Jacques Herbrand

Jacques Herbrand
Herbrand in summer 1931, as photographed by Natascha Artin Brunswick
Born(1908-02-12)12 February 1908
Paris, France
Died27 July 1931(1931-07-27) (aged 23)
La Bérarde, Isère, France
NationalityFrench
Alma materÉcole Normale Supérieure
University of Paris (PhD, 1930)
Known forHerbrand's theorem
Herbrand–Ribet theorem
Herbrand quotient
Scientific career
FieldsMathematical logic, class field theory
ThesisRecherches sur la théorie de la démonstration (Investigations on Proof Theory) (1930)
Doctoral advisorErnest Vessiot

Jacques Herbrand (12 February 1908 – 27 July 1931) was a French mathematician. Although he died at age 23, he was already considered one of "the greatest mathematicians of the younger generation" by his professors Helmut Hasse and Richard Courant.[1]

He worked in mathematical logic and class field theory. He introduced recursive functions. Herbrand's theorem refers to either of two completely different theorems. One is a result from his doctoral thesis in proof theory, and the other one half of the Herbrand–Ribet theorem. The Herbrand quotient is a type of Euler characteristic, used in homological algebra. He contributed to Hilbert's program in the foundations of mathematics by providing a constructive consistency proof for a weak system of arithmetic. The proof uses the above-mentioned, proof-theoretic Herbrand's theorem.

  1. ^ Chevalley, Claude; Lautman, Albert (1971). "Biographical Note on Jacques Herbrand". In Goldfarb, Warren D. (ed.). Logical Writings. Berlin: Springer. pp. 21–23. ISBN 90-277-0176-8.