Helmut V. Koch (5 October 1932 – 12 November 2024) was a German mathematician who specialised in

number theory Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example ...

Life and career

Koch was born in

Potsdam Potsdam () is the capital and largest city of the Germany, German States of Germany, state of Brandenburg. It is part of the Berlin/Brandenburg Metropolitan Region. Potsdam sits on the Havel, River Havel, a tributary of the Elbe, downstream of B ...

on 5 October 1932. Koch studied from 1952 to 1957 at the

Humboldt-Universität zu Berlin The Humboldt University of Berlin (, abbreviated HU Berlin) is a public research university in the central borough of Mitte in Berlin, Germany. The university was established by Frederick William III on the initiative of Wilhelm von Humboldt, ...

. From 1957 to 1959, he worked in the semiconductor plant at

Teltow Teltow () is a town in the Potsdam-Mittelmark district, in Brandenburg, Germany. Geography Teltow is part of the agglomeration of Berlin. The distance to the Berlin city centre is , while the distance to Potsdam is . The Teltow Canal links th ...

. From 1959, he was a member of the Institute for Mathematics of the

Akademie der Wissenschaften der DDR The German Academy of Sciences at Berlin, , in 1972 renamed the Academy of Sciences of the GDR (''Akademie der Wissenschaften der DDR (AdW)''), was the most eminent research institution of East Germany (German Democratic Republic, GDR). The acad ...

, where he received in 1964 his

promotion Promotion may refer to: Marketing * Promotion (marketing), one of the four marketing mix elements, comprising any type of marketing communication used to inform or persuade target audiences of the relative merits of a product, service, brand or i ...

(Ph.D.) and in 1965 his

habilitation 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 ...

. He studied under Hans Reichardt and

Igor Shafarevich Igor Rostislavovich Shafarevich (; 3 June 1923 – 19 February 2017) was a Soviet and Russian mathematician who contributed to algebraic number theory and algebraic geometry. Outside mathematics, he wrote books and articles that criticised social ...

(1960–61 in

Moscow Moscow is the Capital city, capital and List of cities and towns in Russia by population, largest city of Russia, standing on the Moskva (river), Moskva River in Central Russia. It has a population estimated at over 13 million residents with ...

). The famous "Number Theory" textbook by Shafarevich and Borevich was translated by Koch from Russian into German. Koch was from 1969 to 1991 the head of the research group at the Institute for Mathematics and from 1992 to 1996, the head of a working group at the Humboldt University, where he became a full professor in 1992. He was on research sabbaticals in Moscow,

Saint Petersburg Saint Petersburg, formerly known as Petrograd and later Leningrad, is the List of cities and towns in Russia by population, second-largest city in Russia after Moscow. It is situated on the Neva, River Neva, at the head of the Gulf of Finland ...

, and

Novosibirsk Novosibirsk is the largest city and administrative centre of Novosibirsk Oblast and the Siberian Federal District in Russia. As of the 2021 Russian census, 2021 census, it had a population of 1,633,595, making it the most populous city in Siber ...

and at the

University of Paris The University of Paris (), known Metonymy, metonymically as the Sorbonne (), was the leading university in Paris, France, from 1150 to 1970, except for 1793–1806 during the French Revolution. Emerging around 1150 as a corporation associated wit ...

University of Montreal A university () is an institution of tertiary education and research which awards academic degrees in several academic disciplines. ''University'' is derived from the Latin phrase , which roughly means "community of teachers and scholars". Univ ...

University of Alberta The University of Alberta (also known as U of A or UAlberta, ) is a public research university located in Edmonton, Alberta, Canada. It was founded in 1908 by Alexander Cameron Rutherford, the first premier of Alberta, and Henry Marshall Tory, t ...

University of Cambridge The University of Cambridge is a Public university, public collegiate university, collegiate research university in Cambridge, England. Founded in 1209, the University of Cambridge is the List of oldest universities in continuous operation, wo ...

ETH Zürich ETH Zurich (; ) is a public university in Zurich, Switzerland. Founded in 1854 with the stated mission to educate engineers and scientists, the university focuses primarily on science, technology, engineering, and mathematics. ETH Zurich ra ...

, the Stefan Banach International Mathematical Center in

Warsaw Warsaw, officially the Capital City of Warsaw, is the capital and List of cities and towns in Poland, largest city of Poland. The metropolis stands on the Vistula, River Vistula in east-central Poland. Its population is officially estimated at ...

