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, structure, space, models, and change. History On ...

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 Silesia (, also , ) is a historical region of Central Europe that lies mostly within Poland, with small parts in the Czech Republic and Germany. Its area is approximately , and the population is estimated at around 8,000,000. Silesia is split ...

Germany Germany,, officially the Federal Republic of Germany, is a country in Central Europe. It is the second most populous country in Europe after Russia, and the most populous member state of the European Union. Germany is situated betwe ...

(now in

Poland Poland, officially the Republic of Poland, is a country in Central Europe. It is divided into 16 administrative provinces called voivodeships, covering an area of . Poland has a population of over 38 million and is the fifth-most populou ...

), 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, th ...

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 ...

, 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 in ...

, 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 sa ...

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 al ...

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 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 b ...

and defines important concepts like

prime field In mathematics, the characteristic of a ring , often denoted , is defined to be the smallest number of times one must use the ring's multiplicative identity (1) in a sum to get the additive identity (0). If this sum never reaches the additive ide ...

perfect field In algebra, a field ''k'' is perfect if any one of the following equivalent conditions holds: * Every irreducible polynomial over ''k'' has distinct roots. * Every irreducible polynomial over ''k'' is separable. * Every finite extension of ''k' ...

and the

transcendence degree In abstract algebra, the transcendence degree of a field extension ''L'' / ''K'' is a certain rather coarse measure of the "size" of the extension. Specifically, it is defined as the largest cardinality of an algebraically independent subset of ...

of a field extension, and also

normal Normal(s) or The Normal(s) may refer to: Film and television * ''Normal'' (2003 film), starring Jessica Lange and Tom Wilkinson * ''Normal'' (2007 film), starring Carrie-Anne Moss, Kevin Zegers, Callum Keith Rennie, and Andrew Airlie * ''Norma ...

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 In geometry, a polyhedron (plural polyhedra or polyhedrons; ) is a three-dimensional shape with flat polygonal faces, straight edges and sharp corners or vertices. A convex polyhedron is the convex hull of finitely many points, not all on ...

: Steinitz's theorem for polyhedra is that the 1-

skeletons A skeleton is the structural frame that supports the body of an animal. There are several types of skeletons, including the exoskeleton, which is the stable outer shell of an organism, the endoskeleton, which forms the support structure inside ...

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 r ...

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

Biography

Mathematical works

See also

References