1. First contact and the emergence of the project

In 1983, Mehrtens contacted me from West Berlin after he had become aware of my parallel research in East Berlin.Footnote ¹ As Germans dealing with our common past of the Nazi regime, we were looking for reasons and explanations for the adaptation and instrumentalization of mathematics for political use during the National Socialist (NS) period. We wanted to understand the “sense in the nonsense,” where some others only saw the pathological, extreme, and criminal. Other historians, such as Mitchell Ash and Mark Walker,Footnote ² contributed to the topic for their disciplines, and we were in close discussions with them. Mehrtens and I soon realized that we both had only limited access to the sources (archives, persons) due to the political divide of Germany. We therefore exchanged manuscripts and detailed information in our field of common interest.

Mehrtens, seven years older than me, had from the beginning the broader approach, co-editing and contributing to the volumes Sciences, Technology, and NS Ideology (Mehrtens and Richter Reference Mehrtens and Richter1980) and Social History of Nineteenth Century Mathematics (Mehrtens, Bos and Schneider Reference Mehrtens, Bos and Schneider1981). His sociological ideas were influenced, among others, by Niklas Luhmann’s theory of “social systems,” and culminated in his article “The Social System of Mathematics and National Socialism: A Survey” (Mehrtens Reference Mehrtens1987a). This article was reprinted several times and can be considered a kind of theoretical synthesis of Mehrtens’ empirical findings in his work on mathematics in the Third Reich.Footnote ³ Among the more empirical works behind it were Mehrtens’ studies on the political “Gleichschaltung” (toeing the line) of German mathematical societies and associations (Mehrtens Reference Mehrtens1989a), biographical studies on Felix Hausdorff (1862–1943),Footnote ⁴ the Nazi victim (Mehrtens Reference Mehrtens1980), and Ludwig Bieberbach (1886–1982), the Nazi culprit (Mehrtens Reference Mehrtens and Esther1987b), investigations of school mathematics in the Third Reich (Mehrtens Reference Mehrtens and Dithmar1989b), and studies of applied mathematics in the NS period (Mehrtens Reference Mehrtens1996a).

In the 1980s I published several works on mathematics during the Nazi era: on Theodor Vahlen (1869-1945)—the other leading Nazi (besides Bieberbach) in German mathematics, on Nazi strategies for dominance in European mathematics (1986), on mathematical reviewing (1987), and on the mathematical institute of Berlin University in the Third Reich (1989). In addition, I was much occupied with research on the history of mathematical ideas, in particular in function theory and functional analysis, not restricted to Nazi Germany.

Coming from the East with its all-pervading ideology of “dialectical materialism,” I was particularly attracted by Mehrtens’ liberal and pragmatic methodology, which nevertheless connected to some of the same sources and emancipatory convictions, among them Marxist historiographic thinking. As he put it in a widely read essay of 1981: “Drawing on ