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 branch of science devoted to the study of molecular and crystalline structure and properties. The word ''crystallography'' is derived from the Ancient Greek word (; "clear ice, rock-crystal"), and (; "to write"). In J ...

, and for work in

topology Topology (from the Greek language, Greek words , and ) is the branch of mathematics concerned with the properties of a Mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformat ...

. 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 Karl Theodor Wilhelm 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 mathematics and trained as a school t ...

, and was influenced by

Felix Klein Felix Christian Klein (; ; 25 April 1849 – 22 June 1925) was a German mathematician and Mathematics education, mathematics educator, known for his work in group theory, complex analysis, non-Euclidean geometry, and the associations betwe ...

. The Schoenflies problem is to prove that an

(n - 1)

sphere A sphere (from Ancient Greek, Greek , ) is a surface (mathematics), surface analogous to the circle, a curve. In solid geometry, 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 (, abbreviated HU Berlin) is a public research university in the central borough of Mitte in Berlin, Germany. The university was established by Frederick William III on the initiative of Wilhelm von Humbol ...

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 (; ; or ) is a city and commune in the Haut-Rhin department and Alsace region of north-eastern France. The third-largest commune in Alsace (after Strasbourg and Mulhouse), it is the seat of the prefecture of the Haut-Rhin department ...

to teach. Schoenflies was a frequent contributor to Klein's ''Encyclopedia of Mathematical Sciences'': In 1898 he wrote on

set theory Set theory is the branch of mathematical logic that studies Set (mathematics), 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 mathema ...

, in 1902 on

kinematics In physics, kinematics studies the geometrical aspects of motion of physical objects independent of forces that set them in motion. Constrained motion such as linked machine parts are also described as kinematics. Kinematics is concerned with s ...

, 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 (''p ...

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, media theorist, and essayist. An eclectic thinker who combined elements of German idealism, Jewish mysticism, Western M ...

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 Walther Hermann Nernst (; 25 June 1864 – 18 November 1941) was a German physical chemist known for his work in thermodynamics, physical chemistry, electrochemistry, and solid-state physics. His formulation of the Nernst heat theorem helped ...

) * ''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, 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 German scientists Humboldt University of Berlin alumni Academic staff of the University of Königsberg Burials at Frankfurt Main Cemetery German topologists German geometers Presidents of the German Mathematical Society

Selected works

See also

References

External links