Jacques Hadamard

from Wikipedia, the free encyclopedia
Jacques Salomon Hadamard

Jacques Hadamard ( Jacques Salomon Hadamard ; born December 8, 1865 in Versailles , † October 17, 1963 in Paris ) was a French mathematician .

biography

Jacques Salomon Hadamard was the son of Amédée Hadamard, a teacher of Jewish origin. The family moved to Paris in 1867, where the father initially accepted a position at the Lycée Charlemagne and later at the Lycée Louis-le-Grand . Jacques Hadamard attended both schools and graduated in 1883 with honors in mathematics and mechanics.

From 1884 he studied at the École normal supérieure in Paris. His teachers included Charles Hermite and Jean Gaston Darboux . After graduating in 1888, he initially worked as a teacher at various schools. He received his doctorate from Émile Picard in 1892 with a thesis on functions that are defined by Taylor series . In the same year he received the Grand Prix des Sciences Mathématiques for his work on determining the number of prime numbers below a given limit.

Also in 1892 Jacques Hadamard married Louise-Anna Trénel, whom he had known from childhood. Both moved to Bordeaux , where Hadamard was given a position as a lecturer at the university there. On February 1, 1896, he became a professor of astronomy and mechanics there. During his time in Bordeaux, he published 29 papers in various fields of mathematics. The proof of the prime number theorem in 1896 is considered to be the most important work from this period . His two oldest sons were born in Bordeaux.

In 1897 Hadamard moved to the Sorbonne in Paris. During the Dreyfus affair (an example of anti-Semitism in fin de siècle France ) he sided with Alfred Dreyfus , the husband of his cousin Lucie . In 1898 the first volume of his Leçons de Géométrie Elémentaire on two-dimensional geometry appeared, which was followed in 1901 by a volume on three-dimensional geometry.

In 1898 Hadamard received the Prix ​​Poncelet for his work over the past ten years. From then on he concentrated more on mathematical physics, but always emphasized that he was more mathematician than physicist. During this time he wrote groundbreaking work on partial differential equations and geodesy . He also worked on the topics of geometric optics , hydrodynamics and limit value problems .

Another son and two daughters were born during his first five years in Paris.

He received numerous other awards and was elected President of the Société Mathématique de France in 1906. In 1912 he was appointed professor of analysis at the École polytechnique , succeeding Marie Ennemond Camille Jordan . In the same year he accepted the place in the Académie des Sciences that had become vacant through the early death of Henri Poincaré .

In 1916, his two older sons died in the battle of Verdun within a few weeks . Hadamard processed his grief by delving deeper into mathematics. In 1920 he got a chair for analysis at the École Centrale , but kept his posts at the École polytechnique and at the Collège de France . In the same year he was elected to the American Academy of Arts and Sciences , in 1926 to the National Academy of Sciences . Since 1922 he was a corresponding member of the Academy of Sciences of the USSR , in 1929 he became an honorary member of this academy. During this time until 1933 he traveled a lot and visited the United States twice, among other places . He tirelessly published high quality works and books.

Between the world wars, Hadamard's political attitudes changed to the left spectrum. In 1928 he gave a plenary lecture at the International Congress of Mathematicians in Bologna (Le développement et le rôle scientifique du calcul fonctionnel). In 1932 he was elected a foreign member of the Royal Society . After the outbreak of World War II and the fall of France, he was able to flee to the USA with his family. He received a temporary visiting professorship at Columbia University . In 1944 his third son was killed in the war. He left the USA, first went to England and returned to France at the end of the war.

After the war he became a peace activist. His proximity to the Communist Party almost prevented participation in the International Congress in Cambridge, Massachusetts in 1950 . The now 85-year-old was only allowed to enter the country after the advice of his American colleagues. He became honorary chairman of the congress. In 1951 Hadamard was the first recipient of the international Antonio Feltrinelli Prize . In 1956 he received the Médaille d'or du CNRS .

The news of his grandson's fatal mountain accident in 1962 seems to have broken Hadamard's will to live. He never left his home and died in October of the following year.

