Gottfried Maria Hugo Köthe (25 December 1905 – 30 April 1989) was an

Austria Austria, formally the Republic of Austria, is a landlocked country in Central Europe, lying in the Eastern Alps. It is a federation of nine Federal states of Austria, states, of which the capital Vienna is the List of largest cities in Aust ...

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 ...

working in

abstract algebra In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures, which are set (mathematics), sets with specific operation (mathematics), operations acting on their elements. Algebraic structur ...

and

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 (for example, Inner product space#Definition, inner product, Norm (mathematics ...

Scientific career

In 1923 Köthe enrolled in the

University of Graz The University of Graz (, formerly: ''Karl-Franzens-Universität Graz'') is a public university, public research university located in Graz, Austria. It is the largest and oldest university in Styria, as well as the second-largest and second-old ...

. He started studying

chemistry Chemistry is the scientific study of the properties and behavior of matter. It is a physical science within the natural sciences that studies the chemical elements that make up matter and chemical compound, compounds made of atoms, molecules a ...

, but switched to mathematics a year later after meeting the

philosopher Philosophy ('love of wisdom' in Ancient Greek) is a systematic study of general and fundamental questions concerning topics like existence, reason, knowledge, Value (ethics and social sciences), value, mind, and language. It is a rational an ...

Alfred Kastil Alfred Kastil (; 12 May 1874 – 20 July 1950) was an Austrian philosopher and Brentano scholar. Life and work Alfred Kastil was born in Graz, Austria on 12 May 1874. He attended secondary school in Brno. The son of a bank clerk, Alois Kasti ...

. 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 Zurich (; ) is the list of cities in Switzerland, largest city in Switzerland and the capital of the canton of Zurich. It is in north-central Switzerland, at the northwestern tip of Lake Zurich. , the municipality had 448,664 inhabitants. The ...

working with

Paul Finsler Paul Finsler (born 11 April 1894, in Heilbronn, Germany, died 29 April 1970 in Zurich, Switzerland) was a German and Swiss mathematician. Finsler did his undergraduate studies at the Technische Hochschule Stuttgart, and his graduate studies at ...

, Köthe received a fellowship to visit the

University of Göttingen The University of Göttingen, officially the Georg August University of Göttingen (, commonly referred to as Georgia Augusta), is a Public university, public research university in the city of Göttingen, Lower Saxony, Germany. Founded in 1734 ...

, where he attended the lectures of

Emmy Noether Amalie Emmy Noether (23 March 1882 – 14 April 1935) was a German mathematician who made many important contributions to abstract algebra. She also proved Noether's theorem, Noether's first and Noether's second theorem, second theorems, which ...

and

Bartel van der Waerden Bartel Leendert van der Waerden (; 2 February 1903 – 12 January 1996) was a Dutch mathematician and historian of mathematics. Biography Education and early career Van der Waerden learned advanced mathematics at the University of Amste ...

on the emerging subject of abstract algebra. He began working in ring theory and in 1930 published the

Köthe conjecture In mathematics, the Köthe conjecture is a problem in ring theory, open . It is formulated in various ways. Suppose that ''R'' is a ring. One way to state the conjecture is that if ''R'' has no nil ideal, other than , then it has no nil one-sided ...

stating that a sum of two left

nil ideal In mathematics, more specifically ring theory, a left, right or two-sided ideal of a ring is said to be a nil ideal if all of its elements is nilpotent, i.e for each a \in I exists natural number ''n'' for which a^n = 0. If all elements of a ring ...

s in an arbitrary

ring (The) Ring(s) may refer to: * Ring (jewellery), a round band, usually made of metal, worn as ornamental jewelry * To make a sound with a bell, and the sound made by a bell Arts, entertainment, and media Film and TV * ''The Ring'' (franchise), a ...

is a nil ideal. By a recommendation of Emmy Noether, he was appointed an assistant of

Otto Toeplitz Otto Toeplitz (1 August 1881 – 15 February 1940) was a German mathematician working in functional analysis., reprinted in Life and work Toeplitz was born to a Jewish family of mathematicians. Both his father and grandfather were ''Gymnasiu ...

