P R E F A C E WHEN still a graduate student, I discovered by chance and to my fascinated horror that a prominent and distinguished German mathematician had been, as a mathematician, a propagandist for Nazi ideology. At that time, I thought that at some time I would want to investigate this further, to try to understand whether he was simply a freak or, as superﬁcially appeared, the leader of a group of like-minded academic colleagues. I have always had an interest in history, and over the years this developed into a growing amateur interest in the history of science. Sporadic concentration on the subject broadened my original interest to a question of the situation of mathematics under the Nazi regime. An Alexander von Humboldt Fellowship in 1988 enabled me to spend time doing archival research in Germany, as well as talk to a number of mathematicians. Since then, my previous sporadic work has been more concentrated, including several trips to Germany, and this book is the result. From the ﬁrst, I wanted to write a book that was both scholarly, in the sense of documentation and understanding, and also readable by a wider public, as many scholarly works unfortunately are not. In particular, it should be a book that does not require any advanced knowledge about mathematics. Sensitive (perhaps hypersensitive) to the general but perverse social view of mathematicians as disembodied intellects, it also seemed appropriate to explain enough about the nature of mathematics to make its interaction with ideology more interesting and meaningful. From another internal standpoint, this also seemed necessary. To write about the history of mathematics in a period so soaked in ideology and political pressure seemed meaningless unless both a mathematicalhistorical and a general historical context were provided. Thus this book is an attempt at a kind of social history of mathematics and the community of mathematicians in the period. At the same time, it is not a history of mathematics as a scientiﬁc discipline or of mathematical results achieved during the period in question. Information about actual progress in mathematics in Germany during the Nazi period is available in the seven volumes of the FIAT review of German science devoted to mathematics and edited by Wilhelm Süss and Alwin Walther (for applied mathematics). Rather, this is a contribution to the history of the academic community of mathematicians as practitioners of an academic discipline in a time of intense political and ideological pressure. Being a kind of social history also means that the people who ﬁgure in it are not just the mathematically famous, but also those who are mathematically now forgotten. Not only are the Behnkes and Blaschkes, Hasses and Teichmüllers important, but also the Weyrichs and Weinels, Wegners and Torniers. It also means considering mathematicians as more than just members of a certain academic profession. It is easy to refute the naive idea that mathematicians, being “analytically trained” and educated to examine the validity of hypotheses, ought xii P R E F A C E not to have been prone to Nazi fellow-traveling—especially since mathematics (unlike biology, anthropology, history, or architecture) was not a subject that would seem to lend itself to ideologizing. Mathematicians need to be seen in the social context of academics in Germany, as well as in that of the history of their profession. Indeed, there were psychologists like E. R. Jaensch and mathematicians like Ludwig Bieberbach who saw mathematics as a fruitful area in which Nazi ideology could be exempliﬁed and play a signiﬁcant role. There were mathematicians like E. A. Weiss who saw mathematics as the ideal discipline for training those who would be good Nazis. Mathematics also has its own rhetoric, a rhetoric of absolute certainty and inviolate validity. The Nazis were fond of such rhetoric. As early as 1923, the mathematician and early Nazi Theodor Vahlen spoke of mathematics as a mirror of the races that proves the presence of racial qualities in intellectual activities with mathematical, and therefore incontrovertible, certainty. A frequent Nazi argumentation (despite the irrational appeals to blood, soil, and feeling) involved what purported to be the drawing of unremitting logical conclusions from premises. If Jews were literally (and not just ﬁguratively) poisonous parasites on the body politic, then the only solution was to expel, suppress, or, ﬁnally, exterminate them. Nazi intellectuals also practiced a kind of scientiﬁc reductionism. Present-day scientiﬁc reductionism involves the reduction of biology to chemistry, both...

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