Paul Epstein

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24 July 1871
Frankfurt, Germany
11 August 1939
Frankfurt, Germany

Paul Epstein was a German mathematician best-known for his contributions to number theory.


Paul Epstein's parents were Theobald Epstein (22 August 1836 - 23 August 1928) and Mathilde Perels (11 June 1844 - 29 April 1875). It was a Jewish family living in Frankfurt where his father was a professor at the Philanthropin Secondary School, the largest and longest-existing Jewish school in Germany, and an astronomer and Head of the Frankfurt Observatory. Theobald Epstein was a excellent scientist who had been taught astronomy by Karl Schwarzschild. Paul had an older sister Cäcilie Epstein (7 November 1869 - 12 May 1939). His mother died in chidbirth in 1875 and his father married again in 1880. Paul had a step-sister Mathilde "Tilli" Epstein (11 June 1844 - 29 April 1875). Paul studied at the Philanthropin Secondary School, graduating with his Abitur in 1890. He then went to study at the University of Strasbourg which at that time was known as Strassburg and was part of Germany. We should give a little background on the position of Strasbourg as a sometimes French, sometimes German university.

The Franco-German war of 1870-71 had been a humiliation for the French. Germany had captured Strasbourg after a 50-day siege during the 1870-71 war and annexed the city. After taking control of Alsace-Lorraine, the Germans had reorganised the University of Strasbourg and reopened it as the German Kaiser-Wilhelm University of Strassburg in 1872. Two mathematics chairs were founded at this time, the first was filled by Elwin Christoffel and the second was filled by Theodor Reye. Both Christoffel and Reye considered it their patriotic duty to assist in making the University of Strasbourg a German university. Epstein was taught at Strasbourg by Christoffel who became his thesis advisor.

After submitting his thesis Zur Lehre von den hyperelliptischen Integralen on abelian functions, Epstein received his doctorate in 1895 from the University of Strasbourg. He submitted a paper based on the work of his thesis and with the same title, to Acta Mathematica in September 1894. The 58-page paper appeared in print in 1897. In it Epstein acknowledges the help he received from his advisor Christoffel:-
Finally it should be mentioned that writer owes the inspiration for this work, namely the knowledge of the functions φ and with their use in forming integrals to a lecture by Mr Christoffel on elliptic integrals (Winter 1890/91). However Mr Christoffel only sought to study the behaviour of the integrals at infinity, and gave the important equation (7) in §2 without proof.
Epstein also explains in this paper that, as well as being inspired by Christoffel's lectures, his work was based on ideas by Karl Weierstrass and others.

From 1895 to 1918 he remained in Strasbourg, teaching at the Technical School and also at the University where he had been appointed a Privatdozent. During World War I he did military service in the German army. At the end of the war in 1918, however, the city of Strasbourg reverted to France, and Epstein, being German, was forced to leave Alsace. Although he had done good work in Strasbourg, he had remained a Privatdocent. Examples of his research undertaken at Strasbourg are Zur Theorie allgemeiner Zetafunctionen (Part I, 1903; Part II, 1906) and Über Möbiuskettenbrüche und Elementarkettenbrüche (1918). In the first part of Zur Theorie allgemeiner Zetafunctionen (1903) Epstein introduced a function belonging to a class of Dirichlet series generalising the Riemann Zeta-function depending on a given quadratic form. He proved a functional equation, the analytic continuation and the Kronecker limit formula for these functions. Today these function are known as the Epstein Zeta-functions. They play an important role in crystallography and there are several applications in mathematical physics, particularly in quantum field theory. As Sanford Segal remarks in [2], given this outstanding work it is hard to see why he was never promoted unless one accepts that it was due to anti-Semitism:-
Another example of late promotion was Paul Epstein, who was still a Privatdocent at Strassburg when the French dismissed him in the aftermath of World War I.
Forced to leave Strasbourg and having no position to go to, Epstein returned to his native city of Frankfurt. He was appointed to a non-tenured post at the university and he lectured in Frankfurt from 1919. Later he was appointed as an extraordinary professorship at Frankfurt. In 1923-24 he was given a salaried teaching assignment for didactics and the history of mathematics and he made a major contribution to Max Dehn's History of Mathematics seminar which ran at Frankfurt from around this time until the early 1930s. He published Goethe and mathematics in the Jahrbuchs über die Fortschritte der Mathematik in 1924. In [2], Birgit Bergmann explains that this was one of several essays in which Epstein:-
... attempted to equate Goethe's classical poetry with the clarity and precision of mathematical language. He was convinced that Goethe's rejection of mathematics was due to his failure to recognise its true beauty. Epstein sought to eliminate the most obvious and the best known contradiction between Goethe and mathematics by showing that ultimately both approaches to understanding the world had their source in the same motivation and led to the same goal. With these texts, Epstein joined the ranks of German-Jewish intellectuals who attached great importance to the classical German educational ideal known as "Bildung".
Here is a quotation from Epstein's Goethe and mathematics (1924):-
Thus, the language of the mathematician is free from all of the imperfections and shortcomings of colloquial language, which Goethe himself vividly felt, deploring that language as we know it, which had developed from obvious human needs, human activities and general human sentiments and views, is not adequate to correctly express perceptions of the functioning and workings of nature as something which is indeed far removed from common human affairs. the mathematical sign language, however, - correctly understood and used in the fields to which it is suited - is the "Language of the Spirits" which Goethe sought; according to a famous dictum of Galileo, it is the language in which the Book of Nature is written.
We know that in the summer of 1928 Epstein lectured on Étienne Pascal in the History of Mathematics seminar and hand-written lecture notes from this course survive.

