Gottfried Köthe
Encyclopedia
Gottfried Maria Hugo Köthe (born 25 December 1905 in Graz
; died 30 April 1989 in Frankfurt
) was an Austria
n mathematician
working in abstract algebra
and functional analysis
.
. He started studying chemistry, but switched to mathematics a year later after meeting the philosopher Alfred Kastil
. In 1927 he submitted his thesis Beiträge zu Finslers Grundlegung der Mengenlehre ("Contributions to Finsler's foundations of set theory") and was awarded a doctorate. After spending a year in Zürich
working with Paul Finsler
, Köthe received a fellowship to visit the University of Göttingen, where he attended the lectures of Emmy Noether
and Bartel van der Waerden on the emerging subject of abstract algebra. He began working in ring theory
and in 1930 published the Köthe conjecture stating that a sum of two left nil ideals in an arbitrary ring is a nil ideal. By a recommendation of Emmy Noether, he was appointed an assistant of Otto Toeplitz
in Bonn University in 1929–1930. During this time he began transition to functional analysis. He continued scientific collaboration with Toeplitz for several years afterward.
Köthe's Habilitationschrift, Schiefkörper unendlichen Ranges über dem Zentrum ("Skew fields of infinite rank over the center"), was accepted in 1931. He became Privatdozent at University of Münster
under Heinrich Behnke
. During World War II
he was involved in coding work. In 1946 he was appointed the director of the Mathematics Institute at the University of Mainz and he served as a dean (1948–1950) and a rector of the university (1954–1956). In 1957 he became the founding director of the Institute for Applied Mathematics at the University of Heidelberg and served as a rector of the university (1960–1961).
Köthe's best known work has been in the theory of topological vector space
s. In 1960, volume 1 of his seminal monograph Topologische lineare Räume was published (the second edition was translated into English in 1969). It was not until 1979 that volume 2 appeared, this time written in English. He also made contributions to the theory of lattices
.
Graz
The more recent population figures do not give the whole picture as only people with principal residence status are counted and people with secondary residence status are not. Most of the people with secondary residence status in Graz are students...
; died 30 April 1989 in Frankfurt
Frankfurt
Frankfurt am Main , commonly known simply as Frankfurt, is the largest city in the German state of Hesse and the fifth-largest city in Germany, with a 2010 population of 688,249. The urban area had an estimated population of 2,300,000 in 2010...
) was an Austria
Austria
Austria , officially the Republic of Austria , is a landlocked country of roughly 8.4 million people in Central Europe. It is bordered by the Czech Republic and Germany to the north, Slovakia and Hungary to the east, Slovenia and Italy to the south, and Switzerland and Liechtenstein to the...
n 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....
working in abstract algebra
Abstract algebra
Abstract algebra is the subject area of mathematics that studies algebraic structures, such as groups, rings, fields, modules, vector spaces, and algebras...
and functional analysis
Functional analysis
Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure and the linear operators acting upon these spaces and respecting these structures in a suitable sense...
.
Scientific career
In 1923 Köthe enrolled in the University of GrazUniversity of Graz
The University of Graz , a university located in Graz, Austria, is the second-largest and second-oldest university in Austria....
. He started studying chemistry, but switched to mathematics a year later after meeting the philosopher Alfred Kastil
Alfred Kastil
Alfred Kastil [ka:stil] was an Austrian-German philosopher.He taught as a professor at the Innsbruck University .- Literary works :...
. In 1927 he submitted his thesis Beiträge zu Finslers Grundlegung der Mengenlehre ("Contributions to Finsler's foundations of set theory") and was awarded a doctorate. After spending a year in Zürich
Zürich
Zurich is the largest city in Switzerland and the capital of the canton of Zurich. It is located in central Switzerland at the northwestern tip of Lake Zurich...
working with Paul Finsler
Paul Finsler
Paul Finsler was a German and Swiss mathematician.Finsler did his undergraduate studies at the Technische Hochschule Stuttgart, and his graduate studies at the University of Göttingen, where he received his Ph.D. in 1919 under the supervision of Constantin Carathéodory...
