He was one of Weyl's students at the University of Göttingen from 1929 to 1933. His main work was on the foundations of mathematics, in proof theory, specifically natural deduction and the sequent calculus. His cut-elimination theorem is the cornerstone of proof-theoretic semantics, and some philosophical remarks in his "Investigations into Logical Deduction", together with Wittgenstein's aphorism that "meaning is use", constitute the starting point for inferential role semantics.
- Eckart Menzler-Trott. Gentzens Problem: Mathematische Logik im nationalsozialistischen Deutschland. Birkhäuser Verlag, 2001. ISBN 3-7643-6574-9. An English translation is planned.
- M. E. Szabo. Collected Papers of Gerhard Gentzen. North-Holland, 1969.