Despite a tragically short life—he was killed in a mountaineering accident in 1931 at the age of twenty-three—Jacques Herbrand made substantial contributions to the development of mathematical logic, especially to investigations in the metatheory of logic that were the particular concern of Hilbert and his school. The bulk of Herbrand's contributions is to be found in his University of Paris dissertation of 1930, Recherches sur la théorie de la démonstration (published in Travaux de la Société des Sciences et des Lettres de Varsovie, Classe III (33) [1930]: 33–160). This work has much in common with the later "Untersuchungen über das logische Schliessen" of Gerhard Gentzen, but the presentation of proofs and explanations is much less perspicuous than Gentzen's, and even now some aspects of Herbrand's work await further clarification and elaboration.

Herbrand's starting point is the system of classical propositional logic presented in Whitehead and Russell's Principia Mathematica...