Remak, the subject of this biography, studied mathematics and physics in Berlin, Marburg, Göttingen and Freiburg. He undertook research at the University of Berlin where he was supervised by Georg Frobenius for his doctoral work. His doctoral dissertation Über die Zerlegung der endlichen Gruppen in indirekte unzerlegbare Faktoren Ⓣ was submitted in 1911 and Hermann Schwarz served as the other member of the examining committee. 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 Joseph Wedderburn, Erhard Schmidt and Wolfgang Krull.
Although his doctorate was awarded in 1911, it was a long and difficult road for Remak to be awarded his habilitation. Of course, World War I began in 1914 before Remak had attempted to habilitate and he served as a soldier during the conflict. After the war ended, he submitted a thesis for his habilitation several times, and each time it was 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.However, as Segal writes in , Remak had a reputation as a difficult person and this was a factor in his habilitation being refused:-
Robert Remak was a brilliant algebraist and number-theorist, though an apparently more than somewhat difficult colleague. He had the reputation of being a "communist", and there were also rumours in the 1920s that he was "not completely Aryan", but this seems to have been mostly a result of his sarcastic personality, eccentricities, and unkempt habits, rather than stemming from any real knowledge about him or any political activity on his part. In fact, he was Jewish. He was twice denied habilitation and the right to join the teaching faculty in Berlin, in 1919 and 1923, again largely because of his demeanour and habits. However, finally, on 11 January 1929, Remak (who had received his doctorate in 1911) was accepted on his third attempt.Let us look at Remak's problems in a little more detail. In Berlin he had annoyed Max Planck so much that Planck strongly objected to Remak habilitating and this was the main reason that his habilitation thesis was rejected in 1919 and 1923. After this Remak went to Göttingen and his behaviour there is described in detail by Heinrich Behnke in :-
Surely Remak was a peculiar fellow. [In Göttingen] he regularly attended the courses of the young lecturers. He always arrived too late, but took his place on one of the front benches and appeared to immediately fall asleep. However, as soon as the lecturer made a miscalculation or expressed himself in an imprecise way, he woke up and corrected the speaker. ... Courant waited for the opportunity to be able to say: "Mr Remak, I have explained that already while you were still sleeping." ... Everybody was afraid to be seen together with Remak in the streets. Hilbert discussed with a small circle of his colleagues the question whether he could prevent Remak attending all his lectures and seminars. ... But the esteem for Remak among experts continued. ... Remak was known throughout the city. More and more the label 'the communist' was attached to him. It was totally beside the point but the label carried much more weight in those days than it does today. He was treated with suspicion everywhere. One of the reasons was also his foolish clothing. ... Today he would not be conspicuous because of his behaviour. He would only be a pain in the neck of the radical students of the left since he would relentlessly expose all their absurdities and contradictions, and since he would disconcert them in public meetings as he did with the conservatives at that timeRemak was involved in a quarrel with one of the janitors at the University of Göttingen and, after this was reported to the rector, Remak was informed that he would be expelled from the university if he caused any more trouble. But he did create more trouble as Behnke explains :-
At that time Remak wanted to understand politics as profoundly as mathematics. He therefore seriously attended lectures in economics. However, the students felt uneasy because of the arrival of 'the communist' in their lectures and they began to scrape their feet when he entered. He made a polite little speech requesting them to stop their disapproval of him because there was no reason. However, when he entered the next lecture the students scraped their feet more than ever whereupon he boxed the "next culprit's" ears. A great commotion arose just as the professor was entering the lecture-hall and he reported Remak as being the cause of the disturbance. The Rector expelled Remak from the University of Göttingen.Remak returned to Berlin and eventually, in 1928, his habilitation thesis On minimal invariant subgroups in the theory of finite groups was accepted by the examining committee consisting of Issai Schur and Erhard Schmidt. On 11 January 1929, he was given the right to teach at the university by Richard von Mises who insisted that Remak was only permitted to teach pure mathematics. Despite having the right to teach, 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 Kann die Volkswirtschaftslehre eine exakte Wissenschaft werden Ⓣ Remak writes (see ):-
The task of an exact economics ought to be to construct a budget plan of an, in some respects, generic economy. [In order to answer questions about] (i) identification of an economic optimum, (ii) identification of an approximate economic solution, ... we shall try below to formulate these questions in a more exact way by mathematical considerations. First of all, we shall try to make sure, that the range of possible economies from which the optimal one would have to be chosen, is mathematically well defined. ... On the question of which economy is to be considered as optimal and which distribution of goods as justifiable, different opinions will be possible.However, he tried to ensure that his essay was not seen as being political (see for example ):-
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 in the ten years after his death. Further papers by Remak on finite algebraic number fields with unit defect appeared in Compositio Mathematica 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 removing 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, David Hilbert, Richard Dedekind and Emil Artin.
Remak was married to a German woman, Hertha Meyer, 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 Issai Schur wrote a report on Remak (see for example ):-
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. She sent many letter and telegrams to Hermann Weyl requesting affidavits. Weyl wrote to Heinz Hopf, who was in Zürich, on 29 November 1938 telling him about Remak's suffering in Sachsenhausen (see ):-
About Remak, I heard that comrades of his, who have in the meantime been released, are saying that he is suffering more than others. One can imagine what this means, also because it is clear that due to his character, Remak is incapable of adapting in any way. It is generally known that prisoners are released if they have complete emigration papers, ship tickets. etc. The poor (and very clumsy) Mrs Remak desperately tries to achieve something to this effect.On 11 December 1938, Remak had not contacted his wife for four weeks and she wrote again to Weyl (see ):-
Apart from his follies which I do not want to deny, you will agree that my husband is a deeply honest and decent character and an able mathematician. I am an Aryan, so you cannot interpret my letter as a Jewish impertinence.Despite 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. Hertha Remak wrote to Weyl on 20 January 1939 telling him that Remak had returned from the Sachsenhausen concentration camp and was back in Berlin with a temporary permit for the Netherlands. Remak went to the Netherlands in April 1939 but his wife did not go to Amsterdam with him. Instead she started divorce proceedings, almost certainly in an attempt to save her own life. Hans Freudenthal wrote to Heinz Hopf on 7 March 1940 describing the problems that Remak was causing in Amsterdam:-
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.The fact Remak's wife divorced him almost certainly made his position impossible (but had Hertha not done so and had she gone to the Netherlands with Remak, it is doubtful whether this would have saved his life). He was arrested by the German occupying forces in Admiraal de Ruyterweg 8, his Amsterdam address, in early October 1942 and taken to the transit camp at Westerbork. The Nazis transferred about 100,000 Jews from Westerbork to the Auschwitz concentration camp beginning in July 1942. Trains left the Westerbork camp every Tuesday, and the inhabitants panicked on Monday evenings knowing what was about to happen. On Tuesday 10 November 1942 Remak was put into a wagon on a train bound for Auschwitz. He was murdered there three days later. 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