Arthur Moritz Schoenflies (German: [ˈʃøːnfliːs]; 17 April 1853 – 27 May 1928), sometimes written as Schönflies, was a German mathematician, known for his contributions to the application of group theory to crystallography, and for work in topology.
Arthur Moritz Schoenflies | |
|---|---|
 | |
| Born | 17 April 1853 |
| Died | 27 May 1928 (aged 75) |
| Resting place | Frankfurt Main Cemetery |
| Alma mater | University of Berlin |
| Known for | Jordan–Schoenflies theorem Schoenflies notation Schoenflies displacement |
| Spouse | Emma Levin (1868–1939) |
| Children | Hanna (1897–1985), Albert (1898–1944), Elizabeth (1900–1991), Eva (1901–1944), Lotte (1905–1981) |
| Scientific career | |
| Fields | Group theory, crystallography, and topology |
| Thesis | Synthetisch-geometrische Untersuchungen über Flächen zweiten Grades und eine aus ihnen abgeleitete Regelfläche (1877) |
| Doctoral advisors | Ernst Kummer Karl Weierstrass |
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 and Karl Weierstrass,[1] and was influenced by Felix Klein.
The Schoenflies problem 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 from 1870 to 1875. He obtained a doctorate in 1877,[1] and in 1878 he was a teacher at a school in Berlin. In 1880, he went to Colmar to teach.
Schoenflies was a frequent contributor to Klein's Encyclopedia of Mathematical Sciences: 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.
Selected works
edit- Geometrie der Bewegung in synthetischer Darstellung. Teubner, 1886; translated by Charles Speckel as La Géométrie du Mouvement. Exposé synthétique. Gauthier-Villars 1893[2]
- 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, Otto Mügge), in Klein's encyclopedia.
See also
editReferences
edit- ^ a b Arthur Moritz Schoenflies at the Mathematics Genealogy Project
- ^ Morley, Frank. "Review of Geometrie der Bewegung in synthetischer Darstellung by Arthur Schoenflies; translated as La Géométrie du Mouvement. Exposé synthétique by Charles Speckel" (PDF). Bull. Amer. Math. Soc. 5 (10): 476–480. doi:10.1090/S0002-9904-1899-00637-2.