Wolfgang Franz (born 4 October 1905 in
Magdeburg
Magdeburg (; nds, label=Low Saxon, Meideborg ) is the capital and second-largest city of the German state Saxony-Anhalt. The city is situated at the Elbe river.
Otto I, the first Holy Roman Emperor and founder of the Archdiocese of Magdebu ...
, Germany; died 26 April 1996) was a German
mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems.
Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change.
History
On ...
who specialized in
topology
In mathematics, topology (from the Greek words , and ) is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing ...
particularly in
3-manifolds
In mathematics, a 3-manifold is a space that locally looks like Euclidean 3-dimensional space. A 3-manifold can be thought of as a possible shape of the universe. Just as a sphere looks like a plane to a small enough observer, all 3-manifolds ...
, which he generalized to higher dimensions. He is known for the
Reidemeister–Franz torsion. He also made important contributions to the theory of
lens space
A lens space is an example of a topological space, considered in mathematics. The term often refers to a specific class of 3-manifolds, but in general can be defined for higher dimensions.
In the 3-manifold case, a lens space can be visualized ...
s.
During
World War II
World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the vast majority of the world's countries—including all of the great powers—forming two opposing ...
Franz led a group of five mathematicians, recruited by
Wilhelm Fenner, and which included
Ernst Witt
Ernst Witt (26 June 1911 – 3 July 1991) was a German mathematician, one of the leading algebraists of his time.
Biography
Witt was born on the island of Alsen, then a part of the German Empire. Shortly after his birth, his parents moved the ...
,
Georg Aumann,
Alexander Aigner
Alexander Aigner (18 May 1909 – 2 September 1988) was number theorist and a full university professor for mathematics at the Karl Franzens University in Graz, Austria. During World War II he was part of a group of five mathematicians, whic ...
,
Oswald Teichmüller
Paul Julius Oswald Teichmüller (; 18 June 1913 – 11 September 1943) was a German mathematician who made contributions to complex analysis. He introduced quasiconformal mappings and differential geometric methods into the study of Riemann surf ...
and Johann Friedrich Schultze, to form the backbone of the new mathematical research department in the field of cryptology, in the late 1930s. This would eventually be known as: Section IVc of
Cipher Department of the High Command of the Wehrmacht
The Cipher Department of the High Command of the Wehrmacht (german: Amtsgruppe Wehrmachtnachrichtenverbindungen, Abteilung Chiffrierwesen) (also ''Oberkommando der Wehrmacht Chiffrierabteilung'' or ''Chiffrierabteilung of the High Command of the W ...
(abbr. OKW/Chi).
After the war, he returned to teach at the
Goethe University Frankfurt and was awarded the Chair of Mathematics in 1949. In 1967 he became the Chairman of the
German Mathematical Society
The German Mathematical Society (german: Deutsche Mathematiker-Vereinigung, DMV) is the main professional society of German mathematicians and represents German mathematics within the European Mathematical Society (EMS) and the International Math ...
. He became Dean of the Faculty of Science for several periods starting in 1950 before being promoted to
emeritus professor in 1974.
Life
Wolfgang Franz was the son of an Chief Auditor (German:Oberstudiendirektor) and studied
mathematics,
physics
Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which r ...
and
philosophy at the
University of Kiel
Kiel University, officially the Christian-Albrecht University of Kiel, (german: Christian-Albrechts-Universität zu Kiel, abbreviated CAU, known informally as Christiana Albertina) is a university in the city of Kiel, Germany. It was founded in ...
(after his high school diploma in
Kiel
Kiel () is the capital and most populous city in the northern German state of Schleswig-Holstein, with a population of 246,243 (2021).
Kiel lies approximately north of Hamburg. Due to its geographic location in the southeast of the Jutland ...
) with exams in Berlin, Vienna and Halle. In 1930 he passed the Lehramt examination in Kiel. He was promoted in 1930 to
Dr Phil
Phillip Calvin McGraw (born September 1, 1950), better known as Dr. Phil, is an American Celebrity, television personality and author best known for Television presenter, hosting the talk show ''Dr. Phil (talk show), Dr. Phil''. He holds a do ...
on
David Hilbert's Irreduzibilitätssatz problem, with a doctoral thesis titled: Investigations on Hilbert's irreducibility (German:Untersuchungen zum Hilbertschen Irreduzibilitätssatz) in Halle, his doctoral advisor was
Helmut Hasse (after he had started a dissertation with a different topic under
Ernst Steinitz
Ernst Steinitz (13 June 1871 – 29 September 1928) was a German mathematician.
Biography
Steinitz was born in Laurahütte (Siemianowice Śląskie), Silesia, Germany (now in Poland), the son of Sigismund Steinitz, a Jewish coal merchant, and ...