, and the

Max-Planck-Institut für Mathematik The Max Planck Institute for Mathematics (, MPIM) is a research institute located in Bonn, Germany. It is named in honor of the German physicist Max Planck and forms part of the Max Planck Society (''Max-Planck-Gesellschaft''), an association of ...

Bonn Bonn () is a federal city in the German state of North Rhine-Westphalia, located on the banks of the Rhine. With a population exceeding 300,000, it lies about south-southeast of Cologne, in the southernmost part of the Rhine-Ruhr region. This ...

. Koch's research dealt with, among other topics, the

Galois theory In mathematics, Galois theory, originally introduced by Évariste Galois, provides a connection between field (mathematics), field theory and group theory. This connection, the fundamental theorem of Galois theory, allows reducing certain problems ...

algebraic number field In mathematics, an algebraic number field (or simply number field) is an extension field K of the field of rational numbers such that the field extension K / \mathbb has finite degree (and hence is an algebraic field extension). Thus K is a ...

s, p-extensions of number fields, cubic number fields, and class field theory. He was a member of the Akademie der Wissenschaften der DDR. He was a full member of the

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 ...

, the

Academia Europaea The Academia Europaea is a pan-European Academy of humanities, letters, law, and sciences. The Academia was founded in 1988 as a functioning Europe-wide Academy that encompasses all fields of scholarly inquiry. It acts as co-ordinator of Europe ...

, and the Berlin-Brandenburgische Akademie der Wissenschaften. He was a corresponding member of the

Heidelberger Akademie der Wissenschaften The Heidelberg Academy of Sciences and Humanities (German: ''Heidelberger Akademie der Wissenschaften''), established in 1909 in Heidelberg, Germany, is an assembly of scholars and scientists in the German state of Baden-Wuerttemberg. The acade ...

. In 1986 he was an Invited Speaker at the

ICM ICM may refer to: Organizations * Irish Church Missions, an Anglican mission * Institut du Cerveau, the Paris Brain Institute, a research center * Interdisciplinary Centre for Mathematical and Computational Modelling, University of Warsaw * Interna ...

in 1986 in

Berkeley, California Berkeley ( ) is a city on the eastern shore of San Francisco Bay in northern Alameda County, California, United States. It is named after the 18th-century Anglo-Irish bishop and philosopher George Berkeley. It borders the cities of Oakland, Cali ...

. In 1993 he became a member of the editorial staff of the ''

Mathematische Nachrichten ''Mathematische Nachrichten'' (abbreviated ''Math. Nachr.''; English: ''Mathematical News'') is a mathematical journal published in 12 issues per year by Wiley-VCH GmbH. It should not be confused with the ''Internationale Mathematische Nachrichten ...

''. Koch died on 12 November 2024, at the age of 92.

Selected publications

* with Herbert Pieper: ''Zahlentheorie – ausgewählte Methoden und Ergebnisse.'' Deutscher Verlag der Wissenschaften, Berlin 1976 (Einführung) * ''Zahlentheorie – algebraische Zahlen und Funktionen.'' Vieweg 1997 * ''Algebraic Number Theory.'' 2nd edition, Springer 1997 (in Encyclopedia of mathematical sciences, eds. Parshin, Shafarevich) * ''Einführung in die Mathematik – Hintergründe der Schulmathematik.'' Springer, 2nd edition 2004, * ''Einführung in die klassische Mathematik, vol. 1 Vom quadratischen Reziprozitätsgesetz zum Uniformisierungssatz.'' Springer 1986, English: Introduction to classical mathematics – from the quadratic reciprocity law to the uniformization theorem, Kluwer 1991 * ''Galois theory of p-extensions.'' Springer 2002 (older edition: Die Galoissche Theorie der p-Erweiterungen, Deutscher Verlag der Wissenschaften 1970) * ''Über Galoissche Gruppen von p-adischen Zahlkörpern'', Akademie Verlag 1964

Sources

* Gottwald, Ilgauds, Schlote: ''Biographien bedeutender Mathematiker'', Leipzig 1990 *

References

External links

* {{DEFAULTSORT:Koch, Helmut 1932 births 2024 deaths 20th-century German mathematicians 21st-century German mathematicians Members of Academia Europaea Members of the German National Academy of Sciences Leopoldina Humboldt University of Berlin alumni Members of the German Academy of Sciences at Berlin Scientists from Potsdam