On Herbrand’s Thought

Abstract

Jacques Herbrand was born in 1908. In 1925, at the end of his secondary studies, he took first place at the École Normale Supérieure. I entered the École myself in 1926, and immediately noticed the entirely special place he occupied among his comrades, due to the vigor and universality of his spirit. In 1928, he took first place in the Agrégation, and was able to stay a fourth year at the École, during which he completed his thesis, which contains the work in mathematical logic that he had been pursuing for two years. In 1929–1930 he did his military service; during that year he published two notes on the units of algebraic number fields. These notes form the basis of the new methods in class-field theory. He also finished the article 1931, which was a continuation of his thesis. He spent the academic year 1930–1931 in Germany: first in Berlin with von Neumann, where he continued his work in logic, notably comparing his results to those of Gödel (see Herbrand 1931c); then he went to Hamburg and finally to Göttingen. He returned to France at the end of July and left immediately to indulge in his favorite sport, mountaineering. There he died in a fall, on July 27. Thus passed one whom a mathematician described as “one of the greatest of his generation”.¹