Gerhard Gentzen

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Gerhard Gentzen_table_infobox_0

Gerhard GentzenGerhard Gentzen_header_cell_0_0_0
BornGerhard Gentzen_header_cell_0_1_0 (1909-11-24)November 24, 1909

Greifswald, GermanyGerhard Gentzen_cell_0_1_1

DiedGerhard Gentzen_header_cell_0_2_0 August 4, 1945(1945-08-04) (aged 35)

Prague, CzechoslovakiaGerhard Gentzen_cell_0_2_1

Cause of deathGerhard Gentzen_header_cell_0_3_0 StarvationGerhard Gentzen_cell_0_3_1
NationalityGerhard Gentzen_header_cell_0_4_0 GermanGerhard Gentzen_cell_0_4_1
Alma materGerhard Gentzen_header_cell_0_5_0 University of GöttingenGerhard Gentzen_cell_0_5_1
FieldsGerhard Gentzen_header_cell_0_6_0 MathematicsGerhard Gentzen_cell_0_6_1
Doctoral advisorGerhard Gentzen_header_cell_0_7_0 Paul BernaysGerhard Gentzen_cell_0_7_1

Gerhard Karl Erich Gentzen (November 24, 1909 – August 4, 1945) was a German mathematician and logician. Gerhard Gentzen_sentence_0

He made major contributions to the foundations of mathematics, proof theory, especially on natural deduction and sequent calculus. Gerhard Gentzen_sentence_1

He died of starvation in a Soviet prison camp in Prague in 1945, having been interned as a German national after the Second World War. Gerhard Gentzen_sentence_2

Life and career Gerhard Gentzen_section_0

Gentzen was a student of Paul Bernays at the University of Göttingen. Gerhard Gentzen_sentence_3

Bernays was fired as "non-Aryan" in April 1933 and therefore Hermann Weyl formally acted as his supervisor. Gerhard Gentzen_sentence_4

Gentzen joined the Sturmabteilung in November 1933 although he was by no means compelled to do so. Gerhard Gentzen_sentence_5

Nevertheless he kept in contact with Bernays until the beginning of the Second World War. Gerhard Gentzen_sentence_6

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." Gerhard Gentzen_sentence_7

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. Gerhard Gentzen_sentence_8

Between November 1935 and 1939 he was an assistant of David Hilbert in Göttingen. Gerhard Gentzen_sentence_9

Gentzen joined the Nazi Party in 1937. Gerhard Gentzen_sentence_10

In April 1939 Gentzen swore the oath of loyalty to Adolf Hitler as part of his academic appointment. Gerhard Gentzen_sentence_11

From 1943 he was a teacher at the german Charles-Ferdinand University of Prague. Gerhard Gentzen_sentence_12

Under a contract from the SS Gentzen evidently worked for the V-2 project. Gerhard Gentzen_sentence_13

Gentzen was arrested during the citizens uprising against the occupying German forces on May 5, 1945. Gerhard Gentzen_sentence_14

He, along with the rest of the staff of the German University in Prague was subsequently handed over to Soviet forces. Gerhard Gentzen_sentence_15

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. Gerhard Gentzen_sentence_16

Work Gerhard Gentzen_section_1

Gentzen's main work was on the foundations of mathematics, in proof theory, specifically natural deduction and the sequent calculus. Gerhard Gentzen_sentence_17

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. Gerhard Gentzen_sentence_18

One of Gentzen's papers had a second publication in the ideological Deutsche Mathematik that was founded by Ludwig Bieberbach who promoted "Aryan" mathematics. Gerhard Gentzen_sentence_19

Gentzen proved the consistency of the Peano axioms in a paper published in 1936. Gerhard Gentzen_sentence_20

In his Habilitationsschrift, finished in 1939, he determined the proof-theoretical strength of Peano arithmetic. Gerhard Gentzen_sentence_21

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. Gerhard Gentzen_sentence_22

The principle can, however, be expressed in arithmetic, so that a direct proof of Gödel's incompleteness theorem followed. Gerhard Gentzen_sentence_23

Gödel used a coding procedure to construct an unprovable formula of arithmetic. Gerhard Gentzen_sentence_24

Gentzen's proof was published in 1943 and marked the beginning of ordinal proof theory. Gerhard Gentzen_sentence_25

Publications Gerhard Gentzen_section_2

Gerhard Gentzen_unordered_list_0

  • . Mathematische Annalen. 107 (2): 329–350. 1932. doi:.Gerhard Gentzen_item_0_0
  • . Mathematische Zeitschrift. 39 (2): 176–210. 1935. doi:.Gerhard Gentzen_item_0_1
  • . Mathematische Zeitschrift. 39 (3): 405–431. 1935. doi:.Gerhard Gentzen_item_0_2
  • Gentzen, Gerhard (1936). . Mathematische Zeitschrift. 41: 357–366. doi:.Gerhard Gentzen_item_0_3
  • Gentzen, Gerhard (1936). . Mathematische Annalen. 112: 493–565. doi:.Gerhard Gentzen_item_0_4
  • "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)Gerhard Gentzen_item_0_5
  • "Unendlichkeitsbegriff und Widerspruchsfreiheit der Mathematik". Actualités scientifiques et industrielles. 535: 201–205. 1937.Gerhard Gentzen_item_0_6
  • "Die gegenwärtige Lage in der mathematischen Grundlagenforschung". Deutsche Mathematik. 3: 255–268. 1938.Gerhard Gentzen_item_0_7
  • "Neue Fassung des Widerspruchsfreiheitsbeweises für die reine Zahlentheorie". Forschungen zur Logik und zur Grundlegung der exakten Wissenschaften. 4: 19–44. 1938.Gerhard Gentzen_item_0_8
  • Gentzen, Gerhard (1943). . Mathematische Annalen. 119: 140–161. doi:.Gerhard Gentzen_item_0_9

Posthumous Gerhard Gentzen_section_3

Gerhard Gentzen_unordered_list_1

  • . Archiv für mathematische Logik und Grundlagenforschung. 2 (1): 81–93. 1954.Gerhard Gentzen_item_1_10
  • Gentzen, Gerhard (1974). . Archiv für mathematische Logik und Grundlagenforschung. 16 (3–4): 97–118. doi:. – Published by Paul Bernays.Gerhard Gentzen_item_1_11
  • Gentzen, Gerhard (1974). . Archiv für mathematische Logik und Grundlagenforschung. 16 (3–4): 119–132. doi:. – Published by Paul Bernays.Gerhard Gentzen_item_1_12

See also Gerhard Gentzen_section_4

Gerhard Gentzen_unordered_list_2

Credits to the contents of this page go to the authors of the corresponding Wikipedia page: Gentzen.