname=Jacques Salomon Hadamard}}

{{Authority control}}

{{DEFAULTSORT:Hadamard, Jacques}}
[[Category:1865 births]]
[[Category:1963 deaths]]
[[Category:People from Versailles]]
[[Category:19th-century French mathematicians]]
[[Category:20th-century French mathematicians]]
[[Category:Lycée Louis-le-Grand alumni]]
[[Category:École Normale Supérieure alumni]]
[[Category:Academic staff of the Collège de France]]
[[Category:Columbia University faculty]]
[[Category:French atheists]]
[[Category:Jewish atheists]]
[[Category:19th-century French Jews]]
[[Category:French pacifists]]
[[Category:Members of the French Academy of Sciences]]
[[Category:Foreign members of the Royal Society]]
[[Category:Corresponding Members of the Russian Academy of Sciences (1917–1925)]]
[[Category:Corresponding Members of the USSR Academy of Sciences]]
[[Category:Members of the Royal Netherlands Academy of Arts and Sciences]]
[[Category:Foreign associates of the National Academy of Sciences]]
[[Category:French number theorists]]
[[Category:Partial differential equation theorists]]
[[Category:Academic staff of the University of Paris]]
[[Category:French textbook writers]]
[[Category:Academic staff of École Polytechnique]]
[[Category:Academic staff of the University of Bordeaux]]
[[Category:French secular Jews]]