Hermann Amandus Schwarz

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Karl Hermann Amandus Schwarz
“Schwarzscher Stiefel” - an infinite surface with finite content. The jacket of the cylindrical body is divided into ever smaller triangles.

Hermann Amandus Schwarz (born January 25, 1843 in Hermsdorf , Silesia , † November 30, 1921 in Berlin ) was a German mathematician .

Life

Schwarz was the son of the builder Wilhelm Schwarz and Auguste Lohde. He first studied chemistry in Berlin at the Königliches Gewerbeinstitut in Charlottenburg and then switched to studying mathematics at the University of Berlin under the influence of his academic teachers there, Ernst Eduard Kummer and Karl Weierstrass . In 1864 he received his doctorate in mathematics at Kummer (dissertation: De superficiebus in planum explicabilibus primorum septem ordinum). After completing his doctorate, he taught at grammar schools in Berlin. In 1866 he completed his habilitation in Berlin and became a private lecturer. Between 1867 and 1869 he was an associate professor in Halle , then from 1869 a full professor at the ETH Zurich . From 1875 he was a full professor at the University of Göttingen and finally from 1892 a full professor at the then Berlin Friedrich Wilhelms University . In the same year he was elected a full member of the Prussian Academy of Sciences . In 1885 he was elected a member of the Leopoldina , and in 1895 he was accepted as a corresponding member in the Académie des Sciences in Paris and in 1897 in the Russian Academy of Sciences in St. Petersburg . From 1912 he was a corresponding member of the Bavarian Academy of Sciences .

Schwarz was particularly concerned with function theory and the theory of minimal surfaces . Special mention should be made of his work on Riemann's mapping theorem ( Schwarz-Christoffel transformation ), on solving the first boundary value problem for the circle, and his work on the hypergeometric differential equation . Are named after him the Cauchy-Schwarz inequality , the Schwarz Lemma , the lemma of black-and-pick , the Schwarz reflection principle , the Schwarzian derivative and the set of black . Schwarz also developed the alternating method von Schwarz named after him , an iterative domain decomposition method for solving elliptic partial differential equations such as the Laplace equation, which he introduced in search of a replacement for the Dirichlet principle used by Bernhard Riemann to justify his function theory .

He also became known through an example (Schwarzscher Stiefel) which showed the problem of the naive transfer of the definition of the curve length by approximation by polygonal lines (rectification) to two and more dimensions. In his example, an area composed of polygons with an infinitely large content was inscribed in a finite cylinder in this way.

Georg Cantor had been a close friend since his student days in Berlin , and Schwarz also spoke out in favor of Cantor as his successor at ETH Zurich. Later the friendship broke up and Schwarz became an opponent of Cantor, for which he teamed up with Leopold Kronecker , whom he was critical of while studying in Berlin like Cantor.

Among others, Carl Schilling and Paul Koebe did their doctorates with him , other students were Leopold Fejér , Leon Lichtenstein , Gerhard Hessenberg , Chaim Müntz , Robert Remak , Theodor Vahlen and Ernst Zermelo .

In 1868 he married Marie Elisabeth Kummer (1842–1921), the daughter of his doctoral father Kummer, and had six children with her. She was also the daughter of Ottilie Mendelssohn, the daughter of Nathan Mendelssohn and the granddaughter of Moses Mendelssohn . The mathematician Roland Sprague was his grandson.

In 1902 he received an honorary doctorate in Oslo and in 1914 at the ETH Zurich.

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literature

Web links

Individual evidence

  1. ↑ Hermann Amandus Schwarz in the Mathematics Genealogy Project (English)Template: MathGenealogyProject / Maintenance / id used
  2. ^ Members of the previous academies. Hermann Amandus Schwarz. Berlin-Brandenburg Academy of Sciences , accessed on June 15, 2015 .
  3. ^ List of members since 1666: Letter S. Académie des sciences, accessed on February 28, 2020 (French).
  4. ^ Foreign members of the Russian Academy of Sciences since 1724: Schwarz, Karl Hermann Amandus. Russian Academy of Sciences, accessed February 28, 2020 (Russian).
  5. ↑ Schwarz, About a border crossing through alternating procedures, quarterly journal Naturf. Ges. Zurich, Volume 50, 1870, 272–286
  6. ↑ Ilgauds, Purkner Georg Cantor , Teubner 1985, p. 50, they quote from a letter from Cantor to Mittag-Leffler from 1884 in which he complained that Kronecker and Schwarz would intrigue against him
  7. ↑ Hermann Amandus Schwarz in the Mathematics Genealogy Project (English)Template: MathGenealogyProject / Maintenance / name used
  8. ↑ Iris Grötschel, Hermann Amandus Schwarz, Berlin Mathematical Society 2014
personal data
SURNAME Schwarz, Hermann Amandus
BRIEF DESCRIPTION German mathematician
DATE OF BIRTH January 25, 1843
PLACE OF BIRTH Hermsdorf , Silesia
DATE OF DEATH November 30, 1921
Place of death Berlin