Gerhard Gentzen

from Wikipedia, the free encyclopedia
Gerhard Gentzen

Gerhard Karl Erich Gentzen (born November 24, 1909 in Greifswald , † August 4, 1945 in Prague ) was a German mathematician and logician .

Life

Gerhard Gentzen studied in Greifswald, Göttingen, Munich and Berlin and received his doctorate in 1933 at the University of Göttingen . In Greifswald he studied with Hellmuth Kneser and in Berlin probably with Johann von Neumann . He was a student of Paul Bernays , after Bernays was banned from teaching in April 1933, Hermann Weyl officially became his doctoral supervisor. In 1935 he received an assistant position at the retired David Hilbert .

Gentzen was deployed as a radio operator in Braunschweig during the war from 1939 to 1941, but fell ill and was then released from military service. In 1940 he completed his habilitation in Göttingen. In 1943, Hans Rohrbach appointed Gentzen to a lectureship at the German university in Prague . In addition to teaching and researching the consistency of mathematics, Gentzen headed a group of high school students in Prague who carried out calculations. Despite warnings, Gentzen did not flee to Germany at the end of the war. He died on August 4, 1945 in the county jail on Karlsplatz in Prague from malnutrition - three months after his arrest.

Mathematical Achievements

Gentzen is an important co-founder of modern mathematical proof theory . The lasting importance of the methods, rules and structures he developed is particularly evident today in important sub-areas of computer science , the verification of programs . Formal proofs themselves are interpreted as programs.

Gentzen was one of the leading figures in international mathematical basic research and presented the state of basic research in 1936 and 1938. The second work was published by Heinrich Scholz in the National Socialist journal Deutsche Mathematik .

Based on the Hilbert program proved Gentzen for the development of mathematics, the consistency of number theory . He developed as one of the first systems of natural reasoning and sequence calculi (also Gentz ​​type calculus in general ), for which he proved the so-called “ main theorem ”. This means that large parts of logic and mathematics can be proven to be free of contradictions.

Quotes

“ It can also be expressed in such a way that no one-for-all sufficient system of inferences can be given for number theory, but rather that propositions can be found again and again, the proofs of which require novel inferences. "

- Gerhard Gentzen, in: Deutsche Mathematik 1938, p. 260

“ The title“ brilliant ”is right here. Anyone who looks at the work that the Hilbert School produced in those days (to put it anachronistically, a “hacker's paradise”) will experience Gentzen's method as a miracle of beauty. Outsiders think logic (and math) of boring work for mourning money very quickly, but you can take my word for it that you are dealing here with a beauty of an almost symphonic format. "

- Dirk van Dalen , NRC Handelsblad 2002

Fonts

published posthumously
Works
  • ME Szabo (Ed.): The Collected Papers of Gerhard Gentzen . North-Holland, Amsterdam 1969, ISBN 0-7204-2254-X .

literature

  • Dirk van Dalen : A logician among the Nazis - the ingenious scholar Gentzen was above all naive. NRC Handelsblad , issue of March 13-14. July 2002, Wetenschap & Onderwijs, page 33, review of the book by Menzler-Trott, German translation .
  • Marc Dressler: Gentzen's sequences. In: Frankfurter Allgemeine Sonntagszeitung from November 22, 2009, p. 64.
  • Christian Trapp: At the limits of the finite: The Hilbert program in the context of formalism and finitism . Springer Spectrum, Berlin Heidelberg 2013, Chapter 12.
  • Eckart Menzler-Trott : Gentzen's Problem. Mathematical Logic in National Socialist Germany. With an essay by Jan von Plato. Birkhäuser Verlag, Basel 2001, ISBN 3-7643-6574-9 . English translation of Logic's Lost Genius: The Life of Gerhard Gentzen (= History of Mathematics, Volume 33). American Mathematical Society 2007.
  • Jan von Plato : Saved from the Cellar: Gerhard Gentzen's Shorthand Notes on Logic and Foundations of Mathematics. Springer, Cham 2017, ISBN 978-3-319-42119-3 .
  • Peter Schroeder-Heister : Gerhard Gentzen. In: Jürgen Mittelstraß (Hrsg.): Encyclopedia Philosophy and Philosophy of Science. Volume 3, Metzler, Stuttgart and Weimar 2008, ISBN 978-3-476-02102-1 .
  • Kurt Schütte :  Gentzen, Gerhard. In: New German Biography (NDB). Volume 6, Duncker & Humblot, Berlin 1964, ISBN 3-428-00187-7 , p. 194 f. ( Digitized version ).
  • Premysl Vihan: The Last Months of Gerhard Gentzen in Prague. In: Collegium Logicum 1 (1995), pp. 1-7.

Web links

swell

  1. ^ Probably for ballistic studies on the so-called retribution weapon 2 for Werner Osenberg . At least that was the official reason, see Eckart Menzler-Trott: Gentzens Problem.
  2. ^ Pinl: Colleagues in a dark time. In: Annual report DMV. 1976, Pinl himself warned him
  3. ↑ Officially of circulatory failure. According to reports from fellow prisoner Franz Krammer, there was a protein barrier and the health-impaired Gentzen starved to death. In addition, he was unable to work (for which extra rations were available) after a woman smashed two fingers with a stone while the inmates were in Prague for forced labor during the day, as usual. See Sanford L. Segal: Mathematicians under the Nazis. Princeton University Press 2003, p. 470.
  4. ^ In addition to Hermann Weyl , Adolf Fraenkel , Kurt Gödel , Alan Turing , Jacques Herbrand , John von Neumann , Alonzo Church , Albert Thoralf Skolem of the Lemberg-Warsaw School and others.
  5. ↑ Walter Tydecks, Modern History of Mathematics in Germany , this article was reviewed in the same journal in English by the American logician Haskell Brooks Curry .
  6. ↑ Walter Tydecks, modern history of mathematics in Germany
personal data
SURNAME Gentzen, Gerhard
ALTERNATIVE NAMES Gentzen, Gerhard Karl Erich (full name)
BRIEF DESCRIPTION German mathematician
DATE OF BIRTH November 24, 1909
PLACE OF BIRTH Greifswald
DATE OF DEATH August 4, 1945
Place of death Prague