Ernst Steinitz (13 June 1871 – 29 September 1928) 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 ...
.
Biography
Steinitz was born in
Laurahütte (
Siemianowice Śląskie),
Silesia
Silesia (see names #Etymology, below) is a historical region of Central Europe that lies mostly within Poland, with small parts in the Czech Silesia, Czech Republic and Germany. Its area is approximately , and the population is estimated at 8, ...
,
Germany
Germany, officially the Federal Republic of Germany, is a country in Central Europe. It lies between the Baltic Sea and the North Sea to the north and the Alps to the south. Its sixteen States of Germany, constituent states have a total popu ...
(now in
Poland
Poland, officially the Republic of Poland, is a country in Central Europe. It extends from the Baltic Sea in the north to the Sudetes and Carpathian Mountains in the south, bordered by Lithuania and Russia to the northeast, Belarus and Ukrai ...
), 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 and the
University of Berlin, receiving his Ph.D. from Breslau in 1894. Subsequently, he took positions at
Charlottenburg
Charlottenburg () is a Boroughs and localities of Berlin, locality of Berlin within the borough of Charlottenburg-Wilmersdorf. Established as a German town law, town in 1705 and named after Sophia Charlotte of Hanover, Queen consort of Kingdom ...
(now
Technische Universität Berlin), Breslau, and the
University of Kiel, 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 configurations; it contained the result that any abstract description of an
incidence structure 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: Algebraic Theory of Fields, ''
Crelle's Journal''). In this paper he axiomatically studies the properties of
fields and defines important concepts like
prime field,
perfect field and the
transcendence degree of a
field extension
In mathematics, particularly in algebra, a field extension is a pair of fields K \subseteq L, such that the operations of ''K'' are those of ''L'' restricted to ''K''. In this case, ''L'' is an extension field of ''K'' and ''K'' is a subfield of ...
, 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 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 polyhedron, convex polyhedra: they are exactly the vertex connect ...
for polyhedra is that the 1-
skeletons of convex polyhedra are exactly the 3-
connected planar graph
In graph theory, a planar graph is a graph (discrete mathematics), graph that can be graph embedding, embedded in the plane (geometry), plane, i.e., it can be drawn on the plane in such a way that its edges intersect only at their endpoints. ...
s. 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.
See also
*
Hall algebra
*
Hauptvermutung
*
Medial graph
*
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
Academic staff of Technische Universität Berlin
Academic staff of the University of Kiel
Technische Universität Berlin alumni