Jacques Hadamard

Last updated

Jacques Hadamard

Hadamard2 cropped.jpg
Jacques Salomon Hadamard
Born(1865-12-08)8 December 1865
Versailles, France
Died17 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
Awards Grand Prix des Sciences Mathématiques (1892)
Prix Poncelet (1898)
CNRS Gold medal (1956)
Scientific career
Institutions University of Bordeaux
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
Jacques Hadamard signature.png

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 analysis, differential geometry and partial differential equations. [3] [4] [5]



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 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 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 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 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 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 Jewish causes [6] [ failed verification ] 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 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 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 ninety-seven.

Hadamard's students included Maurice Fréchet, Paul Lévy, Szolem Mandelbrojt and André Weil.

On creativity

In his book Psychology of Invention in the Mathematical Field, [6] Hadamard uses the results of introspection to study mathematical thought processes, [6] :2 and tries to report and interpret observations, personal or gathered from other scholars engaged in the work of invention. [6] :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". [6] :13–16

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: [6] :56 Preparation, Incubation, Illumination, and Verification.


See also

Related Research Articles

Gaston Julia

Gaston Maurice Julia was a French mathematician who devised the formula for the Julia set. His works were popularized by French mathematician Benoit Mandelbrot; the Julia and Mandelbrot fractals are closely related.

Élie Cartan French mathematician

Élie Joseph Cartan, ForMemRS was an influential French mathematician who did fundamental work in the theory of Lie groups, differential systems, and differential geometry. He also made significant contributions to general relativity and indirectly to quantum mechanics. He is widely regarded as one of the greatest mathematicians of the twentieth century.

Pierre Boutroux

Pierre Léon Boutroux was a French mathematician and historian of science. Boutroux is chiefly known for his work in the history and philosophy of mathematics.

Charles Jean de la Vallée Poussin

Charles-Jean Étienne Gustave Nicolas, baron de la Vallée Poussin was a Belgian mathematician. He is best known for proving the prime number theorem.

Szolem Mandelbrojt Polish-French mathematician

Szolem Mandelbrojt was a Polish-French mathematician who specialized in mathematical analysis. He was a Professor at the Collège de France from 1938 to 1972, where he held the Chair of Analytical Mechanics and Celestial Mechanics.

Jean Gaston Darboux French mathematician

Jean-Gaston Darboux FAS MIF FRS FRSE was a French mathematician.

Arnaud Denjoy was a French mathematician.

Édouard Goursat French mathematician

Édouard Jean-Baptiste Goursat was a French mathematician, now remembered principally as an expositor for his Cours d'analyse mathématique, which appeared in the first decade of the twentieth century. It set a standard for the high-level teaching of mathematical analysis, especially complex analysis. This text was reviewed by William Fogg Osgood for the Bulletin of the American Mathematical Society. This led to its translation into English by Earle Raymond Hedrick published by Ginn and Company. Goursat also published texts on partial differential equations and hypergeometric series.

Paul Émile Appell French mathematician

Paul Émile Appell was a French mathematician and Rector of the University of Paris. Appell polynomials and Appell's equations of motion are named after him, as is rue Paul Appell in the 14th arrondissement of Paris and the minor planet 988 Appella.

Théophile de Donder

Théophile Ernest de Donder was a Belgian mathematician and physicist famous for his work in developing correlations between the Newtonian concept of chemical affinity and the Gibbsian concept of free energy.

Lucien Godeaux (1887–1975) was a prolific Belgian mathematician. His total of more than 1000 papers and books, 669 of which are found in Mathematical Reviews, made him one of the most published mathematicians. He was the sole author of all but one of his papers.

Stefan Bergman

Stefan Bergman was a Congress of Poland-born American mathematician whose primary work was in complex analysis. His name is also written Bergmann; he dropped the second "n" when he came to the U. S. He is best known for the kernel function he discovered while at Berlin University in 1922. This function is known today as the Bergman kernel. Bergman taught for many years at Stanford University, and served as an advisor to several students.

Pierre Humbert was a French mathematician who worked on the theory of elliptic functions and introduced Humbert polynomials. He was the son of the mathematician Georges Humbert and married the daughter of Henri Andoyer.

Georges Jean Marie Valiron was a French mathematician, notable for his contributions to analysis, in particular, the asymptotic behaviour of entire functions of finite order and Tauberian theorems.

Gabriel Xavier Paul Koenigs was a French mathematician who worked on analysis and geometry. He was elected as Secretary General of the Executive Committee of the International Mathematical Union after the first world war, and used his position to exclude countries with whom France had been at war from the mathematical congresses.

