Although he died at age 23, he was already considered one of "the greatest mathematicians of the younger generation" by his professors Helmut Hasse and Richard Courant.

He contributed to Hilbert's program in the foundations of mathematics by providing a constructive consistency proof for a weak system of arithmetic.

He was awarded a Rockefeller fellowship that enabled him to study in Germany in 1930-1931, first with John von Neumann in Berlin, then during June with Emil Artin in Hamburg, and finally with Emmy Noether in Göttingen.

An earlier letter to Vessiot, of 28 November, explained Gödel's first incompleteness theorem in the form of failure of omega-consistency.

[3] In July 1931, Herbrand was mountain-climbing in the French Alps with two friends when he fell to his death in the granite mountains of Massif des Écrins.