Robert Remak was the grandson of the first Jew in Prussia to be given an habilitation without giving up the Jewish faith. Also called Robert Remak, he was awarded his habilitation from the University of Berlin in 1847 and, with support from Alexander von Humboldt, he went on be made a professor in the medical faculty.
His grandson Robert Remak the mathematician, studied at the University of Berlin and was supervised by Frobenius for his doctoral work. His doctoral dissertation Über die Zerlegung der endlichen Gruppen in indirekte unzerlegbare Faktoren was submitted in 1911 with Schwarz as the other expert involved. This important work considered the decomposition of finite groups into a direct product of irreducible factors, a result that his name is often now attached to along with those of Wedderburn, Schmidt and Krull.
Although his doctorate was awarded in 1911, it was a long and difficult road for Remak to be awarded his habilitation. He had submitted a thesis for his habilitation several times, and each time it had been rejected. However he persevered: as Schappacher writes in :-
The Remak family had something of a tradition in slowly overcoming administrative hurdles at the University of Berlin.
In 1929 Remak eventually received his habilitation and the right to teach at the university, but there was no post for him. He did lecture on groups at the University of Berlin during the summer semester 1929 and these lectures were attended by Bernhard Neumann. The same year 1929 was one in which Remak published an essay on applications of mathematics to economics. He had broad interests, working on mathematical economics as well as group theory and the geometry of numbers.
In his 1929 essay Can economics become an exact science Remak writes:-
I emphasise ... that I have not made any politico-economic statements, but only stated problems and indicated some calculational schemes, ... that it is still open as to if the outcome of the computation favours capitalism, socialism, or communism. ... these equations are very awkward to handle mathematically. There is, however, work in progress concerning the numerical solution of linear equations with several unknowns using electrical circuits.
In this work Remak is far sighted in seeing the applications that computers would have in the subject, but these were areas into which is was unwise for someone like Remak to be venturing in Germany at this time.
Remak made important contributions to algebraic number theory. In a publication in 1932 he gave a lower bound for the regulator of the units of an algebraic number field which depends only on the number of real conjugates and the number of pairs of complex conjugates. He went on to produce further extensions of this work which continued to be published ten years after his death. Further papers by Remak on finite algebraic number fields with unit defect appeared in 1952 and 1954.
On 30 January 1933 Hitler came to power and on 7 April 1933 the Civil Service Law provided the means of removing Jewish teachers from the universities, and of course remove those of Jewish descent from other roles. All civil servants who were not of Aryan descent (having one grandparent of the Jewish religion made someone non-Aryan) were to be retired. Under this law, Remak lost the right to teach at the university in September 1933.
Remak did not leave Berlin at this time, however, and he continued to live in the city and continued with his mathematical research. He was particularly interested in the exciting new mathematical developments which were written up in van der Waerden's two volume Algebra published in 1930 which contained the new developments in ring theory by Emmy Noether, Hilbert, Dedekind and Artin.
Remak was married to a German woman, who did satisfy the Aryan condition, and this certainly made him wish to continue living in Germany. He might also have expected that it would also give him a certain protection against the Nazi policies.
On 10 July 1936 Schur wrote a report on Remak:-
I consider Dr Robert Remak to be an outstanding researcher, who is distinguished by his versatility, originality, strength and brilliance. ... He may, without doubt, be called a leading scholar in the splendid and important field of geometry of numbers.
On the Kristallnacht (so called because of the broken glass in the streets on the following morning), the 9-10 November 1938, Remak was arrested. On that night 91 Jews were murdered, hundreds were seriously injured, and thousands were subjected to horrifying experiences. Thousands of Jewish businesses were burnt down together with over 150 synagogues. The Gestapo arrested 30,000 well-off Jews and a condition of their release was that they emigrate. Remak was put into the Sachsenhausen concentration camp near Berlin and his wife made strenuous attempts to obtain an affidavit which would allow them to emigrate to the United States.
Having failed to obtain permission to emigrate to the United States, Remak was released after over eight weeks in the concentration camp after his wife organised that he go to Amsterdam. This Remak did in April 1939 but his wife did not go to Amsterdam with him. Hans Freudenthal wrote to Hopf on 7 March 1940 describing the problems that Remak was causing:-
My main problem is Remak, who is not satisfied with visiting my lectures but who also gives us no end of trouble. It mostly concerns conflicts with his landlords, who then immediately run to the alien registration office. ... also Remak's expression "then I'd rather go to a concentration camp" has infuriated enough people already. The matter is extremely serious; it is doubtful how long we can still prevent him from being expelled to Germany. ... It is understandable that his wife didn't want to come here, but demonstrates a lack of loyalty to him.
In fact Remak's wife divorced him which almost certainly made his position impossible. He was arrested by the German occupying forces in Amsterdam in 1942 and taken to the concentration camp in Auschwitz. He died there on some unknown day in 1942. Merzbach writes in  that Remak's:-
... refusal - in mathematics and everyday affairs - to compromise, or to be 'realistic', swept him out of the mainstream of mathematics and cost him his life.
Article by: J J O'Connor and E F Robertson