Maurice Janet

Maurice Janet (1888–1983) was a French mathematician.

Charles Edmond Alfred Riquier was a French mathematician.

Gustave Juvet was a Swiss mathematician.

Robert de Montessus de Ballore

Robert Fernand Bernard, Viscount de Montessus de Ballore was a French mathematician, known for his work on continued fractions and Padé approximants.

Adolphe Buhl was a French mathematician and astronomer.


  1. Hadamard, J. (1942). "Emile Picard. 1856–1941". Obituary Notices of Fellows of the Royal Society . 4 (11): 129–150. doi:10.1098/rsbm.1942.0012. S2CID   162244074.
  2. Cartwright, M. L. (1965). "Jacques Hadamard. 1865-1963". Biographical Memoirs of Fellows of the Royal Society . 11: 75–99. doi: 10.1098/rsbm.1965.0005 .
  3. O'Connor, John J.; Robertson, Edmund F., "Jacques Hadamard", MacTutor History of Mathematics archive , University of St Andrews . Archived 7 May 2021 at the Wayback Machine
  4. Jacques Hadamard at the Mathematics Genealogy Project
  5. Mandelbrojt, Szolem; Schwartz, Laurent (1965). "Jacques Hadamard (1865–1963)". Bull. Amer. Math. Soc. 71 (1): 107–129. doi: 10.1090/s0002-9904-1965-11243-5 . MR   0179049.
  6. 1 2 3 4 5 6 Hadamard, Jacques (1954). An essay on the psychology of invention in the mathematical field . New York: Dover Publications. ISBN   0-486-20107-4.
  7. Hadamard, Jacques (March 1988). Mandelbrot, Benoit B. (ed.). Translated by I. H. Rose. "How I did not discover relativity". The Mathematical Intelligencer. Springer. 10 (2): 65–67. doi:10.1007/BF03028360. Lay summary MacTutor: Hadamard on Hermite (March 2006). p. 66: 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[.]
  8. Shaposhnikova, T. O. (1999). Jacques Hadamard: A Universal Mathematician. American Mathematical Soc. pp. 33–34. ISBN   978-0-8218-1923-4.
  9. "Jacques S. Hadamard (1865–1963)". Royal Netherlands Academy of Arts and Sciences. Retrieved 19 July 2015.
  10. "United States". The Times (36594). London. 24 October 1901. p. 3.
  11. Barzun, Jacques (1946). "Review: An essay on the psychology of invention in the mathemathical field by J. Hadamard" (PDF). Bull. Amer. Math. Soc. 52 (3): 222–224. doi: 10.1090/s0002-9904-1946-08528-6 .
  12. Tamarkin, J. D. (1934). "Review: Le Problème de Cauchy et les Équations aux Dérivées Partielles Linéaires Hyperboliques by J. Hadamard" (PDF). Bull. Amer. Math. Soc. 40 (3): 203–204. doi: 10.1090/s0002-9904-1934-05815-4 .
  13. Hedrick, E. R. (1914). "Review: Leçons sur le Calcul des Variations, par J. Hadamard; recueillies par M. Fréchet. Tome Premier" (PDF). Bull. Amer. Math. Soc. 21 (1): 30–32. doi: 10.1090/s0002-9904-1914-02567-4 .
  14. Wilson, Edwin Bidwell (1904). "Review: Leçons sur la Propagation des Ondes et les Equations de l'Hydrodynamique by Jacques Hadamard" (PDF). Bull. Amer. Math. Soc. 10 (6): 305–317. doi: 10.1090/s0002-9904-1904-01115-5 .
  15. Moore, C. N. (1917). "Review: Four Lectures on Mathematics (Delivered at Columbia University in 1911) by J. Hadamard" (PDF). Bull. Amer. Math. Soc. 23 (7): 317–319. doi: 10.1090/S0002-9904-1917-02949-7 .
  16. Morley, Frank (1898). "Review: Leçons de Géométrie élémentaire (vol. 1), par Jacques Hadamard" (PDF). Bull. Amer. Math. Soc. 4 (10): 550–551. doi: 10.1090/s0002-9904-1898-00547-5 .
  17. Hildebrandt, T. H. (1928). "Review: Cours d'Analyse, vol. 1, by J. Hadamard" (PDF). Bull. Amer. Math. Soc. 34 (6): 781–782. doi: 10.1090/s0002-9904-1928-04650-5 .
  18. Moore, C. N. (1933). "Review: Cours d'Analyse, vol. 2, by J. Hadamard" (PDF). Bull. Amer. Math. Soc. 39 (3): 185–186. doi: 10.1090/s0002-9904-1933-05568-4 .

Further reading