Arthur Moritz Schoenflies (; 17 April 1853 – 27 May 1928), sometimes written as Schönflies, was a German

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

, known for his contributions to the application of

group theory In abstract algebra, group theory studies the algebraic structures known as group (mathematics), groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as ring (mathematics), rings, field ...

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 wo ...

, and for work in

topology In mathematics, topology (from the Greek words , and ) is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing ho ...

. Schoenflies was born in

Landsberg an der Warthe Landsberg may refer to: * Landsberg (surname) * Margraviate of Landsberg, a march of the Holy Roman Empire * Palatinate-Landsberg, a state of the Holy Roman Empire Places * Landsberg (district), Bavaria, Germany * Landsberg, Saxony-Anhalt, Germ ...

(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 ...

and

Karl Weierstrass Karl Theodor Wilhelm Weierstrass (german: link=no, Weierstraß ; 31 October 1815 – 19 February 1897) was a German mathematician often cited as the "father of modern analysis". Despite leaving university without a degree, he studied mathematic ...

, 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 grou ...

. 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. ...

is to prove that an

(n - 1)

sphere A sphere () is a Geometry, geometrical object that is a solid geometry, three-dimensional analogue to a two-dimensional circle. A sphere is the Locus (mathematics), set of points that are all at the same distance from a given point in three ...

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 The Humboldt University of Berlin (german: link=no, Humboldt-Universität zu Berlin, abbreviated HU Berlin) is a public research university in the central borough of Mitte in Berlin, Germany. The university was established by Frederick Will ...

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), ...

to teach. Schoenflies was a frequent contributor to

Klein's encyclopedia Felix Klein's ''Encyclopedia of Mathematical Sciences'' is a German mathematical encyclopedia published in six volumes from 1898 to 1933. Klein and Wilhelm Franz Meyer were organizers of the encyclopedia. Its full title in English is ''Encyclopedi ...

: In 1898 he wrote on

set theory Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory, as a branch of mathematics, is mostly concer ...

, in 1902 on kinematics, and on

projective geometry In mathematics, projective geometry is the study of geometric properties that are invariant with respect to projective transformations. This means that, compared to elementary Euclidean geometry, projective geometry has a different setting, pr ...

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 Jewi ...

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 1908
Project Gutenberg ebook
*Articles: ''Mengenlehre'' (1898), ''Projektive Geometrie'' (1909), ''Kinematik'' (1902), ''Kristallographie'' (with

Theodor Liebisch Theodor Liebisch (29 April 1852, Breslau – 9 February 1922, Berlin) was a German mineralogist and crystallographer. Biography In 1874 he received his doctorate from the University of Breslau, then worked as an assistant to Gerhard vom R ...

, Otto Mügge), in Klein's encyclopedia.

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

Selected works

See also

References

External links