Bonn University The University of Bonn, officially the Rhenish Friedrich Wilhelm University of Bonn (), is a public research university in Bonn, North Rhine-Westphalia, Germany. It was founded in its present form as the () on 18 October 1818 by Frederick Will ...

in 1929–1930. During this time he began transition to functional analysis. He continued scientific collaboration with Toeplitz for several years afterward. Köthe's

Habilitationsschrift Habilitation is the highest university degree, or the procedure by which it is achieved, in Germany, France, Italy, Poland and some other European and non-English-speaking countries. The candidate fulfills a university's set criteria of excelle ...

, ''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 The University of Münster (, until 2023 , WWU) is a public research university located in the city of Münster, North Rhine-Westphalia in Germany. With more than 43,000 students and over 120 fields of study in 15 departments, it is Germany's ...

under Heinrich Behnke. During

World War II World War II or the Second World War (1 September 1939 – 2 September 1945) was a World war, global conflict between two coalitions: the Allies of World War II, Allies and the Axis powers. World War II by country, Nearly all of the wo ...

he was involved in coding work. In 1946 he was appointed the director of the Mathematics Institute at the

University of Mainz The Johannes Gutenberg University Mainz () is a public research university in Mainz, Rhineland Palatinate, Germany. It has been named after the printer Johannes Gutenberg since 1946. it had approximately 32,000 students enrolled in around 100 a ...

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 Heidelberg University, officially the Ruprecht Karl University of Heidelberg (; ), is a public university, public research university in Heidelberg, Baden-Württemberg, Germany. Founded in 1386 on instruction of Pope Urban VI, Heidelberg is List ...

and served as a rector of the university (1960–1961). Köthe's best known work has been in the theory of

topological vector space In mathematics, a topological vector space (also called a linear topological space and commonly abbreviated TVS or t.v.s.) is one of the basic structures investigated in functional analysis. A topological vector space is a vector space that is als ...

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.

Awards and honors

* Invited Speaker of the ICM in 1928 in Bologna,Köthe, Gottfried. "Struktur der Ringe die die Durschschnittsminimalbedingung erfüllen." In ''Atti del Congresso Internazionale dei Matematici: Bologna del 3 al 10 de settembre di 1928'', vol. 2, pp. 75–78. 1929. in 1932 in Zurich, and in 1936 in Oslo * Heidelberg Academy of Sciences (1960) * Gauss medal, Brunswick Academy of Sciences (1963) *

German Academy of Sciences Leopoldina The German National Academy of Sciences Leopoldina (), in short Leopoldina, is the national academy of Germany, and is located in Halle (Saale). Founded on 1 January 1652, based on academic models in Italy, it was originally named the ''Academi ...

, Halle (1968) * Honorary degrees from

University of Montpellier The University of Montpellier () is a public university, public research university located in Montpellier, in south-east of France. Established in 1220, the University of Montpellier is one of the List of oldest universities in continuous opera ...

(1965),

(1980),

(1981) and

Saarland University Saarland University (, ) is a public research university located in Saarbrücken, the capital of the German state of Saarland. It was founded in 1948 in Homburg in co-operation with France and is organized in six faculties that cover all major ...

(1981).

Books

* * *

References

External links

*
Gottfried Köthe, 1905-1989
by Joachim Weidmann, digital edition Univ. Heidelberg
Vita
(in German) by Heinz Günther Tillmann, digital edition Univ. Heidelberg {{DEFAULTSORT:Kothe 20th-century German mathematicians Scientists from Graz 1905 births 1989 deaths Algebraists Functional analysts Topologists Austrian mathematicians Mathematicians from Austria-Hungary University of Graz alumni University of Bonn alumni Academic staff of the University of Münster Academic staff of Johannes Gutenberg University Mainz Academic staff of Heidelberg University People from Graz Members of the German National Academy of Sciences Leopoldina Presidents of the German Mathematical Society