To install click the Add extension button. That's it.

The source code for the WIKI 2 extension is being checked by specialists of the Mozilla Foundation, Google, and Apple. You could also do it yourself at any point in time.

Kelly Slayton
Congratulations on this excellent venture… what a great idea!
Alexander Grigorievskiy
I use WIKI 2 every day and almost forgot how the original Wikipedia looks like.
What we do. Every page goes through several hundred of perfecting techniques; in live mode. Quite the same Wikipedia. Just better.

Gerhard Gentzen

From Wikipedia, the free encyclopedia

Gerhard Gentzen
Gerhard Gentzen.jpg
Gerhard Gentzen in Prague, 1945.
Born(1909-11-24)24 November 1909
Died4 August 1945(1945-08-04) (aged 35)
Cause of deathStarvation
Alma materUniversity of Göttingen
Scientific career
Doctoral advisorPaul Bernays

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, proof theory, especially on natural deduction and sequent calculus. He died of starvation in a Czech prison camp in Prague in 1945, having been interned as a German national after the Second World War.

YouTube Encyclopedic

  • 1/5
    1 337
  • FA'18 06: Truth & Proof - Logical Foundations of Cyber-Physical Systems
  • Focusing Gentzen's LK proof system
  • Lecture 10: Classical Logic and Continuations
  • 11: Differential Equations & Proofs - Logical Foundations of Cyber-Physical Systems
  • Mathematical Logic, part 1: a brief history


Life and career

Gentzen was a student of Paul Bernays at the University of Göttingen. Bernays was fired as "non-Aryan" in April 1933 and therefore Hermann Weyl formally acted as his supervisor. Gentzen joined the Sturmabteilung in November 1933, although he was by no means compelled to do so.[1] Nevertheless, he kept in contact with Bernays until the beginning of the Second World War. In 1935, he corresponded with Abraham Fraenkel in Jerusalem and was implicated by the Nazi teachers' union as one who "keeps contacts to the Chosen People." In 1935 and 1936, Hermann Weyl, head of the Göttingen mathematics department in 1933 until his resignation under Nazi pressure, made strong 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. In April 1939 Gentzen swore the oath of loyalty to Adolf Hitler as part of his academic appointment.[2] From 1943 he was a teacher at the German Charles-Ferdinand University of Prague.[3] Under a contract from the SS, Gentzen worked for the V-2 project.[4]

Gentzen was arrested during the citizens uprising against the occupying German forces on 5 May 1945. He, along with the rest of the staff of the German University in Prague were detained in a prison camp, where he died of starvation on 4 August 1945.[5][6]


Gentzen's 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 Ludwig Wittgenstein's later work, constitute the starting point for inferential role semantics.

One of Gentzen's papers had a second publication in the ideological Deutsche Mathematik that was founded by Ludwig Bieberbach who promoted "Aryan" mathematics.[7]

Gentzen proved the consistency of the Peano axioms in a paper published in 1936. In his Habilitationsschrift, finished in 1939, he determined the proof-theoretical strength of Peano arithmetic. This was done by a direct proof of the unprovability of the principle of transfinite induction, used in his 1936 proof of consistency, within Peano arithmetic. The principle can, however, be expressed in arithmetic, so that a direct proof of Gödel's incompleteness theorem followed. Gödel used a coding procedure to construct an unprovable formula of arithmetic. Gentzen's proof was published in 1943 and marked the beginning of ordinal proof theory.



See also



External links

This page was last edited on 27 April 2023, at 00:50
Basis of this page is in Wikipedia. Text is available under the CC BY-SA 3.0 Unported License. Non-text media are available under their specified licenses. Wikipedia® is a registered trademark of the Wikimedia Foundation, Inc. WIKI 2 is an independent company and has no affiliation with Wikimedia Foundation.