, but he died). Together with Hasse, Franz went to
Marburg
Marburg ( or ) is a university town in the German federal state (''Bundesland'') of Hesse, capital of the Marburg-Biedenkopf district (''Landkreis''). The town area spreads along the valley of the river Lahn and has a population of approxima ...
, where he was assistant to Hasse from 1930 to 1934, and remained there when Hasse received a call to the
University of Göttingen
The University of Göttingen, officially the Georg August University of Göttingen, (german: Georg-August-Universität Göttingen, known informally as Georgia Augusta) is a public research university in the city of Göttingen, Germany. Founded ...
in 1934. Working with Hasse, he dealt with
algebraic number theory and produced a script of Hassen's lecture on class-field theory. In 1934 he joined the
SA, the paramilitary wing of the
Nazi Party
The Nazi Party, officially the National Socialist German Workers' Party (german: Nationalsozialistische Deutsche Arbeiterpartei or NSDAP), was a far-right political party in Germany active between 1920 and 1945 that created and supported t ...
in
Nazi Germany
Nazi Germany (lit. "National Socialist State"), ' (lit. "Nazi State") for short; also ' (lit. "National Socialist Germany") (officially known as the German Reich from 1933 until 1943, and the Greater German Reich from 1943 to 1945) was ...
, to increase his career chances. In 1936, Franz
habilited in the field of
algebraic topology
Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariants that classify topological spaces up to homeomorphism, though usually most classify ...
under
Kurt Reidemeister
Kurt Werner Friedrich Reidemeister (13 October 1893 – 8 July 1971) was a mathematician born in Braunschweig (Brunswick), Germany.
Life
He was a brother of Marie Neurath.
Beginning in 1912, he studied in Freiburg, Munich, Marburg, and Götting ...
in
Marburg
Marburg ( or ) is a university town in the German federal state (''Bundesland'') of Hesse, capital of the Marburg-Biedenkopf district (''Landkreis''). The town area spreads along the valley of the river Lahn and has a population of approxima ...
. In 1937 he moved to the
University of Giessen
University of Giessen, official name Justus Liebig University Giessen (german: Justus-Liebig-Universität Gießen), is a large public research university in Giessen, Hesse, Germany. It is named after its most famous faculty member, Justus von ...
, where he taught as a lecturer from 1939 onwards.
Franz wanted to change to Frankfurt in 1940, but in the summer of 1940 he was promoted to the command post of the Wehrmacht. Nevertheless, at the request of the Faculty of Science, he was appointed an extraordinary professor in 1943.
The faculty's application states:
:''His work is characterized as a pattern of clarity, mastery in expression and matter, he has shown himself as a researcher of rank and is well known in his teaching abilities. As a teacher as well as a researcher, he is one of the best hopes ... ''
War Work
In the Second World War, he worked in the
OKW/Chi, the cipher bureau of the High Command of the
Wehrmacht
The ''Wehrmacht'' (, ) were the unified armed forces of Nazi Germany from 1935 to 1945. It consisted of the ''Heer'' (army), the '' Kriegsmarine'' (navy) and the ''Luftwaffe'' (air force). The designation "''Wehrmacht''" replaced the previo ...
. He worked in Chi IVc with duties that included scientific decoding of enemy crypts, the development of code breaking methods and working on re-cyphering systems not solved by practical decoding. He had a staff of 48. From March 1941 he lived in
Berlin-Zehlendorf
Zehlendorf () is a locality within the borough of Steglitz-Zehlendorf in Berlin. Before Berlin's 2001 administrative reform Zehlendorf was a borough in its own right, consisting of the locality of Zehlendorf as well as Wannsee, Nikolassee and ...
and was released from teaching duties in
Frankfurt
Frankfurt, officially Frankfurt am Main (; Hessian: , " Frank ford on the Main"), is the most populous city in the German state of Hesse. Its 791,000 inhabitants as of 2022 make it the fifth-most populous city in Germany. Located on it ...
. Franz first successfully solved Mexican and Greek codes and then the M-138-A Strip Cipher of the US Department of Foreign Affairs (named by the Germans as Am-10). An electronic machine called a clock tower was used.
Post-war
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
Goethe University Frankfurt, immediately after their reopening.
In 1949 he received the Chair of Mathematics (as successor to
William Threlfall
William Richard Maximilian Hugo Threlfall (25 June 1888, in Dresden – 4 April 1949, in Oberwolfach) was a British-born German mathematician who worked on algebraic topology. He was a coauthor of the standard textbook Lehrbuch der Topologie.
In ...
