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He worked in mathematical logic, and class field theory.
He introduced recursive functions in about 1932. Herbrand's Theorem refers to two completely different theorems, one is an early result 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 algebraHomological algebra Abstract algebra Algebraic topology Algebraic geometry Homological algebra is that branch of mathematics which studies the methods of homology and cohomology in a general setting. These concepts originated in algebraic topology. Cohomo.
Herbrand finished his doctorate at École Normale SupérieureThe cole Normale Superieure (also known as Normale Sup Normale ENS ENS-Ulm or Ulm is an elite French grande ecole whose main campus is located around the rue d'Ulm ( Ulm Street) in the 5th arrondissement of Paris. Originally meant to train high school tea in Paris under Ernest VessiotErnest Vessiot ( March 8, 1865 October 17, 1952) was a french mathematician who was born in Marseilles, France and died in La Bauche, Savoie, France. External link Vessiot, Ernest. in 1929. Herbrand joined the army in October, 1929. He was awarded a Rockefeller fellowship that enabled him to study in Germany in 1931, first with John von NeumannA separate article covers Saint John Neumann, the American priest. John von Neumann (Neumann Janos) ( December 28, 1903 February 8, 1957) was a Hungarian- American mathematician who made important contributions in quantum physics, set theory, computer sci in BerlinBerlin [ bɛrˈliːn ] is the national capital of Germany and its largest city, with 3,387,404 inhabitants (as of September 2004); down from 4. 5 million before World War II. Berlin is located on the rivers Spree and Havel in the northea, then during June with Emil ArtinEmil Artin ( March 3, 1898- December 20, 1962) was a mathematician born in Vienna, Austria who spent his career in Germany (mainly in Hamburg) until the Nazi threat when he emigrated to the USA in 1937 where he was at Princeton University 1946-1958. He wa in HamburgHamburg is Germany's second largest city (after Berlin) and its principal port. The official name Freie und Hansestadt Hamburg recalls its membership in the mediaeval Hanseatic League and the fact that Hamburg is a city state and one of Germany's sixteen, and finally with Emmy NoetherEmmy Noether ( March 23 1882 April 14 1935) was one of the most talented mathematicians of the early 20th century, with penetrating insights that she used to develop elegant abstractions which she formalized beautifully. She was born Amalie Noether in Erl in Göttingen.
In July 1931 he was mountain-climbing in the French Alps with two friends when he fell to his death in the granite mountains of La Bérarde, near Isère.