Gerhard Karl Erich Gentzen (November 24, 1909, Greifswald, Germany – August 4, 1945, Prague, Czechoslovakia) was a German mathematician and logician. Events 380 - Theodosius I makes his adventus, or formal Year 1909 ( MCMIX) was a Common year starting on Friday (link will display full calendar of the Gregorian calendar (or a Common year starting Greifswald (ˈɡʁaɪ̯fsvalt from German: popular etymology Greif, "griffin" proper etymology akin to "grip a plot not yet cleared and taken Germany, officially the Federal Republic of Germany ( ˈbʊndəsʁepuˌbliːk ˈdɔʏtʃlant is a Country in Central Europe. Events 70 - The Destruction of the Second Temple in Jerusalem by the Romans. Year 1945 ( MCMXLV) was a Common year starting on Monday (link will display the full calendar Prague (ˈprɑːg Praha (ˈpraɦa see also other names) is the Capital and Largest city of the Czech Republic. Czechoslovakia may also refer to what is now the Czech Republic and Slovakia. Germany, officially the Federal Republic of Germany ( ˈbʊndəsʁepuˌbliːk ˈdɔʏtʃlant is a Country in Central Europe. A mathematician is a person whose primary area of study and research is the field of Mathematics. Logic is the study of the principles of valid demonstration and Inference.
He was one of Hermann Weyl's students at the University of Göttingen from 1929 to 1933. Hermann Klaus Hugo Weyl ( 9 November 1885 – 8 December 1955) was a German Mathematician. The University of Göttingen ( German: Georg-August-Universität Göttingen) is a University in the city of Göttingen, Germany. Year 1929 ( MCMXXIX) was a Common year starting on Tuesday (link will display the full calendar of the Gregorian calendar. Year 1933 ( MCMXXXIII) was a Common year starting on Sunday (link will display full calendar of the Gregorian calendar. Gentzen's main work was on the foundations of mathematics, in proof theory, specifically natural deduction and the sequent calculus. Mathematics is the body of Knowledge and Academic discipline that studies such concepts as Quantity, Structure, Space and Proof theory is a branch of Mathematical logic that represents proofs as formal Mathematical objects facilitating their analysis by mathematical techniques In Philosophical logic, natural deduction is an approach to Proof theory that attempts to provide a Deductive system which is a formal model of logical In Proof theory and Mathematical logic, the sequent calculus is a widely known Proof calculus for First-order logic (and Propositional logic 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 aphorism that "meaning is use", constitute the starting point for inferential role semantics. The cut-elimination theorem is the central result establishing the significance of the Sequent calculus. Proof-theoretic semantics is an approach to the semantics of logic that attempts to locate the meaning of propositions and Logical connectives not in terms of Inferential role semantics (also conceptual role semantics functional role semantics procedural semantics is an approach to the theory of meaning heavily influenced by Ludwig Wittgenstein He proved the consistency of the Peano axioms in 1936. Gentzen's theorem In 1936 Gerhard Gentzen proved the consistency of First-order arithmetic using combinatorial methods In Mathematical logic, the Peano axioms, also known as the Dedekind-Peano axioms or the Peano postulates, are a set of Axioms for the Natural
Gentzen was a member of the NSDAP and the SA. The, officially National Socialist German Workers' Party, ( abbreviated NSDAP) was a Political party in Germany between 1919 and 1945 The, abbreviated SA, ( German for "Assault detachment" or "Assault section" usually translated as " stormtroop(ers Between 1934 and 1943 he was assistant of David Hilbert in Göttingen. David Hilbert ( January 23, 1862 &ndash February 14, 1943) was a German Mathematician, recognized as one of the most Since 1943 he was a professor at the University of Prague. [1] After war he starved to death in Prague, after being arrested like all other Germans in Prague on May 7, 1945. Prague (ˈprɑːg Praha (ˈpraɦa see also other names) is the Capital and Largest city of the Czech Republic. [1]
Contents |
Work
- Die Widerspruchsfreiheit der reinen Zahlentheorie. In Mathematische Annalen 112 (1936): 493-565
See also
Notes
- ^ Menzler-Trott, p. Gentzen's theorem In 1936 Gerhard Gentzen proved the consistency of First-order arithmetic using combinatorial methods The cut-elimination theorem is the central result establishing the significance of the Sequent calculus. 273 ff.
References
- Eckart Menzler-Trott: Gentzens Problem: Mathematische Logik im nationalsozialistischen Deutschland. Birkhäuser Verlag 2001, ISBN 3-7643-6574-9
- Edward Griffor and Craig Smorynski (trans. ): Logic's Lost Genius: The Life of Gerhard Gentzen (History of Mathematics, vol. 33). American Mathematical Society 2007, ISBN 978-0821835500 (an English translation)
- M. E. Szabo: Collected Papers of Gerhard Gentzen. North-Holland 1969
External links
- O'Connor, John J. & Robertson, Edmund F. , “Gerhard Gentzen”, MacTutor History of Mathematics archive
- Gerhard Gentzen at the Mathematics Genealogy Project
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