Person: Schottky, Friedrich Hermann
Friedrich Schottky was a German mathematician who worked on elliptic, abelian, and theta functions.
Mathematical Profile (Excerpt):
- Friedrich attended the Humanistisches Gymnasium St Magdalenen in Breslau beginning his studies there in 1860.
- After graduating from the Gymnasium, Schottky entered the University of Breslau in 1870, graduating in 1874.
- Certainly the quality of Schottky's thesis was outstanding.
- In the case of a domain bounded by p closed curves (p ≥ 2), Schottky discovered that there exist 3p - 3 real constants that characterize the conformal class to which this region belongs.
- After obtaining his doctorate, Schottky remained at the University of Berlin for a while but submitted his habilitation thesis to the University of Breslau in 1878.
- Schottky taught as a docent at Breslau until 1882 when he was appointed professor of mathematics in the Eidgenössische Technische Hochschule Zürich.
- During his four years lecturing at Breslau, Schottky published two papers: Abriss einer Theorie der Abel'schen Functionen von drei Variabeln Ⓣ(Outline of the theory of Abelian functions of three variables) (1880) and Über eindeutige Functionen mit linearen Transformationen in sich Ⓣ(On uniform functions with linear transformations into themselves) (1882).
- It was Lazarus Fuchs's chair at Berlin to which Schottky was appointed and many felt that his personal friendship with Frobenius was a factor in his appointment.
- Certainly Schottky had made highly significant mathematical contributions (which we will comment on below) but it was clear to most people that his best years as a mathematician were behind him by 1902.
- When Schottky retired from his Berlin chair it allowed Issai Schur, who had been an extraordinary professor since 1916, to become a full professor.
- Most of Schottky's work concerns elliptic, abelian and theta functions.
- Schottky's thesis also discusses conformal mappings of domains bounded by circular and conic arcs.
- Schottky's paper Über eine specielle Function, welche bei einer bestimmten linearen Transformation ihres Arguments unverändert bleibt Ⓣ(On a special function which remains unchanged at a given linear transformation of its argument) (1887), advanced the theory of Poincaré series considerably.
- The Schottky problem is the problem of finding characterizations of Jacobians among all principally polarized abelian varieties.
- Schottky's Theorem (1904) is related to Picard's Theorem and has become a classical result in the theory of functions of a complex variable.
- Schottky published 55 papers and, in 1880, a book Abriss einer Theorie der Abel'schen Functionen von drei Variablen Ⓣ(Outline of the theory of Abelian functions of three variables).
- Among Schottky's doctoral students we should mention Heinrich Jung who was his student at Marburg.
- Schottky and Jung jointly authored the important 1909 paper Neue Sätze über Symmetralfunktionen und die Abel'schen Funktionen der Riemann'schen Theorie which made a significant contribution to the Schottky problem.
- Perhaps it is worth noting that these two papers with Jung were the only two joint papers which Schottky published.
- Walter Schottky died on 4 March 1976.
- Another of Schottky's sons, Hermann Schottky (1885-1974) was a metallurgist, and Ernst Schottky (1888-1915) was a botanist who died in World War I.
- Schottky was elected a corresponding member of the Prussian Academy of Sciences (now the Berlin Academy) in 1900 and was made a full member two years later.
Born 24 July 1851, Breslau, Prussia (now Wrocław, Poland). Died 12 August 1935, Berlin, Germany.
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Adapted from other CC BY-SA 4.0 Sources:
- O’Connor, John J; Robertson, Edmund F: MacTutor History of Mathematics Archive