On 30 January 1933, however, 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 also to 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. However, there was an exemption clause which exempted non-Aryans who had fought for Germany in World War I. Epstein certainly qualified under this clause and this allowed him to keep his lecturing post in Frankfurt in 1933.

Decisions at the Nuremberg party congress in the autumn of 1935 made it clear that non-Aryans would no longer be able to keep their posts even if they had served in World War I. Carl Siegel writes in [2]:-
Epstein voluntarily relinquished his teaching position before the Nuremberg laws went into effect. As he explained to me, he had wanted to save the German authorities the trouble of doing to him what the French had done back in 1918.
Epstein did not attempt to emigrate. He was 64 years old and had he emigrated he would have lost all his money except 10 Marks. There was no prospect of a 64 year old obtaining a post. On the Kristallnacht (so called because of the broken glass in the streets on the following morning), the 9-10 November 1938, 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. The Gestapo broke into Epstein's house but found that he was seriously ill and could not be moved. At this point Epstein must have known that his only chance was to leave Germany. Siegel suggests that it would have been possible for [2]:-
... one of his sisters had emigrated earlier and could have supported him. But despite the possibility of escape, he hesitated leaving his books and his native city.
However, Siegel seems to be incorrect in believing that Epstein's sister had already emigrated. Tilly Epstein was a teacher at the Philanthropin Secondary School in Frankfurt from 1901. In November 1938, following Kristallnacht, all the male teachers at the school were sent to the Buchenwald concentration camp and she was left with the task of closing the school. She emigrated to England, but this was not until 1941 after Paul Epstein had committed suicide. Let us return to the story of Epstein's last days.

Epstein moved to Dornbusch, a northern suburb of Frankfurt, and was visited there by Carl Siegel [2]:-
I visited Epstein in August 1939 and we sat in the sunny garden of the house he was living in then in Dornbusch. He told me that he had a favourite cat put to sleep simply because it liked to chase birds and might have irritated the neighbours, but he didn't seem otherwise distressed. I still remember how he pointed to the trees and flowers in the garden and said, "Isn't it lovely here?"
About a week after Siegel's visit, Epstein received a summons from the Gestapo. He knew what had happened to others who had received such a summons, many had been tortured and killed. He wanted to avoid the suffering so he took a lethal dose of Veronal. The Gestapo later claimed that they had only summoned him to get him to sign a document to fix a date on which he would emigrate [2]:-
Everyone knew that a summons from the Gestapo often meant torture and death, and with that in mind Epstein decided to initiate the irreversible process with his own hand: After his death it was alleged that the Gestapo merely wanted him to sign a statement fixing the date of his impending emigration. I don't know if he actually was threatened with anything worse than this, but he certainly had had the feeling that he had reached the end of the road, and drew his conclusion from that. Emigration would probably have been impossible in any case with the outbreak of war only a few weeks away, and Hitler's so-called final solution to the Jewish problem following shortly thereafter. I really think that Epstein acted as wisely as he could.
Epstein's most important work was in number theory, in particular the zeta function which we mentioned above. Also, as we have seen above, he worked on the history of mathematics and mathematics in culture. Perhaps we should mention one other of Epstein's talents which was music, and he took part energetically in the cultural life of Frankfurt.

References (show)

  1. B Bergman, M Epple and R Ungar, Transcending tradition. Jewish mathematicians in German-speaking academic culture (Springer, London-New York, 2012).
  2. S L Segal, Mathematicians under the Nazis (Princeton University Press, Princeton, NJ, 2003).
  3. W Magnus, Vignette of a cultural episode, in Studies in numerical analysis: papers in honour of Cornelius Lanczos on the occasion of his 80th birthday (London, 1974), 7-13.
  4. C L Siegel, On the history of the Frankfurt Mathematics Seminar, Math. Intelligencer 1 (4) (1978/79), 223-230.

Additional Resources (show)

Written by J J O'Connor and E F Robertson
Last Update January 2014