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Wolfgang Franz (mathematician)
Wolfgang Franz (born 4 October 1905 in Magdeburg, Germany; died 26 April 1996) was a German mathematician who specialized in topology particularly in 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 spaces. During World War II Franz led a group of five mathematicians, recruited by Wilhelm Fenner, and which included Ernst Witt, Georg Aumann, Alexander Aigner, Oswald Teichmüller 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 (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. He became Dean of the Faculty of Scien ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 Magdeburg, was buried in the city's cathedral after his death. Magdeburg's version of German town law, known as Magdeburg rights, spread throughout Central and Eastern Europe. In the Late Middle Ages, Magdeburg was one of the largest and most prosperous German cities and a notable member of the Hanseatic League. One of the most notable people from the city is Otto von Guericke, famous for his experiments with the Magdeburg hemispheres. Magdeburg has been destroyed twice in its history. The Catholic League sacked Magdeburg in 1631, resulting in the death of 25,000 non-combatants, the largest loss of the Thirty Years' War. During the World War II the Allies bombed the city in 1945 and destroying much of it. After World War II the city b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 look like our universe does to a small enough observer. This is made more precise in the definition below. Introduction Definition A topological space ''X'' is a 3-manifold if it is a second-countable Hausdorff space and if every point in ''X'' has a neighbourhood that is homeomorphic to Euclidean 3-space. Mathematical theory of 3-manifolds The topological, piecewise-linear, and smooth categories are all equivalent in three dimensions, so little distinction is made in whether we are dealing with say, topological 3-manifolds, or smooth 3-manifolds. Phenomena in three dimensions can be strikingly different from phenomena in other dimensions, and so there is a prevalence of very specialized techniques that do not generalize to dimensions gre ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Philosophy
Philosophy (from , ) is the systematized study of general and fundamental questions, such as those about existence, reason, Epistemology, knowledge, Ethics, values, Philosophy of mind, mind, and Philosophy of language, language. Such questions are often posed as problems to be studied or resolved. Some sources claim the term was coined by Pythagoras ( BCE), although this theory is disputed by some. Philosophical methodology, Philosophical methods include Socratic questioning, questioning, Socratic method, critical discussion, dialectic, rational argument, and systematic presentation. in . Historically, ''philosophy'' encompassed all bodies of knowledge and a practitioner was known as a ''philosopher''."The English word "philosophy" is first attested to , meaning "knowledge, body of knowledge." "natural philosophy," which began as a discipline in ancient India and Ancient Greece, encompasses astronomy, medicine, and physics. For example, Isaac Newton, Newton's 1687 ''Phil ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 relates to the order of nature, or, in other words, to the regular succession of events." Physics is one of the most fundamental scientific disciplines, with its main goal being to understand how the universe behaves. "Physics is one of the most fundamental of the sciences. Scientists of all disciplines use the ideas of physics, including chemists who study the structure of molecules, paleontologists who try to reconstruct how dinosaurs walked, and climatologists who study how human activities affect the atmosphere and oceans. Physics is also the foundation of all engineering and technology. No engineer could design a flat-screen TV, an interplanetary spacecraft, or even a better mousetrap without first understanding the basic laws of physics ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting poin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Emeritus
''Emeritus'' (; female: ''emerita'') is an adjective used to designate a retired chair, professor, pastor, bishop, pope, director, president, prime minister, rabbi, emperor, or other person who has been "permitted to retain as an honorary title the rank of the last office held". In some cases, the term is conferred automatically upon all persons who retire at a given rank, but in others, it remains a mark of distinguished service awarded selectively on retirement. It is also used when a person of distinction in a profession retires or hands over the position, enabling their former rank to be retained in their title, e.g., "professor emeritus". The term ''emeritus'' does not necessarily signify that a person has relinquished all the duties of their former position, and they may continue to exercise some of them. In the description of deceased professors emeritus listed at U.S. universities, the title ''emeritus'' is replaced by indicating the years of