Arthur Moritz Schoenflies
Born(1853-04-17)17 April 1853
Died27 May 1928(1928-05-27) (aged 75)
Resting placeFrankfurt Main Cemetery
Alma materUniversity of Berlin
Known forSchoenflies problem
Jordan–Schoenflies theorem
Schoenflies notation
Schoenflies displacement
SpouseEmma Levin (1868–1939)
ChildrenHanna (1897–1985), Albert (1898–1944), Elizabeth (1900–1991), Eva (1901–1944), Lotte (1905–1981)
Scientific career
FieldsGroup theory, crystallography, and topology
Thesis Synthetisch-geometrische Untersuchungen über Flächen zweiten Grades und eine aus ihnen abgeleitete Regelfläche  (1877)
Doctoral advisorsErnst Kummer
Karl Weierstrass
Schoenflies' grave at the Frankfurt Main Cemetery

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.

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: 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

See also


  1. ^ a b Arthur Moritz Schoenflies at the Mathematics Genealogy Project
  2. ^ 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.