Recollections of a Jewish Mathematician in Germany

Every mathematician knows that Abraham Fraenkel was, together with Ernst Zermelo, one of the founders of axiomatic set theory. Fewer know that Fraenkel had an important role in the foundations of abstract algebra as well. Indeed, his Ph.D. thesis was an investigation of the abstract theory of rings, inspired by Ernst Steinitz’s 1910 work on field theory.

Given Fraenkel’s historical importance, it is somewhat surprising that we have had to wait 50 years for an English translation of this memoir, originally published in German in 1967. Thanks to Jiska Cohen-Mansfield, the editor of this volume, and to Allison Brown, the translator, English readers can have access to a valuable historical source.

Fraenkel’s plan had been to write three volumes of memoirs, but he died after writing only this first one, about his life in Germany up to 1929. As the title indicates, the focus is on being a Jewish mathematician in Germany; the story ends as Fraenkel decides to settle permanently in Jerusalem with his family. Fraenkel moved there in 1929, and only a brief epilogue carries the narrative further to 1933, when his position at the Hebrew University in Jerusalem was made permanent.

Fraenkel clearly intended that his memoir be read by non-mathematicians, so there is essentially no discussion of his mathematical work. The main concern is the life of the Orthodox Jewish community in Germany. Fraenkel writes about a recently-unified Germany that still thought of itself as several different nations, so perhaps it is truer to his account to say that the focus of the story is on the Jewish communities in Bavaria, where Fraenkel grew up, and in Prussia, where he studied and taught.

As one would expect, anti-Semitism is a central topic, especially as it relates to the universities. Here Fraenkel’s account is not as negative as one might expect. While there was significant prejudice that kept many Jews from getting the recognition they deserved, in mathematics it seems to have been possible to overcome it. Fraenkel thinks that this is because the criteria for excellence in mathematics are more objective than in other fields. In any case, he tells of many Jewish mathematicians and mathematicians of Jewish descent who found good university positions and were successful. (As an Orthodox Jew, Fraenkel clearly did not approve of those who chose to assimilate or convert, but this is mostly left unstated, to be inferred from the tone of his comments.)

Another topic that gets much attention is Zionism, in particular the rifts it created in the Orthodox Jewish community in Europe. Many leaders were vehemently opposed to the Zionist movement. Fraenkel was very much a Zionist, but he seems to have been repelled by the contentious discussions, and so avoided some of the Zionist meetings and associations. Nevertheless, he does not refrain from commenting on those who criticized him for his decision to move to Jerusalem: “only ten short years later some of these attackers were to send telegrams to me, then rector of the Hebrew University, beseeching me to send them student certificates that would enable them to leave Germany and remain alive!” (p. 163)

For historians of mathematics, there are useful descriptions of leading mathematicians, often focused on their personalities and their attitude towards the Jews. I was particularly interested in Fraenkel’s remarks about his doctoral advisor, Kurt Hensel. Anyone interested in the history of the Jewish community in Germany before the Nazi period would also find this memoir to contain valuable source material.

To the English translation (by Allison Brown) the editor Jiska Cohen-Mansfield has added an introduction discussing some of Fraenkel’s set-theoretical work and an appendix outlining the events of Fraenkel’s life in Jerusalem until 1965. There are many good illustrations and an extensive bibliography of Fraenkel’s writing. The editor notes, however, that since Fraenkel wrote many articles for various Jewish publications it is hard to know whether the bibliography is complete. There is also a good index of names (but not an index of topics).

Fraenkel’s distinctive voice makes his memoir a fascinating read. His importance makes it a valuable historical source. I found it both enjoyable and instructive.

Fernando Q. Gouvêa is Carter Professor of Mathematics at Colby College and the editor of MAA Reviews.