Jacques Herbrand
French mathematician, 1908-1931 / From Wikipedia, the free encyclopedia
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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]
Jacques Herbrand | |
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Born | (1908-02-12)12 February 1908 Paris, France |
Died | 27 July 1931(1931-07-27) (aged 23) La Bérarde, Isère, France |
Nationality | French |
Alma mater | École Normale Supérieure University of Paris (PhD, 1930) |
Known for | Herbrand's theorem Herbrand–Ribet theorem Herbrand quotient |
Scientific career | |
Fields | Mathematical logic, class field theory |
Thesis | Recherches sur la théorie de la démonstration (Investigations on Proof Theory) (1930) |
Doctoral advisor | Ernest Vessiot |
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.