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Arthur Moritz Schoenflies (; 17 April 1853 – 27 May 1928), sometimes written as Schönflies, was a German mathematician, known for his contributions to the application of
Project Gutenberg ebook
*Articles: ''Mengenlehre'' (1898), ''Projektive Geometrie'' (1909), ''Kinematik'' (1902), ''Kristallographie'' (with Theodor Liebisch, Otto Mügge), in Klein's encyclopedia.
Arthur Moritz Schoenflies (; 17 April 1853 – 27 May 1928), sometimes written as Schönflies, was a German mathematician, known for his contributions to the application of group theory
In abstract algebra, group theory studies the algebraic structures known as groups.
The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces, can all be seen as ...
to crystallography
Crystallography is the experimental science of determining the arrangement of atoms in crystalline solids. Crystallography is a fundamental subject in the fields of materials science and solid-state physics (condensed matter physics). The wor ...
, and for work in topology.
Schoenflies was born in Landsberg an der Warthe (modern Gorzów, Poland). Arthur Schoenflies married Emma Levin (1868–1939) in 1896. He studied under Ernst Kummer
Ernst Eduard Kummer (29 January 1810 – 14 May 1893) was a German mathematician. Skilled in applied mathematics, Kummer trained German army officers in ballistics; afterwards, he taught for 10 years in a '' gymnasium'', the German equivalent of h ...
and Karl Weierstrass, and was influenced by Felix Klein
Christian Felix Klein (; 25 April 1849 – 22 June 1925) was a German mathematician and mathematics educator, known for his work with group theory, complex analysis, non-Euclidean geometry, and on the associations between geometry and group ...
.
The Schoenflies problem
In mathematics, the Schoenflies problem or Schoenflies theorem, of geometric topology is a sharpening of the Jordan curve theorem by Arthur Schoenflies. For Jordan curves in the plane it is often referred to as the Jordan–Schoenflies theorem.
O ...
is to prove that an - sphere in Euclidean ''n''-space bounds a topological ball, however embedded. This question is much more subtle than it initially appears.
He studied at the University of Berlin
Humboldt-Universität zu Berlin (german: Humboldt-Universität zu Berlin, abbreviated HU Berlin) is a German public research university in the central borough of Mitte in Berlin. It was established by Frederick William III on the initiative o ...
from 1870 to 1875. He obtained a doctorate in 1877, and in 1878 he was a teacher at a school in Berlin. In 1880, he went to Colmar
Colmar (, ; Alsatian: ' ; German during 1871–1918 and 1940–1945: ') is a city and commune in the Haut-Rhin department and Grand Est region of north-eastern France. The third-largest commune in Alsace (after Strasbourg and Mulhouse), it i ...
to teach.
Schoenflies was a frequent contributor to Klein's encyclopedia: In 1898 he wrote on set theory, in 1902 on kinematics, and on projective geometry in 1910.
He was a great-uncle of Walter Benjamin
Walter Bendix Schönflies Benjamin (; ; 15 July 1892 – 26 September 1940) was a German Jewish philosopher, cultural critic and essayist.
An eclectic thinker, combining elements of German idealism, Romanticism, Western Marxism, and Jewish my ...
.
Selected works
* ''Geometrie der Bewegung in synthetischer Darstellung.'' Teubner, 1886; translated by Charles Speckel as ''La Géométrie du Mouvement. Exposé synthétique.'' Gauthier-Villars 1893 * ''Einführung in die mathematische Behandlung der Naturwissenschaft.'' 1st edition, Dr. E. Wolff, 1895; 2nd editions 1931 (with Walther Nernst) * ''Entwicklung der Mengenlehre und ihrer Anwendungen.'' Teubner, 1913 (with Hans Hahn). *''Kristallsysteme und Kristallstruktur'', Teubner 1891 * ''Theorie der Kristallstruktur. Ein Lehrbuch.'' Gebr. Borntraeger, 1923. *''Einführung in die Hauptgesetze der zeichnerischen Darstellungsmethoden'', Teubner 1908Project Gutenberg ebook
*Articles: ''Mengenlehre'' (1898), ''Projektive Geometrie'' (1909), ''Kinematik'' (1902), ''Kristallographie'' (with Theodor Liebisch, Otto Mügge), in Klein's encyclopedia.
See also
* Fyodorov–Schoenflies–Bieberbach theorem *Jordan–Schoenflies theorem
In mathematics, the Schoenflies problem or Schoenflies theorem, of geometric topology is a sharpening of the Jordan curve theorem by Arthur Schoenflies. For Jordan curves in the plane it is often referred to as the Jordan–Schoenflies theorem.
O ...
* Schoenflies notation
*Schoenflies displacement Schoenflies (or Schönflies) displacement (or motion) named after Arthur Moritz Schoenflies is a rigid body motion consisting of linear motion in three dimensional space plus one orientation around an axis with fixed direction. In robotic manipulat ...
* Heine–Borel theorem
References
External links
* * * {{DEFAULTSORT:Schoenflies, Arthur Moritz 1853 births 1928 deaths People from Gorzów Wielkopolski People from the Province of Brandenburg 19th-century German mathematicians 20th-century German mathematicians Jewish scientists Humboldt University of Berlin alumni University of Königsberg faculty Burials at Frankfurt Main Cemetery Topologists Geometers