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Ludwig Bieberbach | |
---|---|

Born | |

Died | 1 September 1982 95) | (aged

Nationality | German |

Alma mater | University of Göttingen University of Heidelberg |

Known for | Fatou–Bieberbach domain Bieberbach conjecture |

Scientific career | |

Fields | Mathematics |

Institutions | University of Berlin University of Frankfurt |

Doctoral advisor | Felix Klein |

Doctoral students | Werner Fenchel Maximilian Herzberger Heinz Hopf Kurt Schröder Wilhelm Süss Johann Friedrich Schultze |

**Ludwig Georg Elias Moses Bieberbach** (German: [ˈbiːbɐˌbaχ] ; 4 December 1886 – 1 September 1982) was a German mathematician and Nazi.^{ [1] }

Born in Goddelau, near Darmstadt, he studied at Heidelberg and under Felix Klein at Göttingen, receiving his doctorate in 1910.^{ [2] } His dissertation was titled *On the theory of automorphic functions* (German : *Theorie der automorphen Funktionen*). He began working as a Privatdozent at Königsberg in 1910 and as Professor ordinarius at the University of Basel in 1913. He taught at the University of Frankfurt in 1915 and the University of Berlin from 1921–45.

Bieberbach wrote a habilitation thesis in 1911 about groups of Euclidean motions – identifying conditions under which the group must have a translational subgroup whose vectors span the Euclidean space – that helped solve Hilbert's 18th problem. He worked on complex analysis and its applications to other areas in mathematics. He is known for his work on dynamics in several complex variables, where he obtained results similar to Fatou's. In 1916 he formulated the Bieberbach conjecture, stating a necessary condition for a holomorphic function to map the open unit disc injectively into the complex plane in terms of the function's Taylor series. In 1984 Louis de Branges proved the conjecture (for this reason, the Bieberbach conjecture is sometimes called de Branges' theorem). There is also a Bieberbach theorem on space groups. In 1928 Bieberbach wrote a book with Issai Schur titled *Über die Minkowskische Reduktiontheorie der positiven quadratischen Formen*.

Bieberbach was a speaker at the International Congress of Mathematicians held at Zurich in 1932.

Bieberbach joined the Sturmabteilung in 1933 and the NSDAP in 1937. He was enthusiastically involved in the efforts to dismiss his Jewish colleagues, including Edmund Landau and his former coauthor Issai Schur, from their posts. He also facilitated the Gestapo arrests of some close colleagues, such as Juliusz Schauder. Bieberbach was heavily influenced by Theodore Vahlen, another German mathematician and anti-Semite, who along with Bieberbach founded the "Deutsche Mathematik" ("German mathematics") movement and journal of the same name. The purpose of the movement was to encourage and promote a "German" (in this case meaning intuitionistic) style in mathematics. Bieberbach's and Vahlen's idea of having German mathematics was only part of a wider trend in the scientific community in Nazi Germany towards giving the sciences racial character; there were also pseudoscientific movements for "Deutsche Physik", "German chemistry", and "German biology". In 1945, Bieberbach was dismissed from all his academic positions because of his support of Nazism, but in 1949 was invited to lecture at the University of Basel by Ostrowski, who considered Bieberbach's political views irrelevant to his contributions to the field of mathematics.^{ [3] }

"… the spatial imagination is a characteristic of the Germanic races, while pure logical reasoning has a richer development among Romanic and Hebraic races. … In the intellectual sphere the race shows in the manner of creation, the evaluation of the results, and I guess also in the standpoint considering foundational questions. … Formalism wants to build a realm of mathematical truths which is independent of man, whereas Intuitionism is based on the idea that mathematical thinking is a human endeavor and thus cannot be separated from man." (in *Stilarten mathematischen Schaffens*, i.e. Styles of mathematical creation/endeavour, p. 357).

- Author profile in the database zbMATH

**Gerhard Karl Erich Gentzen** was a German mathematician and logician. He made major contributions to the foundations of mathematics, proof theory, especially on natural deduction and sequent calculus. 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.

**Louis de Branges de Bourcia** is a French-American mathematician. He is the Edward C. Elliott Distinguished Professor of Mathematics at Purdue University in West Lafayette, Indiana. He is best known for proving the long-standing Bieberbach conjecture in 1984, now called de Branges's theorem. He claims to have proved several important conjectures in mathematics, including the generalized Riemann hypothesis.

**Paul Julius Oswald Teichmüller** 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.

In complex analysis, **de Branges's theorem**, or the **Bieberbach conjecture**, is a theorem that gives a necessary condition on a holomorphic function in order for it to map the open unit disk of the complex plane injectively to the complex plane. It was posed by Ludwig Bieberbach (1916) and finally proven by Louis de Branges (1985).

**Issai Schur** was a Russian mathematician who worked in Germany for most of his life. He studied at the University of Berlin. He obtained his doctorate in 1901, became lecturer in 1903 and, after a stay at the University of Bonn, professor in 1919.

**Hugo Hadwiger** was a Swiss mathematician, known for his work in geometry, combinatorics, and cryptography.

**Wilhelm Johann Eugen Blaschke** was an Austrian mathematician working in the fields of differential and integral geometry.

**Hellmuth Kneser** was a Baltic German mathematician, who made notable contributions to group theory and topology. His most famous result may be his theorem on the existence of a prime decomposition for 3-manifolds. His proof originated the concept of normal surface, a fundamental cornerstone of the theory of 3-manifolds.

**Karl Theodor Vahlen** was an Austrian-born mathematician who was an ardent supporter of the Nazi Party. He served as the first *Gauleiter* of Pomerania and was a member of both the SA and SS.