). He was Dean of the Faculty of Science from 1950–1951, 1963–1964, and from 1964 to 1965
rector
Rector (Latin for the member of a vessel's crew who steers) may refer to:
Style or title
*Rector (ecclesiastical), a cleric who functions as an administrative leader in some Christian denominations
*Rector (academia), a senior official in an edu ...
and from 1965 to 1967 rector. Franz was also Chairman of the
German Mathematical Society
The German Mathematical Society (german: Deutsche Mathematiker-Vereinigung, DMV) is the main professional society of German mathematicians and represents German mathematics within the European Mathematical Society (EMS) and the International Math ...
in 1967.
From 1971 to 1973, Franz was Dean of the newly founded Department of Mathematics at Frankfurt. During this time, he supervised about twenty PhD theses and numerous habilitations, including those of
Wolfgang Haken
Wolfgang Haken (June 21, 1928 – October 2, 2022) was a German American mathematician who specialized in topology, in particular 3-manifolds.
Biography
Haken was born in Berlin, Germany. His father was Werner Haken, a physicist who had Max ...
.
Franz was promoted
emeritus professor in 1974, but remained active in teaching and as a lecturer of the foundation of the studies.
Publications
* ''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
* ''Supernatants of topological complexes with hypercomplex systems'',
Journal für die reine und angewandte Mathematik
''Crelle's Journal'', or just ''Crelle'', is the common name for a mathematics journal, the ''Journal für die reine und angewandte Mathematik'' (in English: ''Journal for Pure and Applied Mathematics'').
History
The journal was founded by Augus ...
173 (1935), 174–184.
* ''On the torsion of a covering'',
Journal für die reine und angewandte Mathematik
''Crelle's Journal'', or just ''Crelle'', is the common name for a mathematics journal, the ''Journal für die reine und angewandte Mathematik'' (in English: ''Journal for Pure and Applied Mathematics'').
History
The journal was founded by Augus ...
173 (1935), 245–254.
* ''Torsion ideals, torsion classes and torsion'',
Journal für die reine und angewandte Mathematik
''Crelle's Journal'', or just ''Crelle'', is the common name for a mathematics journal, the ''Journal für die reine und angewandte Mathematik'' (in English: ''Journal for Pure and Applied Mathematics'').
History
The journal was founded by Augus ...
176 (1936), 113–124,
[The main result (Reidemeister torsion obeying a duality property similar to ]Poincaré duality
In mathematics, the Poincaré duality theorem, named after Henri Poincaré, is a basic result on the structure of the homology and cohomology groups of manifolds. It states that if ''M'' is an ''n''-dimensional oriented closed manifold (compact ...
) was re-proved by John Milnor
John Willard Milnor (born February 20, 1931) is an American mathematician known for his work in differential topology, algebraic K-theory and low-dimensional holomorphic dynamical systems. Milnor is a distinguished professor at Stony Brook Univ ...
in 1961, without knowing the work of Franz: John Milnor, ''A duality theorem for Reidemeister torsion'', Annals of Mathematics
The ''Annals of Mathematics'' is a mathematical journal published every two months by Princeton University and the Institute for Advanced Study.
History
The journal was established as ''The Analyst'' in 1874 and with Joel E. Hendricks as the ...
76 (1962), no. 1, 137–147.
* ''On the Twist of Manifolds'' , Annual Report DMV, Vol. 46, 1936, p. 171.
* ''Imaging classes and fixed-point classes of three-dimensional lens spaces'',
Journal für die reine und angewandte Mathematik
''Crelle's Journal'', or just ''Crelle'', is the common name for a mathematics journal, the ''Journal für die reine und angewandte Mathematik'' (in English: ''Journal for Pure and Applied Mathematics'').
History
The journal was founded by Augus ...
185 (1943), 65–77.
* ''Euclid from the perspective of the mathematical and natural sciences of the present'', Frankfurter Universitätsreden, vol. 38, 1965.
* ''Cryptology: Construction and deciphering of secret documents'', session reports of the scientific society at the Johann-Wolfgang-Goethe-University Frankfurt am Main; Vol. 24, No. 5, 1989.
* ''Three-dimensional and multi-dimensional geometry: the regular polytope'', meeting reports of the scientific society at the Johann-Wolfgang-Goethe-University Frankfurt am Main; 9, No. 3, 1971, pp. 67–104.
* ''On mathematical statements, which are demonstrably demonstrable together with their negation. The incompleteness rate of Gödel'', conference reports of the Scientific Society at the Johann-Wolfgang-Goethe-University Frankfurt am Main; Vol. 14, No. 1, Franz Steiner Verlag, Wiesbaden, 1977, .
* ''Torsion and Symmetrical Spaces'', Order of the Scientific Society at the Johann Wolfgang Goethe University, Frankfurt am Main, 1981, pp. 125–131.
References
{{DEFAULTSORT:Franz, Wolfgang
1905 births
1996 deaths
German cryptographers
20th-century German mathematicians
Topologists
Academic staff of Goethe University Frankfurt
University of Kiel alumni
Scientists from Magdeburg