Ernst Steinitz (13 June 1871 – 29 September 1928) was a German
mathematician.
Biography
Steinitz was born in
Laurahütte (
Siemianowice Śląskie
Siemianowice Śląskie also known as Siemianowice (; german: Siemianowitz-Laurahütte; szl, Siymianowice) is a city in Upper Silesia in southern Poland, near Katowice, in its central district in the Upper Silesian Metropolitan Union - a metropoli ...
),
Silesia,
Germany (now in
Poland), the son of Sigismund Steinitz, a Jewish coal merchant, and his wife Auguste Cohen; he had two brothers. He studied at the
University of Breslau
A university () is an institution of higher (or tertiary) education and research which awards academic degrees in several academic disciplines. Universities typically offer both undergraduate and postgraduate programs. In the United States, ...
and the
University of Berlin
Humboldt-Universität zu Berlin (german: Humboldt-Universität zu Berlin, abbreviated HU Berlin) is a German public research university in the central borough of Mitte in Berlin. It was established by Frederick William III on the initiative o ...
, receiving his Ph.D. from Breslau in 1894. Subsequently, he took positions at
Charlottenburg
Charlottenburg () is a locality of Berlin within the borough of Charlottenburg-Wilmersdorf. Established as a town in 1705 and named after Sophia Charlotte of Hanover, Queen consort of Prussia, it is best known for Charlottenburg Palace, the ...
(now the
Technical University of Berlin), Breslau, and the
University of Kiel
Kiel University, officially the Christian-Albrecht University of Kiel, (german: Christian-Albrechts-Universität zu Kiel, abbreviated CAU, known informally as Christiana Albertina) is a university in the city of Kiel, Germany. It was founded ...
, Germany, where he died in 1928. Steinitz married Martha Steinitz and had one son.
Mathematical works
Steinitz's 1894 thesis was on the subject of
projective configuration
In mathematics, specifically projective geometry, a configuration in the plane consists of a finite set of points, and a finite arrangement of lines, such that each point is incident to the same number of lines and each line is incident to the ...
s; it contained the result that any abstract description of an
incidence structure
In mathematics, an incidence structure is an abstract system consisting of two types of objects and a single relationship between these types of objects. Consider the points and lines of the Euclidean plane as the two types of objects and ignore a ...
of three lines per point and three points per line could be realized as a configuration of straight lines in the Euclidean plane with the possible exception of one of the lines. His thesis also contains the proof of
Kőnig's theorem for regular bipartite graphs, phrased in the language of configurations.
In 1910 Steinitz published the very influential paper ''Algebraische Theorie der Körper'' (
German
German(s) may refer to:
* Germany (of or related to)
**Germania (historical use)
* Germans, citizens of Germany, people of German ancestry, or native speakers of the German language
** For citizens of Germany, see also German nationality law
**Ge ...
: Algebraic Theory of Fields, ''
Crelle's Journal
''Crelle's Journal'', or just ''Crelle'', is the common name for a mathematics journal, the ''Journal für die reine und angewandte Mathematik'' (in English: ''Journal for Pure and Applied Mathematics'').
History
The journal was founded by Augus ...
''). In this paper he axiomatically studies the properties of
fields
Fields may refer to:
Music
*Fields (band), an indie rock band formed in 2006
*Fields (progressive rock band), a progressive rock band formed in 1971
* ''Fields'' (album), an LP by Swedish-based indie rock band Junip (2010)
* "Fields", a song by ...
and defines important concepts like
prime field,
perfect field and the
transcendence degree of a
field extension, and also
normal and
separable extensions (the latter he called ''algebraic extensions of the first kind''). Besides numerous, today standard, results in field theory, he proved that every field has an (essentially unique)
algebraic closure
In mathematics, particularly abstract algebra, an algebraic closure of a field ''K'' is an algebraic extension of ''K'' that is algebraically closed. It is one of many closures in mathematics.
Using Zorn's lemmaMcCarthy (1991) p.21Kaplansky ( ...
and a theorem, which characterizes the
existence of primitive elements of a field extension in terms of its intermediate fields. Bourbaki called this article "a basic paper which may be considered as having given rise to the current conception of Algebra".
Steinitz also made fundamental contributions to the theory of
polyhedra:
Steinitz's theorem
In polyhedral combinatorics, a branch of mathematics, Steinitz's theorem is a characterization of the undirected graphs formed by the edges and vertices of three-dimensional convex polyhedra: they are exactly the 3-vertex-connected planar gra ...
for polyhedra is that the 1-
skeletons of convex polyhedra are exactly the 3-
connected
Connected may refer to:
Film and television
* ''Connected'' (2008 film), a Hong Kong remake of the American movie ''Cellular''
* '' Connected: An Autoblogography About Love, Death & Technology'', a 2011 documentary film
* ''Connected'' (2015 TV ...
planar graphs. His work in this area was published posthumously as a 1934 book, ''Vorlesungen über die Theorie der Polyeder unter Einschluss der Elemente der Topologie'',
by
Hans Rademacher
Hans Adolph Rademacher (; 3 April 1892, Wandsbeck, now Hamburg-Wandsbek – 7 February 1969, Haverford, Pennsylvania, USA) was a German-born American mathematician, known for work in mathematical analysis and number theory.
Biography
Rademacher ...
.
See also
*
Hall algebra
*
Hauptvermutung
*
Medial graph
In the mathematical discipline of graph theory, the medial graph of plane graph ''G'' is another graph ''M(G)'' that represents the adjacencies between edges in the faces of ''G''. Medial graphs were introduced in 1922 by Ernst Steinitz to study ...
*
Steinitz class
*
Steinitz exchange lemma
*
Supernatural numbers
*
Lévy–Steinitz theorem
References
*
*
* .
* . As cited by Gropp.
{{DEFAULTSORT:Steinitz, Ernst
1871 births
1928 deaths
19th-century German mathematicians
Linear algebraists
20th-century German mathematicians
German people of Jewish descent
People from Siemianowice Śląskie
People from the Province of Silesia
University of Breslau alumni
Humboldt University of Berlin alumni
Technical University of Berlin faculty
University of Kiel faculty
Technical University of Berlin alumni