Wolfgang Franz (mathematician)

Wolfgang Franz (born October 4, 1905 in Magdeburg , † April 26, 1996 in Frankfurt ) was a German mathematician .

Life

Wolfgang Franz was the son of a senior studies director and after graduating from high school in Kiel studied mathematics , physics and philosophy at the University of Kiel (with semesters abroad in Berlin, Vienna, Halle). In 1930 he passed the teaching examination in Kiel. It was in 1930 on the Hilbert Irreduzibilitätssatz in Halle doctorate , his thesis supervisor was Helmut Hasse (having previously with a different theme at Ernst Steinitz began a dissertation, but died). Franz went to Marburg with him, where he was Hasse's assistant from 1930 to 1934 and stayed there when Hasse was offered a position in Göttingen in 1934 . At Hasse, he dealt with algebraic number theory and created a script of Hasse's lecture on class field theory. In 1934 he joined the SA to increase his career opportunities. Franz completed his habilitation in 1936 under Kurt Reidemeister in Marburg in the field of algebraic topology . In 1937 Franz moved to the University of Giessen as an assistant , where he taught as a lecturer from 1939.

In 1940 Franz wanted to move to Frankfurt as a dietician , but in the summer of 1940 he was assigned to the Wehrmacht High Command and was unable to take up the position. Nevertheless, at the request of the Faculty of Natural Sciences, he was appointed adjunct professor in 1943.

The faculty's application states:

“His work is characterized as a pattern of clarity, mastery of expression and matter; he has shown himself to be a researcher of standing and is well known in his teaching qualifications. As a teacher as well as a researcher, it gives rise to high hopes ... "

During the Second World War he worked in the encryption department of the Wehrmacht High Command . From March 1941 he therefore lived in Berlin-Zehlendorf and was released from teaching duties in Frankfurt. Franz first successfully solved Mexican and Greek codes and then the US State Department's M 138 A Strip Cipher (called Am 10 by the Germans). An electronic machine called a tower clock was used. He experienced the end of the war in Helmstedt and returned to Frankfurt in 1945. In the summer semester of 1946, he began teaching at the university, immediately after it reopened.

In 1949 he received the chair of mathematics (as successor to William Threlfall ). He was dean of the Faculty of Natural Sciences from 1950–1951 and 1963–1964 , rector from 1964 to 1965 and prorector from 1965 to 1967. From 1971 to 1973 Franz was dean of the newly founded department of mathematics. During this time, he supervised around twenty doctoral theses and numerous habilitation theses, including that of Wolfgang Haken . Franz retired in 1974, but remained active in teaching and as a liaison professor for the Studienstiftung.

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His research was on topology . He made important contributions a. on the theory of lens spaces and on the Reidemeister torsion (which is sometimes also named after Franz and Georges de Rham ). He wrote a textbook on topology. In his habilitation from Reidemeister in 1934 (About the torsion of an overlap), he classified higher-dimensional lens spaces (more than three dimensions) using the Reidemeister torsion and number-theoretic results. In the 1940s he determined the fixed point classes of images of lens spaces.

Honors, memberships, private matters

In 1967 he was President of the German Mathematicians Association .

In 1961 he became a member of the Scientific Society at the University of Frankfurt. On July 8, 2005, a celebratory colloquium was held at the Johann Wolfgang Goethe University in Frankfurt in honor of Franz's hundredth birthday.

Franz was a very good pianist.

Works

• Topology 1, General Topology , De Gruyter, Göschen Collection, 1960, 4th edition 1973
  • English edition: General Topology , New York: Ungar 1965
• Topology 2, Algebraic Topology , De Gruyter, Göschen Collection, 1965, 2nd edition 1974
  • English edition: Algebraic Topology , New York: Ungar 1968
• Coverings of topological complexes with hypercomplex systems , J. Reine Angew. Math., Volume 173, 1935, pp. 174-184, digitized
• About the torsion of a cover , J. Reine Angew. Math., Volume 173, 1935, pp. 245-254, digitized
• Torsion ideals , torsion classes and torsion , J. Reine Angew. Math., Volume 176, 1936, pp. 113-124, digitized
• About the torsion of manifolds , DMV annual report, Volume 46, 1936, p. 171, digitized
• Imaging classes and fixed point classes of three-dimensional lens spaces , J. Reine Angew. Math., Volume 185, 1943, pp. 65-77, digitized
• Euclid from the perspective of the mathematical and scientific world of the present , Frankfurter Universitätsreden, Heft 38, 1965
• Cryptology: construction and deciphering of secret scripts , meeting reports of the Scientific Society at the Johann Wolfgang Goethe University in Frankfurt am Main; Vol. 24, No. 5, 1989
• Three-dimensional and multi-dimensional geometry: the regular polytopes , meeting reports of the Scientific Society at the Johann Wolfgang Goethe University in Frankfurt am Main; Vol. 9, No. 3, 1971, pp. 67-104
• About mathematical statements that, including their negation, are demonstrably unprovable. Gödel's sentence of incompleteness , reports from the meetings of the Scientific Society at the Johann Wolfgang Goethe University in Frankfurt am Main; Vol. 14, No. 1, Franz Steiner Verlag, Wiesbaden, 1977, ISBN 3-515-02612-6 .
• Torsion and symmetrical spaces , Festschrift of the Scientific Society at the Johann Wolfgang Goethe University Frankfurt am Main, 1981, pp. 125–131

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• G. Burde and W. Schwarz: Wolfgang Franz in memory. Annual report of the German Mathematicians Association, Volume 100, Issue 4, 1998, pp. 284–292; online (pdf; 9.5 MB)

Web links

• Wolfgang Franz in the Mathematics Genealogy Project (English)
• Literature by and about Wolfgang Franz in the catalog of the German National Library
• Professor Wolfgang Franz and OKW / Chi's mathematical research department, blog by Christos Triantafyllopoulos 2014 (with link to Franz's interrogation document)

Individual evidence

1. ↑ Published in Investigations on Hilbert's Irreducibility Theorem , Math. Zeitschrift, Volume 33, 1931, pp. 275–293
2. ↑ The main result that the Reidemeister torsion fulfills a duality relation similar to the Poincaré duality was proven anew in 1961 by John Milnor , without knowing the work of Franz, Milnor, A duality theorem for Reidemeister torsion, Annals of Mathematics, Volume 76 , 1962, pp. 137-147