Hadamard was a dominant figure in French mathematics and had a school education with his seminar in Paris. His doctoral students include Maurice Fréchet , Paul Lévy , Szolem Mandelbrojt , André Weil , Marc Krasner .

Other about the work

According to Hadamard, for example, the Hadamard code , the Cauchy-Hadamard theorem, the Cartan-Hadamard theorem , the Hadamard inequality , Hadamard matrices , Hadamard's theorem , the Hadamard gate , the Hadamard's tri-circle theorem and the Hadamard transformation named.

Various problems were initiated by him and named after him. For example, there is the Hadamard problem of the maximum determinant, which asks for the maximum value of the determinant for matrices whose coefficients are appropriately constrained. Hadamard himself proved in 1893 an upper bound for the absolute value of the determinant of complex n-by-n matrices, the coefficients of which come from the unit disk. In the theory of partial differential equations, there is a Hadamard problem that asks whether the wave equation is the only equation that satisfies Huygens' principle , which, according to Hadamard, can only hold in even dimensions . It was later resolved negatively ( Karl Stellmacher , Paul Günther ). More generally, the Hadamard problem asks for a characterization of the equations that satisfy a Huygens principle.

See also

Quotes

"Logic only approves the campaigns of conquest of intuition."

- Jacques Hadamard (1945)

Publications

  • An Essay on the Psychology of Invention in the Mathematical Field. Princeton University Press, 1945; New edition entitled The Mathematician's Mind: The Psychology of Invention in the Mathematical Field. ibid. 1996; ISBN 0-691-02931-8 , online
  • Uvres de Jacques Hadamard. Volumes I, II, III, IV. Éditions du Center National de la Recherche Scientifique, Paris, 1968.
  • Leproblemème de Cauchy et les équations aux dérivées partielles linéaires hyperboliques , Hermann 1932 (Lectures Yale, English edition 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 edition, Gauthier-Villars 1926
  • La théorie des equations aux dérivées partielles , Beijing, Editions Scientifiques, 1964
  • Leçons sur le calcul des variations , Volume 1, Paris, Hermann 1910, online
  • Leçons sur la propagation des ondes et les equations de l'hydrodynamique , Paris, Hermann 1903, online
  • Non-Euclidean geometry in the theory of automorphic functions , American Mathematical Society 1999
  • Four lectures on Mathematics, delivered at Columbia University 1911 , Columbia University Press 1915 (1. The definition of solutions of linear partial differential equations by boundary conditioins, 2. Contemporary researches in differential equations, integral equations and integro-differential equations, 3. Analysis Situs in connection with correspondendes and differential equations, 4th Elementary solutions of partial differential equations and Greens functions), Online
  • Leçons de géométrie élémentaire , 2 volumes, Paris, Colin, 1898 1906 (English translation Lessons in Geometry , American Mathematical Society 2008), Volume 1 , Volume 2
  • Cours d'analysis professé à l'École polytechnique , 2 volumes, Paris, Hermann 1925/27, 1930 (Volume 1: Compléments de calcul différentiel, intégrales simples et multiples, applications analytiques et géométriques, équations différentielles élémentaires , Volume 2 Potentiel, calcul des variations, fonctions analytiques, equations 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, online
  • Sur la distribution des zéros de la fonction et ses conséquences arithmétiques , Bulletin de la Société Mathématique de France, Volume 24, 1896, pp. 199-220 (proof of prime number theorem) online

literature

Web links

Individual evidence

  1. ^ Foreign members of the Russian Academy of Sciences since 1724: Hadamard, Jacques Salomon. Russian Academy of Sciences, accessed December 13, 2019 (Russian).
  2. ^ Mathematics Genealogy Project
  3. ^ Hadamard's Maximum Determinant Problem, Mathworld
  4. ^ Hadamard Lectures on Cauchy's problem in linear partial differential equations , Yale University Press 1923
personal data
SURNAME Hadamard, Jacques
ALTERNATIVE NAMES Hadamard, Jacques Salomon
BRIEF DESCRIPTION French mathematician
DATE OF BIRTH December 8, 1865
PLACE OF BIRTH Versailles
DATE OF DEATH 17th October 1963
Place of death Paris