**Isaak Moiseevich Milin**, ; * February 16, 1919, Oster, Ukrainian Soviet Socialist Republic – † November 17, 1992 Saint-Petersburg, Russian Federation) was a prominent Soviet/Russian mathematician, doctor of science in physics and mathematics, senior researcher, specialist in Geometric Theory of Functions of a Complex Variable and Applied Mathematics, engineer-lieutenant-colonel at the Soviet Air Force.

**Walter Gautschi** is a Swiss-American mathematician, known for his contributions to numerical analysis. He has authored over 200 papers in his area and published four books.

* Deutsche Mathematik* was a mathematics journal founded in 1936 by Ludwig Bieberbach and Theodor Vahlen. Vahlen was publisher on behalf of the German Research Foundation (DFG), and Bieberbach was chief editor. Other editors were Fritz Kubach, Erich Schönhardt, Werner Weber, Ernst August Weiß, Karl Dörge, Wilhelm Süss, Günther Schulz (de), Erhard Tornier, Georg Feigl, Gerhard Kowalewski, Maximilian Krafft, Willi Rinow, Max Zacharias, and Oswald Teichmüller. In February 1936, the journal was declared the official organ of the German Student Union (DSt) by its

**Helmut Grunsky** was a German mathematician who worked in complex analysis and geometric function theory. He introduced Grunsky's theorem and the Grunsky inequalities.

**Karl August Reinhardt** was a German mathematician whose research concerned geometry, including polygons and tessellations. He solved one of the parts of Hilbert's eighteenth problem, and is the namesake of the Reinhardt polygons.

**Willi Ludwig August Rinow** was a German mathematician who specialized in differential geometry and topology. Rinow was the son of a schoolteacher. In 1926, he attended the Humboldt University of Berlin, studying mathematics and physics under professors such as Max Planck, Ludwig Bieberbach, and Heinz Hopf. There, he received his doctorate in 1931. In 1933, he worked at the Jahrbuch über die Fortschritte der Mathematik in Berlin. In 1937, he joined the Nazi Party. During 1937—1940, he was an editor of the journal *Deutsche Mathematik*. In 1937, he became a professor in Berlin and lectured there until 1950. His lecturing was interrupted because of his work as a mathematician at the Oberspreewerk in Berlin from 1946 to 1949.

**Jacob "Jaap" Korevaar** is a Dutch mathematician. He was part of the faculty of the University of California San Diego and University of Wisconsin–Madison, as well as the University of Amsterdam.

**Julius Bogdan Borcea** was a Romanian Swedish mathematician. His scientific work included vertex operator algebra and zero distribution of polynomials and entire functions, via correlation inequalities and statistical mechanics.

**Menahem Max Schiffer** was a German-born American mathematician who worked in complex analysis, partial differential equations, and mathematical physics.

**Rudolf Paul Joachim Kochendörffer** was a German mathematician who was a Professor of mathematics in the University of Rostock specialising in algebra, Group theory and theory of finite groups and their representation. During World War II, Kochendörffer worked as a mathematical cryptanalyst in the mathematical referat of Inspectorate 7/IV, that would later become part of Referat I of Group IV of the General der Nachrichtenaufklärung, the signals intelligence agency of the Wehrmacht and was known as a cryptographic tester of the Enigma cipher machine. Kochendörffer was a Member of the Scientific Advisory Council for Mathematics at the State Secretariat for the Higher and Specialist Schools of the GDR, a staff member of Mathematical Reviews and collaborated with the Zentralblatt MATH

**Mathematics in Nazi Germany** was governed by racist Nazi policies like the Civil Service Law of 1933, which led to the dismissal of many Jewish mathematics professors and lecturers at German universities. During this time many Jewish mathematicians left Germany and took positions at American universities. Jews had faced discrimination in academic institutions before 1933, yet before the Nazi rise to power, some Jewish mathematicians like Hermann Minkowski and Edmund Landau had achieved success and even been appointed to full professorships with the support of David Hilbert at the University of Göttingen.

- ↑ O'Connor, John J.; Robertson, Edmund F., "Ludwig Bieberbach",
*MacTutor History of Mathematics archive*, University of St Andrews . - ↑ Ludwig Bieberbach at the Mathematics Genealogy Project
- ↑ Gautschi, Walter (2010), "Alexander M. Ostrowski (1893–1986): His life, work, and students" (PDF),
*math.ch/100: Swiss Mathematical Society, 1910–2010*, Zürich: European Mathematical Society Publishing House, pp. 257–278. See in particular p. 263: "This high esteem of scientific merits, regardless of political, personal, or other shortcomings of this attaining them, came across already in 1949, when he [Ostrowski] had the courage of inviting Bieberbach – then disgraced by his Nazi past and ostracized by the European intelligentsia – to spend a semester as guest of the university of Basel and conduct a seminar on geometric constructions."

- Cornwell, John (2003),
*Hitler's Scientist: Science, War and the Devil's Pact*, New York: Penguin Books, ISBN 0-14-200480-4 - Mehrtens, Herbert (1987), "Ludwig Bieberbach and "Deutsche Mathematik"", in Phillips, Esther R. (ed.),
*Studies in the history of mathematics*, MAA Stud. Math.,**26**, Washington, DC: Math. Assoc. America, pp. 195–241, ISBN 978-0-88385-128-9, MR 0913104 - Segal, Sanford L. (2003), "Chapter seven: Ludwig Bieberbach and Deutsche Mathematik",
*Mathematicians under the Nazis*, Princeton University Press, pp. 334–418, ISBN 978-0-691-00451-8, MR 1991149

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