Robert Fricke

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Karl Emanuel Robert Fricke (born September 24, 1861 in Helmstedt ; † July 18, 1930 in Bad Harzburg ) was a German mathematician who worked closely with Felix Klein on functional theory.

Live and act

Fricke grew up in Braunschweig as the second of four children of a civil servant and graduated from high school there in 1880 at the Martino-Katharineum . He then studied physics, mathematics and philosophy at the Universities of Göttingen , Zurich (summer 1881), Berlin , Strasbourg and, from the winter semester of 1883, with Felix Klein in Leipzig. In 1885 he passed his teaching degree there and received his doctorate in the same year with the thesis on systems of elliptical module functions of low number of levels . After completing his doctorate, he first worked as a grammar school teacher at two Braunschweig grammar schools and then, on leave of absence from regular school work, as a private teacher for the sons of Prince Albrecht of Prussia , who was then regent of Braunschweig . That left him time for mathematical research, and he reunited closely with Felix Klein, who had become a professor in nearby Göttingen in 1886. From 1887 both began to work together on a two-volume monograph on elliptical module functions, which appeared in 1890 and 1892. In 1891 he completed his habilitation at the University of Kiel (with the first volume of the elliptical module functions), in September 1892 he became a private lecturer in Göttingen. On April 1, 1894, he was appointed professor of higher mathematics at the Carolo-Wilhelmina Technical University in Braunschweig . From 1904 to 1906 and from 1921 to 1923 he was rector of the TU Braunschweig. His successor in Braunschweig after his death in 1930 was Kurt Friedrichs .

In Braunschweig, Fricke was responsible for the mathematical training of engineering students, a task that he took very seriously, as shown by a debate in the 1890s about the relevance of higher mathematics (analysis) in the beginners' training of engineers, which some professors are doing completely wanted to. Fricke took the opposite point of view and, together with Fritz Süchting, translated a textbook by the Englishman John Perry (1850–1920) Calculus for engineers into German.

His friendly cooperation with Felix Klein also continued until Klein's death in 1925 (Fricke married a niece of Felix Klein, Eleonora Flender, in 1894). Together they followed up the monograph on module functions with one on automorphic functions, this time Fricke having the main authorship. The first part appeared in 1897, the last not until 1912. Fricke also incorporated the ideas of Henri Poincaré , Klein's great competitor in the field of automorphic functions (who at that time had already turned to other areas), a (Poincaré series), partly using the work of the early deceased student Ernst Ritter (1867–1895). One of the reasons for the delay in the last volume was the progress made in the theory of uniformity in the 1910s, particularly with regard to more stringent topological foundations. Fricke also authored the sections on automorphic and elliptic functions in the Encyclopedia of Mathematical Sciences , published in 1913.

Fricke was also interested in group theory, primarily due to his study of automorphic functions - according to Jeremy Gray , the roots of the Galois theory of function bodies lie in these investigations by Klein and Fricke . The monographs on elliptical modular functions and automorphic functions are the continuation of Felix Klein's lectures on the icosahedron (published in 1884), in which he combines ideas from geometric, functional theory and group theory. The monograph on modular functions by Fricke and Klein also contains brief explanations on Galois theory, which Fricke returned to in his 1924 algebra textbook (based on Heinrich Weber's algebra). The high reputation that Fricke enjoyed among contemporary mathematicians is shown, among other things, in an exchange of letters with William Burnside , the English pioneer of group theory, in which the Burnside problem can be found for the first time in writing .

Together with Øystein Ore and Emmy Noether, he published the collected works of Richard Dedekind , his predecessor in Braunschweig, and also planned a biography of Dedekind, but it remained unfinished upon his death, which also did not allow him to experience the publication of Dedekind's works . With H. Vermeil, Erich Bessel-Hagen and Alexander Ostrowski , he published the collected works of his teacher Felix Klein from 1921 to 1923 .

