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Jacques Herbrand entered the École Normale Supérieure at the age of 17. This was quite exceptional at that time. For his doctoral thesis he studied mathematical logic which was a surprising choice, given the lack of interest in that topic in France in this period. His doctoral thesis was approved in April 1929 and in October of that year Jacques joined the army for his military service.
After his spell in the army, Herbrand was awarded a Rockefeller fellowship to allow him to study at various places in Europe. His first period, until May 1931, was spent at the University of Berlin where he worked with von Neumann. From Berlin, Herbrand went to Hamburg where he spent the month of June working with Artin. His final visit was to Göttingen where he spent the month of July 1931 studying with Emmy Noether.
After leaving Göttingen, Herbrand decided on a holiday in the Alps before his intended return to France. However he was never to complete his plans for he died in a mountaineering accident in the Alps only a few days after his holiday began. His death at the age of 23 in one of the tragic losses to mathematics.
It is incredible how much Herbrand achieved in the short time he had to undertake mathematical research. He made contributions to mathematical logic where Herbrand's theorem on the theory of quantifiers appears in his doctoral thesis. See [5] for discussion of a gap which was found in Herbrand's proof in 1963.
Herbrand's theorem establishes a link between quantification theory and sentential logic which is important in that it gives a method to test a formula in quantification theory by successively testing formulas for sentential validity. Since testing for sentential validity is a mechanical process, Herbrand's theorem is today of major importance in software developed for theorem proving by computer.
Herbrand also worked on field theory considering abelian extensions of algebraic number fields. In the few months on which he worked on this topic, Herbrand published ten papers. These papers simplify proofs of results by Kronecker, Heinrich Weber, Hilbert, Takagi and Artin. Herbrand also generalised some of the results by these workers in class field theory as well as proving some important new theorems of his own.
Texto original por: J J O'Connor and E F Robertson
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| JOC/EFR December 1996 | School of
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