Herbrand finished his doctorate at
École Normale Supérieure in Paris under
Ernest Vessiot in
1929. He joined the army in October 1929, however, and so did not defend his thesis at the
Sorbonne until the following year. He was awarded a
Rockefeller fellowship that enabled him to study in
Germany in
1931, first with
John von Neumann in
Berlin, then during June with
Emil Artin in
Hamburg, and finally with
Emmy Noether in
Göttingen.
He submitted his principal study of proof theory and general recursive functions "On the consistency of arithmetic" early in 1931. While the essay was under consideration,
Gödel's "On formally undecidable sentences of
Principia Mathematica and related systems I" announced the impossibility of formalizing within a theory that theory's consistency proof. Herbrand studied Gödel's essay and wrote an appendix to his own study explaining why Gödel's result did not contradict his own. In July of that year he was mountain-climbing in the French
Alps with two friends when he fell to his death in the granite mountains of
Massif des Écrins. "On the consistency of arithmetic" was published posthumously.
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