Jacques Herbrand

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Jacques Herbrand

Jacques Herbrand (born February 12, 1908 in Paris , † July 27, 1931 in La Bérarde ) was a French logician, algebraist and number theorist.

Life

Herbrand was first in the national entrance exams for the École normal supérieure (ENS) in 1925 and was also the best student of the ENS in the final exams in 1928. Even then he began to be interested in mathematical logic (which was hardly studied in France at the time) and read it Principia Mathematica by Bertrand Russell and Alfred North Whitehead . In 1929 he received his doctorate with Ernest Vessiot with a thesis in mathematical logic.

After completing his military service, he went to John von Neumann at the Humboldt University in Berlin , Emil Artin at the University of Hamburg and Emmy Noether at the University of Göttingen on a Rockefeller scholarship in 1931 . Before returning to France, he wanted to spend a holiday in the Alps and had a fatal mountaineering accident at the age of 23. Emmy Noether regretted in an obituary: One of the strongest mathematical talents went with him, right out of the most intense work, full of ideas for the future .

As part of Hilbert's program of the finitistic justification of mathematics, Herbrand gave a proof of the consistency of a branch of arithmetic with restricted induction. He started doing this in his dissertation in Paris and continued it later during his stay in Germany in 1930. Wilhelm Ackermann (1924) and John von Neumann (1927) gave proof of the consistency of parts of arithmetic . After the incompleteness of Kurt Godel (1930) a consistency proof of the complete arithmetic is not possible, what Herbrand then learned about John von Neumann and what he was still in his essay of 1931 took into account the day of his death in Crelle's Journal was received. He also corresponded with Kurt Gödel on the concept of recursive functions .

The Herbrand universe and Herbrand's theorem in predicate logic are named after him. His findings in predicate logic are summarized as Herbrand theory .

Herbrand also made significant contributions to algebraic number theory, although he only dealt with it for a few months (a total of ten papers by him appeared on it). His study friend Claude Chevalley published some of his work after his death.

In his honor, the Academie des Sciences presents the Prix ​​Jacques Herbrand and the Conference on Automated Deduction (CADE) the Herbrand Award .

Fonts

  • Sur la theory de la demonstration , Comptes rendus Acad. Sci., Paris, Volume 186, 1928, pp. 1274-1276
  • Non-contradiction des axiomes arithméthiques , Comptes rendus Acad. Sci., Paris, Volume 188, 1929, pp. 303-304
  • Sur quelques propriétés des propositions vraies et leurs applications , Comptes rendus Acad. Sci., Vol. 188, 1929, pp. 1076-1078
  • Sur leproblemème fundamentale des mathématiques , Comptes rendus Acad. Sci., Vol. 189, 1929, pp. 554-556, 720
  • Sur leproblemème fundamentale de la logique mathématique , Comptes Rendus Soc. Sci. et L. de Varsovie, 1931
  • Les bases de la logique hilbertienne , Revue de métaphysique et de morale, Volume 37, 1930, pp. 243-255
  • Recherches sur la théorie de la demonstration , Thesis University Paris 1930 (and in Travaux Soc. Des Sci. Et L. de Varsovie), online , English translation: Investigations in proof theory: the properties of true dispositions , 1930, in Jean Van Heijenoort (Editor) From Frege to Gödel , Harvard University Press 1967, p. 525
  • On the theory of algebraic functions (from letters to Emmy Noether) , Mathematische Annalen, Volume 106, 1932, p. 52 (posthumous reports of results from Herbrand by Emmy Noether)
  • Théorie arithmétique des corps de nombres de degré infini , Part I: Extensions algébriques finies de corps infinie , Mathematische Annalen, Volume 106, 1932, p. 473 (with obituary by Emmy Noether), Part II: Extensions algébriques de degré infini , Mathematische Annalen , Volume 109, 1933, p. 699 (from the estate of Claude Chevalley)
  • Sur la non-contradiction de l'arithmétique , Journal for pure and applied mathematics, Volume 166, 1931, pp. 1-8 (with foreword by Helmut Hasse ), English translation in Heijenoort From Frege to Gödel , Harvard UP, 1967, The consistency of arithmetic , pp. 618-628

See also

literature

Web links

Individual evidence

  1. ^ Math. Annalen, Volume 106, 1932, p. 473
  2. ↑ Herbrand Sur la non-contradiction de l'arithmétique , Journal for pure and applied mathematics, Volume 166, 1931, pp. 1-8, preliminary remark by Hasse
  3. ↑ Gödel quoted in Heijenoort From Frege to Gödel , introduction to the reprint of Herbrand's essay
personal data
SURNAME Herbrand, Jacques
BRIEF DESCRIPTION French logician
DATE OF BIRTH February 12, 1908
PLACE OF BIRTH Paris , France
DATE OF DEATH July 27, 1931
Place of death La Bérarde , Isere department , France