their appointmentsThe Protoc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 Mathematical Union (IMU). It was founded in 1890 in Bremen with the set theorist Georg Cantor as first president. Founding members included Georg Cantor, Felix Klein, Walther von Dyck, David Hilbert, Hermann Minkowski, Carl Runge, Rudolf Sturm, Hermann Schubert, and Heinrich Weber. The current president of the DMV is Ilka Agricola (2021–2022). Activities In honour of its founding president, Georg Cantor, the society awards the Cantor Medal. The DMV publishes two scientific journals, the ''Jahresbericht der DMV'' and ''Documenta Mathematica''. It also publishes a quarterly magazine for its membership the ''Mitteilungen der DMV''. The annual meeting of the DMV is called the ''Jahrestagung''; the DMV traditionally meets every four ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 Wehrmacht'' or ''Chiffrierabteilung of the OKW'' or ''OKW/Chi'' or ''Chi'') was the Signal Intelligence Agency of the Supreme Command of the Armed Forces of the German Armed Forces before and during World War II. OKW/Chi, within the formal order of battle hierarchy OKW/WFsT/Ag WNV/Chi, dealt with the cryptanalysis and deciphering of enemy and neutral states' message traffic and security control of its own key processes and machinery, such as the rotor cipher machine ENIGMA machine. It was the successor to the former Chi bureau (german: Chiffrierstelle) of the Reichswehr Ministry. Short name The letter "Chi" for the ''Chiffrierabteilung'' ("cipher department") is, contrary to what one might expect, not the Greek letter Chi , nor anythin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 surfaces. Teichmüller spaces are named after him. He was a supporter of the Nazi regime. Born in Nordhausen, Teichmüller attended the University of Göttingen, where he graduated in 1935 under the supervision of Helmut Hasse. His doctoral dissertation was on operator theory, though this was his only work on functional analysis. His next few papers were algebraic, but he switched his focus to complex analysis after attending lectures given by Rolf Nevanlinna. In 1937, he moved to the University of Berlin to work with Ludwig Bieberbach. Bieberbach was the editor of ''Deutsche Mathematik'' and much of Teichmüller's work was published in the journal, which made his papers hard to find in modern libraries before the release of his collected works ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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, which was recruited by the military cryptanalyst Wilhelm Fenner, and which included Ernst Witt, Georg Aumann, Oswald Teichmueller and Johann Friedrich Schultze, to form the backbone of the new mathematical research department in the late 1930s, which would eventually be called Section IVc of Cipher Department of the High Command of the Wehrmacht. (abbr. OKW/Chi).TICOM reports DF-187 A-G and DF-176, ‘European Axis Signal Intelligence in World War II’ vol 2 The group was led by the German professor of mathematics Wolfgang Franz. Life Alexander Aigner was the son of noted medical doctor Oktavia Aigner-Rollett and anatomist Walter Aigner (1878–1950). He is the grandson of noted physiologist and histologist of Alexander Rollett. He st ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Georg Aumann
Georg Aumann (11 November 1906, Munich, Germany – 4 August 1980), was a German mathematician. He was known for his work in general topology and regulated functions. During World War II, he worked as part of a group of five mathematicians, recruited by Wilhelm Fenner, and which included Ernst Witt, Alexander Aigner, Oswald Teichmueller and Johann Friedrich Schultze, and led by Wolfgang Franz, to form the backbone of the new mathematical research department in the late 1930s, which would eventually be called: Section IVc of Cipher Department of the High Command of the Wehrmacht (abbr. OKW/Chi). He also worked as a cryptanalyst, on the initial breaking of the most difficult cyphers. He also researched and developed cryptography theory. Life Born in Munich, George Aumann initially considered a career as a civil servant. From 1925, Aumann studied mathematics and physics at the Ludwig-Maximilian-University of Munich, among others with Professor Constantin Carathéodory and Pro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 family to China to work as missionaries, and he did not return to Europe until he was nine. After his schooling, Witt went to the University of Freiburg and the University of Göttingen. He joined the NSDAP (Nazi Party) and was an active party member. Witt was awarded a Ph.D. at the University of Göttingen in 1934 with a thesis titled: "Riemann-Roch theorem and zeta-Function in hypercomplexes" (Riemann-Rochscher Satz und Zeta-Funktion im Hyperkomplexen) that was supervised by Gustav Herglotz with Emmy Noether suggesting the top for the doctorate. He qualified to become a lecturer and gave guest lectures in Göttingen and Hamburg. He became associated with the team led by Helmut Hasse who led his habilitation. In June 1936 gave his h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
