Ludwig Bieberbach

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Ludwig Bieberbach (1930)

Ludwig Georg Elias Moses Bieberbach (born December 4, 1886 in Goddelau near Darmstadt , † September 1, 1982 in Oberaudorf in Upper Bavaria ) was a German mathematician .


As the son of Eberhard Bieberbach, director of the insane asylum in Heppenheim / Bergstrasse , and his wife Lina Ludwig, he studied at the universities of Heidelberg and Göttingen . He completed his doctorate in 1910. In the same year he submitted his habilitation at the University of Zurich . He returned the Venia Legendi he had received in July a few months later and took up a position as a private lecturer at the University of Königsberg . In 1913 he taught as a full professor at the University of Basel , and in 1915 at the University of Frankfurt am Main . He taught at Berlin University from 1921 to 1945.

From 1924 to 1945 Bieberbach was a member of the Prussian Academy of Sciences in Berlin. From 1924 he was also a member of the German Academy of Natural Scientists ( Leopoldina ). During the Third Reich, Bieberbach was one of the most active National Socialists at Berlin University. He had been a member of the SA since 1933 and an active member of the NSDAP since 1937. As long-time dean and prorector, he held important management positions at the university. Because of his active involvement in the persecution of Jewish scientists, the history of the Berlin University calls him the "Grand Inquisitor of the University". Among the victims of his activities were Hilda Geiringer , Edmund Landau and Issai Schur , with whom he had published in 1928 on the geometry of numbers. He tried to found a " German Mathematics " and founded a magazine with this name. In his attempt to instrumentalize the German Mathematicians Association in his own way, he encountered resistance from Helmut Hasse, among others, and had to back off. His open letter to the well-known Danish mathematician Harald Bohr in the annual report of the DMV 1934, published without consultation with his colleagues, caused a scandal and he had to resign from his offices in the DMV. 1945 Bieberbach was dismissed from all offices. In 1949 Alexander Ostrowski invited him to give lectures in Basel , but was heavily criticized for this. In the 1950s he lived in Berlin-Dahlem , later in Oberaudorf.

In 1932 he gave a plenary lecture at the International Congress of Mathematicians in Zurich (operational areas of functions).

The central archive of German mathematicians' bequests at the Lower Saxony State and University Library in Göttingen keeps part of Bieberbach's estate.


Ludwig Bieberbach worked on function theory and its connections to other areas of mathematics and wrote 130 articles and textbooks on these topics. Of particular interest are his three Bieberbach theorems , which show that there is only a finite number of space groups in each dimension , with which he solved the 18th of David Hilbert's 23 mathematical problems . Furthermore, in 1916 he established the Bieberbach hypothesis that for the coefficients each simple, i.e. H. holomorphic and one-to-one ( i.e. injective ) function

the inequalities on the open unit disk in the complex number plane

for all

be valid. Bieberbach proved the case , Löwner the case in 1923 . The conjecture was only fully proven in 1984 by Louis de Branges de Bourcia .

Bieberbach's other areas of work were analysis, function theory and the theory of conformal mapping. The Bieberbach group and the Fatou-Bieberbach areas are named after him.


  • On the theory of automorphic functions. Inaugural dissertation to obtain a doctorate from the high philosophical faculty of the Georg-August-Universität Göttingen , Göttingen, 1910.
  • About a theorem of Mr. C. Jordan in the theory of finite groups of linear substitutions. Publishing house of the Royal Prussian Academy of Sciences, Berlin 1911. (= session reports of the Royal Prussian Academy of Sciences X, 1911), online  - Internet Archive
  • Introduction to conformal mapping. de Gruyter, Berlin 1915
  • Function theory. Teubner, Leipzig 1922. (= Teubner's technical guides, 14)
  • Theory of differential equations. Lectures from the entire field of ordinary and partial differential equations. 1923, Berlin (= basic teaching of mathematical sciences 6)
  • Differential and integral calculus. Volume 1 differential calculus . 1927
  • Textbook of the theory of functions. Volume 2 Modern Function Theory. Teubner, Leipzig and Berlin 1927
  • Lectures on algebra, using the third edition of the work of the same name by Dr. Gustav Bauer . 4th edition, Teubner, Berlin and Leipzig 1928.
  • Theory of differential equations. Lectures from the entire field of ordinary and partial differential equations. Third revised edition. Springer, Berlin 1930 (= The basic teachings of the mathematical sciences in individual representations with special consideration of the areas of application. Volume VI)
  • Textbook of the theory of functions. Volume I Elements of Function Theory. Leipzig 1930
  • Analytical geometry. Leipzig 1930.
  • Projective geometry. Teubner, Leipzig and Berlin 1931.
  • Differential geometry . 1932
  • On the theory of cubic constructions , topic: right-angled hooks to divide the angle into three . Published in the Journal for Pure and Applied Mathematics by K. Hensel , H. Hasse and L. Schlesinger , Volume 167 Berlin Walter de Gruyter Co. 1932
  • Introduction to higher geometry. Leipzig 1933 (= Teubner's mathematical guidelines, Volume 39)
  • Galileo and the Inquisition . Munich 1938
  • Carl Friedrich Gauss. A German scholarly life. Keil, Berlin 1938.
  • Introduction to conformal mapping. De Gruyter, Berlin 1949.
  • Theory of geometric constructions. Basel 1952 (= Mathematical Series, Volume 13)
  • Theory of ordinary differential equations presented on the basis of function theory. Berlin 1953. (= The basic teachings of the mathematical sciences in individual representations, Volume LXVI)
  • Analytical continuation. Berlin 1955 (= results of mathematics and its border areas, volume 3)
  • Introduction to the theory of differential equations in the real domain. Springer, Berlin, Göttingen, Heidelberg 1956.
  • Introduction to analytical geometry. 6th edition, Bielefeld 1962.


  • Michael Grüttner : Biographical Lexicon on National Socialist Science Policy , Synchron, Heidelberg 2004, ISBN 3-935025-68-8 , p. 24.
  • Helmut Grunsky : Ludwig Bieberbach in memory . Annual report DMV 1986 ( PDF )
  • de Branges: The mathematical legacy of Ludwig Bieberbach . Nieuw Archiv Wiskunde, Vol. 9, 1991, p. 366

Web links

Individual evidence

  1. Sven Kinas, mass dismissals and emigration, in: Michael Grüttner u. a., The Berlin University between the World Wars 1918–1945, Berlin 2012 (History of the University of Unter den Linden, Vol. 2), p. 382.
  2. ^ Volker Remmert History of the DMV in the Third Reich , Communications DMV 2004
  3. see Math. Intelligencer Vol. 7 (1985), No. 2, pp. 23-32