Jacques Herbrand

Who was Jacques Herbrand?

Jacques Herbrand was a French mathematician. Although he died at only 23 years of age, he was already considered one of "the greatest mathematicians of the younger generation" by his professors Helmut Hasse, and Richard Courant.

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.