Jacques Herbrand
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.
Jacques Herbrand | |
|---|---|
Herbrand in summer 1931, as photographed by Natascha Artin Brunswick | |
| Born | 12 February 1908 Paris, France |
| Died | 27 July 1931 (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.