Gerhard Gentzen

Gerhard Karl Erich Gentzen (24 November 1909 – 4 August 1945) was a German mathematician and logician. He made major contributions to the foundations of mathematics, and proof theory, especially on natural deduction and the sequent calculus. His cut-elimination theorem is the cornerstone of proof-theoretic semantics. Gentzen was a student of Paul Bernays at the University of Göttingen. Bernays was fired as "non-Aryan" in April 1933, and Hermann Weyl formally acted as his supervisor. Gentzen joined the Sturmabteilung in November 1933, but kept contact with Bernays. He corresponded with Abraham Fraenkel and was implicated by the Nazi teachers' union. Weyl made efforts to bring him to the Institute for Advanced Study in Princeton. Between November 1935 and 1939 he was an assistant of David Hilbert in Göttingen. Gentzen joined the Nazi Party in 1937 and swore an oath of loyalty to Adolf Hitler in 1939. From 1943 he was a teacher at the German Charles-Ferdinand University of Prague. Under a contract from the SS, Gentzen worked for the V-2 project. Gentzen was arrested during the Prague uprising on 5 May 1945 and detained in a Soviet prison camp, where he died of starvation on 4 August 1945. He is probably buried in an unmarked grave at the Ďáblice Cemetery in Prague. 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. Gentzen proved the consistency of the Peano axioms in 1936. In his *Habilitationsschrift*, finished in 1939, he determined the proof-theoretical strength of Peano arithmetic and published a proof of Gödel's incompleteness theorem. This marked the beginning of ordinal proof theory.