Background
Herbrand, Jacques was born in 1908 in Paris.
Herbrand, Jacques was born in 1908 in Paris.
Ecole Normale Supérieure and in Berlin and Hamburg.
Main publications:
(1930) Recherches sur ta théorie de la démonstration, Warsaw: Dziewulski.
(1936) Le développement moderne de la théorie des corps algébriques, corps de classes et lois de réciprocité, Paris: Gauthier-Villars.
(1968) Ecrits logiques, Paris: Presses Universitaires de France (English translation. Logical Writings, Cambridge, Mass.: Harvard University Press,
1971
contains many of Herbrand's articles on mathematics and logic, and a useful summary of his thought).
Jacques Herbrand's approach to mathematics is consistently anti-Platonic. The Platonist conception of mathematics is that it consists of statements about a timeless world of abstract entities and their interrelationships, and its truths are true independently of all minds. By contrast, Herbrand asserts that mathematics and logic are intersubjective human creations.
Their objectivity consists of their symbolism being regarded as purely formal. The symbolic formulae of mathematics and logic should not be considered to be about, or to arise from, anything given by the real world. The two disciplines are to be concerned only with the form of arguments, and any application of mathematics and logic should be left to scientists or philosophers.
Following Hilbert.
Herbrand worked on proof theory, which examines the structure of the proofs.