Born in Greifswald, Germany, he died in Prague, Czechoslovakia in a prisoner of war camp, after being arrested by the Russians due to his Nazi loyalties.
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.
References
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.
In 1933Gentzen was awarded his doctorate by Göttingen but the intense study in different environments had taken its toll so he was forced at this stage to return home to rest and recover his health.
At first Gentzen worried that it affected what he wanted to achieve on the foundations of mathematics and he withdrew what would have been his second paper after he had corrected the final proofs because of worries about the significance of Gödel's theorems.
Gentzen was interned by the Russian forces and held in poor conditions.
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