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*{{Citation|last=Menzler-Trott|first=Eckart|author-link=Eckart Menzler-Trott|date=2001-08-01|title=Gentzens Problem: Mathematische Logik im nationalsozialistischen Deutschland|publisher=Birkhäuser Verlag|location=Basel, Switzerland|isbn=3-7643-6574-9}} |
*{{Citation|last=Menzler-Trott|first=Eckart|author-link=Eckart Menzler-Trott|date=2001-08-01|title=Gentzens Problem: Mathematische Logik im nationalsozialistischen Deutschland|publisher=Birkhäuser Verlag|location=Basel, Switzerland|isbn=3-7643-6574-9}} |
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*{{Citation|last=Menzler-Trott|first=Eckart|author-link=Eckart Menzler-Trott|translator=Griffor, Edward|translator-link=Edward Griffor|translator2=Smorynski, Craig|translator2-link=Craig Smorynski|date=November 21, 2007|title=Logic's Lost Genius: The Life of Gerhard Gentzen|publisher=American Mathematical Society|series=History of Mathematics|volume=vol. 33|isbn=978-0-8218-3550-0|url=http://www.ams.org/bookstore-getitem/item=hmath-33}} - an English translation. |
*{{Citation|last=Menzler-Trott|first=Eckart|author-link=Eckart Menzler-Trott|translator=Griffor, Edward|translator-link=Edward Griffor|translator2=Smorynski, Craig|translator2-link=Craig Smorynski|date=November 21, 2007|title=Logic's Lost Genius: The Life of Gerhard Gentzen|publisher=American Mathematical Society|series=History of Mathematics|volume=vol. 33|isbn=978-0-8218-3550-0|url=http://www.ams.org/bookstore-getitem/item=hmath-33}} - an English translation. |
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*{{cite book|last=Wolfram|first=Stephen|authorlink=Stephen Wolfram|title=A New Kind of Science|url=https://www.wolframscience.com/nks/notes-12-9--examples-of-unprovable-statements/|publisher=Wolfram Media, Inc.|year=2002|page=1163|isbn=1-57955-008-8}} |
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==External links== |
==External links== |
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Revision as of 16:14, 8 January 2021
Gerhard Gentzen | |
|---|---|
 Gerhard Gentzen in Prague, 1945. | |
| Born | November 24, 1909 |
| Died | August 4, 1945 (aged 35) |
| Cause of death | Starvation |
| Nationality | German |
| Alma mater | University of Göttingen |
| Scientific career | |
| Fields | Mathematics |
| Doctoral advisor | Paul Bernays |
Gerhard Karl Erich Gentzen (November 24, 1909 – August 4, 1945) was a
Second World War
.
Life and career
Gentzen was a student of
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
V-2 project.[4]
Gentzen was arrested during the citizens uprising against the occupying German forces on May 5, 1945. He, along with the rest of the staff of the German University in Prague was subsequently handed over to Soviet forces. Because of his past association with the SA, NSDAP and NSD Dozentenbund, Gentzen was detained in a prison camp, where he died of starvation on August 4, 1945.[5][6]
Work
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
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
.
Publications
- "Über die Existenz unabhängiger Axiomensysteme zu unendlichen Satzsystemen". Mathematische Annalen. 107 (2): 329–350. 1932. S2CID 119534269.
- "Untersuchungen über das logische Schließen. I". Mathematische Zeitschrift. 39 (2): 176–210. 1935. S2CID 121546341.
- "Untersuchungen über das logische Schließen. II". Mathematische Zeitschrift. 39 (3): 405–431. 1935. S2CID 186239837.
- Gentzen, Gerhard (1936). "Die Widerspruchsfreiheit der Stufenlogik". Mathematische Zeitschrift. 41: 357–366. S2CID 122979277.
- Gentzen, Gerhard (1936). "Die Widerspruchsfreiheit der reinen Zahlentheorie". Mathematische Annalen. 112: 493–565. S2CID 122719892.
- "Der Unendlichkeitsbegriff in der Mathematik. Vortrag, gehalten in Münster am 27. Juni 1936 am Institut von Heinrich Scholz". Semester-Berichte Münster: 65–80. 1936–1937. (Lecture hold in Münster at the institute of Heinrich Scholz on 27 June 1936)
- "Unendlichkeitsbegriff und Widerspruchsfreiheit der Mathematik". Actualités scientifiques et industrielles. 535: 201–205. 1937.
- "Die gegenwärtige Lage in der mathematischen Grundlagenforschung". Deutsche Mathematik. 3: 255–268. 1938.[8]
- "Neue Fassung des Widerspruchsfreiheitsbeweises für die reine Zahlentheorie". Forschungen zur Logik und zur Grundlegung der Exakten Wissenschaften. 4: 19–44. 1938.[8]
- Gentzen, Gerhard (1943). "Beweisbarkeit und Unbeweisbarkeit von Anfangsfällen der transfiniten Induktion in der reinen Zahlentheorie". Mathematische Annalen. 119: 140–161. S2CID 120335524.
Posthumous
- "Zusammenfassung von mehreren vollständigen Induktionen zu einer einzigen". Archiv für mathematische Logik und Grundlagenforschung. 2 (1): 81–93. 1954.
- Gentzen, Gerhard (1974). "Der erste Widerspruchsfreiheitsbeweis für die klassische Zahlentheorie". Archiv für mathematische Logik und Grundlagenforschung. 16 (3–4): 97–118. S2CID 117444881. – Published by Paul Bernays.
- Gentzen, Gerhard (1974). "Über das Verhältnis zwischen intuitionistischer und klassischer Arithmetik". Archiv für mathematische Logik und Grundlagenforschung. 16 (3–4): 119–132. S2CID 120131107. – Published by Paul Bernays.
See also
Notes
- ^ Menzler-Trott, p. 52.
- ^ Menzler-Trott, p. 119.
- ^ Gerhard Gentzen at math.muni.cz
- ^ Menzler-Trott, p. 238.
- ^ Menzler-Trott, p. 273 ff.
- ^ http://www-history.mcs.st-and.ac.uk/Biographies/Gentzen.html
- ^ Dipl.Math. Walter Tydecks, Neuere Geschichte der Mathematik in Deutschland (in German)
- ^ .
References
- Gentzen, Gerhard (1969), ISBN 0-7204-2254-X- (English translation).
- ISBN 3-7643-6574-9
- ) - an English translation.
- ISBN 1-57955-008-8.
External links
- O'Connor, John J.; Robertson, Edmund F., "Gerhard Gentzen", MacTutor History of Mathematics Archive, University of St Andrews
- Gerhard Gentzen at the Mathematics Genealogy Project
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