In 1900 he was elected a member of the Leopoldina . In 1904 he was elected a corresponding member of the Göttingen Academy of Sciences . In 1920 he was President of the German Mathematicians Association . The Fricke space is named after him , the module space of hyperbolic metrics on a surface or the equivalent of the discrete, faithful representations of a group of surfaces in the isometric group of the hyperbolic plane.

Fonts

  • with Felix Klein: Lectures on the theory of elliptical module functions . 2 volumes, Teubner, Leipzig 1890, 1892.
  • with Felix Klein: Lectures on the theory of automorphic functions . 2 volumes, Teubner, Leipzig 1897, 1912.
  • The elliptical functions and their applications. Teubner, Volume 1 ( The functional theoretical and analytical foundations. ), Leipzig 1916, Volume 2 ( The algebraic versions. ) Leipzig 1922, Johnson Reprint 1972. Reprint Springer Verlag, Berlin 2011, Volume 1, ISBN 3-642-19556-3 , Volume 2, ISBN 3-642-19560-1 .
  • Clemens Adelmann, Jürgen Elstrodt , Elena Klimenko (editor): Robert Fricke: The elliptical functions and their applications. Third part. Applications. Springer Verlag, Berlin 2012 (from the estate of Fricke).
  • Analytical geometry. Teubner, Leipzig 1915.
  • Main theorems of differential and integral calculus, as a guide for use in lectures, compiled by Dr. Robert Fricke. Vieweg, 5th edition 1909.
  • Textbook of differential and integral calculus and their applications. 2 volumes, Teubner, Leipzig 1918, 1919, 3rd edition 1921.
  • Translation by John Perry: Advanced Analysis for Engineers. Teubner, Leipzig 1910.
  • Fricke: About mathematics at university . Annual report DMV 1902
  • Fricke, Weber: "Textbook of Algebra" . Volume 1. Vieweg, Braunschweig 1924
  • Elliptic functions and automorphic functions . In: Encyclopedia of Mathem. Sciences

See also

literature

Web links

Individual evidence

  1. ↑ Biographical data in Helmuth Albrecht: "Technical education between science and practice". 1987, p. 549.
  2. ↑ In his article on this in the annual report of DMV 1902, he quotes Kelvin as saying that there is no applicable mathematics that cannot be taught to engineers.
  3. ^ Which is also expressed in the order in which the authors are named, as Felix Klein underlines in the commentary on Fricke-Klein in his collected works.
  4. ↑ He contracted typhus on the crossing to New York and died on Ellis Island .
  5. ↑ In the foreword of Volume 2 of the Automorphic Functions, Fricke explicitly mentions LEJ Brouwer with regard to the topological foundations and Paul Koebe with regard to the uniformization theory .
  6. ↑ Jeremy Gray: The Riemann-Roch Theorem and Geometry. Proc. ICM, Berlin 1998.
  7. ↑ C.Adelmann and EH A.Gerbracht: Letters from William Burnside to Robert Fricke: automorphic functions, and the emergence of the Burnside problem. Archive for History of Exact Sciences, Volume 63, 2009, pp. 33-50.
  8. ↑ Holger Krahnke: The members of the Academy of Sciences in Göttingen 1751-2001 (= Treatises of the Academy of Sciences in Göttingen, Philological-Historical Class. Volume 3, Volume 246 = Treatises of the Academy of Sciences in Göttingen, Mathematical-Physical Class. Series 3, volume 50). Vandenhoeck & Ruprecht, Göttingen 2001, ISBN 3-525-82516-1 , p. 86.
  9. ↑ a third volume was planned based on Felix Klein's comments in his collected works. It only appeared in 2012 from the estate.
personal data
SURNAME Fricke, Robert
ALTERNATIVE NAMES Fricke, Karl Emanuel Robert (full name)
BRIEF DESCRIPTION German mathematician
DATE OF BIRTH September 24, 1861
PLACE OF BIRTH Helmstedt
DATE OF DEATH July 18, 1930
Place of death Bad Harzburg