Arthur Moritz Schönflies
Encyclopedia
Arthur Moritz Schoenflies (April 17, 1853 – May 27, 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). He studied under Kummer
and Weierstrass, and was influenced by Felix Klein
.
The Schoenflies problem is to prove that an (n − 1)-sphere
in Euclidean n-space bounds a topological ball, however embedded. This question is much more subtle than initially appears.
He studied at the University of Berlin from 1870-1875. He obtained a doctorate in 1877, and in 1878 he was a teacher at a school in Berlin. In 1880, he went to Colmar 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
.
Germany
Germany , officially the Federal Republic of Germany , is a federal parliamentary republic in Europe. The country consists of 16 states while the capital and largest city is Berlin. Germany covers an area of 357,021 km2 and has a largely temperate seasonal climate...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
, known for his contributions to the application of group theory
Group theory
In mathematics and 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 groups endowed with additional operations and...
to crystallography
Crystallography
Crystallography is the experimental science of the arrangement of atoms in solids. The word "crystallography" derives from the Greek words crystallon = cold drop / frozen drop, with its meaning extending to all solids with some degree of transparency, and grapho = write.Before the development of...
, and for work in topology
Topology
Topology is a major area of mathematics concerned with properties that are preserved under continuous deformations of objects, such as deformations that involve stretching, but no tearing or gluing...
.
Schoenflies was born in Landsberg an der Warthe (modern Gorzów
Gorzów
Gorzów may refer to the following places in Poland:*Gorzów Wielkopolski, a city in Lubusz Voivodeship *Gorzów Śląski, a town in Opole Voivodeship *Gorzów, Lesser Poland Voivodeship...
, Poland). He studied under Kummer
Kummer
Kummer may refer to: , German doctor , German , German painter , German fluetist, composer , Austrian female TV presenter , German actor, playwright , Austrian singer...
and Weierstrass, and was influenced by Felix Klein
Felix Klein
Christian Felix Klein was a German mathematician, known for his work in group theory, function theory, non-Euclidean geometry, and on the connections between geometry and group theory...
.
The Schoenflies problem is to prove that an (n − 1)-sphere
Sphere
A sphere is a perfectly round geometrical object in three-dimensional space, such as the shape of a round ball. Like a circle in two dimensions, a perfect sphere is completely symmetrical around its center, with all points on the surface lying the same distance r from the center point...
in Euclidean n-space bounds a topological ball, however embedded. This question is much more subtle than initially appears.
He studied at the University of Berlin from 1870-1875. He obtained a doctorate in 1877, and in 1878 he was a teacher at a school in Berlin. In 1880, he went to Colmar to teach.
Schoenflies was a frequent contributor to Klein's encyclopedia
Klein's encyclopedia
In mathematics, Klein’s encyclopedia refers to a German mathematical encyclopedia published in six volumes from 1898 to 1933. Felix Klein and Wilhelm Meyer were organizers of the encyclopedia. Its title in English is "Encyclopedia of mathematical sciences including their applications", which is...
: In 1898 he wrote on set theory
Set theory
Set theory is the branch of mathematics that studies sets, which are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics...
, in 1902 on kinematics
Kinematics
Kinematics is the branch of classical mechanics that describes the motion of bodies and systems without consideration of the forces that cause the motion....
, and on projective geometry
Projective geometry
In mathematics, projective geometry is the study of geometric properties that are invariant under projective transformations. This means that, compared to elementary geometry, projective geometry has a different setting, projective space, and a selective set of basic geometric concepts...
in 1910.
He was a great-uncle of Walter Benjamin
Walter Benjamin
Walter Bendix Schönflies Benjamin was a German-Jewish intellectual, who functioned variously as a literary critic, philosopher, sociologist, translator, radio broadcaster and essayist...
.
See also
- Fyodorov–Schoenflies–Bieberbach theorem
- Jordan–Schoenflies theorem
- Schoenflies notationSchoenflies notationThe Schoenflies notation or Schönflies notation, named after the German mathematician Arthur Moritz Schoenflies, is one of two conventions commonly used to describe Point groups. This notation is used in spectroscopy. The other convention is the Hermann–Mauguin notation, also known as the...
- Schoenflies displacement