Gerhard Gentzen

German mathematician and logician

Gerhard Gentzen

Gerhard Gentzen

Gerhard Karl Erich Gentzen (24 November 1909 – 4 August 1945) was a German mathematician and logician. He is best known for his work in the field of proof theory, particularly for the development of natural deduction and the sequent calculus.

Early Life and Education

Gerhard Gentzen was born in Greifswald, Germany. He studied mathematics and physics at the University of Göttingen, where he was influenced by the work of David Hilbert and Paul Bernays. Gentzen completed his doctoral dissertation under the supervision of Hermann Weyl in 1933.

Contributions to Logic

Gentzen's most significant contributions to logic were in the area of proof theory. He introduced the concept of natural deduction, which provides a formal system for deriving logical conclusions in a way that mirrors natural reasoning. This system was a major advancement in the formalization of logic.

In addition to natural deduction, Gentzen developed the sequent calculus, a formal system that represents logical deductions as sequences of formulas. The sequent calculus has been influential in both theoretical and applied logic, particularly in the development of automated theorem proving.

Consistency Proofs

One of Gentzen's most notable achievements was his consistency proof for Peano arithmetic. Using transfinite induction up to the ordinal __, Gentzen demonstrated the consistency of arithmetic, which was a significant result in the foundations of mathematics.

Later Life and Death

During World War II, Gentzen worked at the University of Prague. After the war, he was interned by the Soviet authorities and died in 1945 under unclear circumstances.

Related Pages

• Proof theory
• Natural deduction
• Sequent calculus
• David Hilbert
• Peano arithmetic