Robert Erich Remak (14 February 1888 – 13 November 1942) was a German mathematician. He is chiefly remembered for his work in

group theory In abstract algebra, group theory studies the algebraic structures known as group (mathematics), groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as ring (mathematics), rings, field ...

( Remak decomposition). His other interests included algebraic number theory, mathematical economics and

geometry of numbers Geometry of numbers is the part of number theory which uses geometry for the study of algebraic numbers. Typically, a ring of algebraic integers is viewed as a lattice in \mathbb R^n, and the study of these lattices provides fundamental informatio ...

. Robert Remak was the son of the neurologist Ernst Julius Remak and the grandson of the embryologist

Robert Remak Robert Remak (26 July 1815 – 29 August 1865) was a Jewish Polish-German embryologist, physiologist, and neurologist, born in Poznań, Posen, Prussia, who discovered that the origin of cells was by the Cell division, division of pre-existing cel ...

Biography

Robert Remak was born in

Berlin Berlin ( , ) is the capital and List of cities in Germany by population, largest city of Germany by both area and population. Its 3.7 million inhabitants make it the European Union's List of cities in the European Union by population within ci ...

. He studied at

Humboldt 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 ...

under Ferdinand Georg Frobenius and received his doctorate in 1911. His dissertation, ''Über die Zerlegung der endlichen Gruppen in indirekte unzerlegbare Faktoren'' ("On the decomposition of a finite group into indirect indecomposable factors") established that any two decompositions of a finite group into a direct product are related by a central automorphism. A weaker form of this statement, uniqueness, was first proved by

Joseph Wedderburn Joseph Henry Maclagan Wedderburn FRSE FRS (2 February 1882 – 9 October 1948) was a Scottish mathematician, who taught at Princeton University for most of his career. A significant algebraist, he proved that a finite division algebra is a fi ...

in 1909. Later the theorem was generalized by

Wolfgang Krull Wolfgang Krull (26 August 1899 – 12 April 1971) was a German mathematician who made fundamental contributions to commutative algebra, introducing concepts that are now central to the subject. Krull was born and went to school in Baden-Baden. H ...

and

Otto Schmidt Otto Yulyevich Shmidt, be, Ота Юльевіч Шміт, Ota Juljevič Šmit (born Otto Friedrich Julius Schmidt; – 7 September 1956), better known as Otto Schmidt, was a Soviet scientist, mathematician, astronomer, geophysicist, statesm ...

to some classes of infinite groups and became known as the

Krull–Schmidt theorem In mathematics, the Krull–Schmidt theorem states that a group subjected to certain finiteness conditions on chains of subgroups, can be uniquely written as a finite direct product of indecomposable subgroups. Definitions We say that a group ''G ...

or the Krull–Remak–Schmidt theorem. Although the dissertation was first submitted in 1911, it was rejected several times and Remak did not obtain his Habilitation until 1929. In the meantime, he wrote several papers on the

. Between 1929 and 1933 Remak lectured as a Privatdozent at Humboldt University. In the 1929 essay ''Kann die Volkwirtschaftslehre eine exakte Wissenschaft werden?'' ("Can economics become an exact science?"), Remak analyzed price formation in socialist and capitalist economies. He also anticipated the role played by digital computers in

numerical solution Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods th ...

systems of linear equations In mathematics, a system of linear equations (or linear system) is a collection of one or more linear equations involving the same variables. For example, :\begin 3x+2y-z=1\\ 2x-2y+4z=-2\\ -x+\fracy-z=0 \end is a system of three equations in th ...

. Remak's analysis may have influenced

John von Neumann John von Neumann (; hu, Neumann János Lajos, ; December 28, 1903 – February 8, 1957) was a Hungarian-American mathematician, physicist, computer scientist, engineer and polymath. He was regarded as having perhaps the widest cove ...

, who was a fellow lecturer in Berlin, but most of it has not been translated into English and it remains little known and appreciated in the English-speaking world.Kurz and Salvadori, pp 40–46. In 1932 Remak published a paper giving a lower bound for the regulator of an algebraic number field in terms of the numbers ''r''₁ and ''r''₂ of real embeddings and pairs of complex embeddings. He went on to investigate relations between the regulator and the discriminant of an algebraic number field, isolating an important class of

CM-field In mathematics, a CM-field is a particular type of number field, so named for a close connection to the theory of complex multiplication. Another name used is J-field. The abbreviation "CM" was introduced by . Formal definition A number field '' ...

s ("fields with unit defect"). His last two papers on the subject appeared in '' Compositio Mathematica'' in 1952 and 1954, more than ten years after his death. Stolperstein Robert Remak, Berlin 05

After the Nazis seized power in 1933 and the

Civil Service Law The Law for the Restoration of the Professional Hitler Service (german: Gesetz zur Wiederherstellung des Berufsbeamtentums, shortened to ''Berufsbeamtengesetz''), also known as Civil Service Law, Civil Service Restoration Act, and Law to Re-es ...

was passed a few months later, Remak, who was of Jewish ancestry, lost his right to teach in September 1933. He was arrested on

Kristallnacht () or the Night of Broken Glass, also called the November pogrom(s) (german: Novemberpogrome, ), was a pogrom against Jews carried out by the Nazi Party's (SA) paramilitary and (SS) paramilitary forces along with some participation fro ...

, 9 November 1938, and was interned at

Sachsenhausen concentration camp Sachsenhausen () or Sachsenhausen-Oranienburg was a German Nazi concentration camp in Oranienburg, Germany, used from 1936 until April 1945, shortly before the defeat of Nazi Germany in May later that year. It mainly held political prisoner ...

for several weeks. After an unsuccessful campaign by his wife to secure a permission for him to emigrate to the United States, he was released and permitted to leave for

Amsterdam Amsterdam ( , , , lit. ''The Dam on the River Amstel'') is the capital and most populous city of the Netherlands, with The Hague being the seat of government. It has a population of 907,976 within the city proper, 1,558,755 in the urban ar ...

. In 1942, however, he was arrested by the German occupational authorities in the Netherlands and deported to Auschwitz, where he was murdered.

Notes

Bibliography

* Harald Hagemann: ''Robert Remak.'' In: ''Neue Deutsche Biographie.'' Band 21. Duncker & Humblot, Berlin 2003, , p. 410ff. * Heinz D.Kurz and Neri Salvadori, ''von Neumann's 'growth model' and the classical tradition.'' In ''Understanding "classical" economics: studies in long-period theory'', Routledge studies in the history of economics, 2003. * Uta C. Merzbach, ''Robert Remak and the estimation of units and regulators''. Amphora, 481–522, Birkhäuser, Basel, 1992 * Reinhard Siegmund-Schultze: ''Dokumente zur Geschichte der Mathematik. Quellen und Studien zur Emigration einer Wissenschaft.'' Band 10: ''Mathematiker auf der Flucht vor Hitler.'' Vieweg, Wiesbaden 1998,

External links

* * * Willy Tiabou, Christoph Bichlmeier
Verfolgte Mathematiker
{{DEFAULTSORT:Remak, Robert 20th-century German mathematicians Mathematical economists German people who died in Auschwitz concentration camp 1942 deaths 1888 births Scientists from Berlin German civilians killed in World War II German Jews who died in the Holocaust Lists of stolpersteine in Germany