, Köthe received a fellowship to visit the University of Göttingen, where he attended the lectures of Emmy Noether
Emmy Noether
Amalie Emmy Noether was an influential German mathematician known for her groundbreaking contributions to abstract algebra and theoretical physics. Described by David Hilbert, Albert Einstein and others as the most important woman in the history of mathematics, she revolutionized the theories of...
and Bartel van der Waerden on the emerging subject of abstract algebra. He began working in ring theory
Ring theory
In abstract algebra, ring theory is the study of rings—algebraic structures in which addition and multiplication are defined and have similar properties to those familiar from the integers...
and in 1930 published the Köthe conjecture stating that a sum of two left nil ideals in an arbitrary ring is a nil ideal. By a recommendation of Emmy Noether, he was appointed an assistant of Otto Toeplitz
Otto Toeplitz
Otto Toeplitz was a German Jewish mathematician working in functional analysis.- Life and work :...
in Bonn University in 1929–1930. During this time he began transition to functional analysis. He continued scientific collaboration with Toeplitz for several years afterward.
Köthe's Habilitationschrift, Schiefkörper unendlichen Ranges über dem Zentrum ("Skew fields of infinite rank over the center"), was accepted in 1931. He became Privatdozent at University of Münster
University of Münster
The University of Münster is a public university located in the city of Münster, North Rhine-Westphalia in Germany. The WWU is part of the Deutsche Forschungsgemeinschaft, a society of Germany's leading research universities...
under Heinrich Behnke
Heinrich Behnke
Heinrich Behnke was a German mathematician and rector at the University of Münster.- Life and career :...
. During World War II
World War II
World War II, or the Second World War , was a global conflict lasting from 1939 to 1945, involving most of the world's nations—including all of the great powers—eventually forming two opposing military alliances: the Allies and the Axis...
he was involved in coding work. In 1946 he was appointed the director of the Mathematics Institute at the University of Mainz and he served as a dean (1948–1950) and a rector of the university (1954–1956). In 1957 he became the founding director of the Institute for Applied Mathematics at the University of Heidelberg and served as a rector of the university (1960–1961).
Köthe's best known work has been in the theory of topological vector space
Topological vector space
In mathematics, a topological vector space is one of the basic structures investigated in functional analysis...
s. In 1960, volume 1 of his seminal monograph Topologische lineare Räume was published (the second edition was translated into English in 1969). It was not until 1979 that volume 2 appeared, this time written in English. He also made contributions to the theory of lattices
Lattice (order)
In mathematics, a lattice is a partially ordered set in which any two elements have a unique supremum and an infimum . Lattices can also be characterized as algebraic structures satisfying certain axiomatic identities...
.
Awards and honors
- Heidelberg Academy of Sciences (1960)
- Gauss medal, Brunswick Academy of Sciences (1963)
- German Academy of Sciences Leopoldina, Halle (1968)
- Honorary degrees from University of MontpellierUniversity of MontpellierThe University of Montpellier was a French university in Montpellier in the Languedoc-Roussillon région of the south of France. Its present-day successor universities are the University of Montpellier 1, Montpellier 2 University and Paul Valéry University, Montpellier III.-History:The university...
(1965), University of MünsterUniversity of MünsterThe University of Münster is a public university located in the city of Münster, North Rhine-Westphalia in Germany. The WWU is part of the Deutsche Forschungsgemeinschaft, a society of Germany's leading research universities...
(1980), University of Mainz (1981) and Saarland UniversitySaarland UniversitySaarland University is a university located in Saarbrücken, the capital of the German state of Saarland, and Homburg. It was founded in 1948 in Homburg in co-operation with France and is organized in 8 faculties that cover all major fields of science...
(1981).
Books
- Köthe, Gottfried. Topological vector spaces. I. (Translated from German by D. J. H. Garling). Grundlehren der mathematischen Wissenschaften, 159 Springer-Verlag New York 1969
- Köthe, Gottfried. Topological vector spaces. II. Grundlehren der Mathematischen Wissenschaften, 237. Springer-Verlag, New York-Berlin, 1979. xii+331 pp. ISBN 0-387-90400-X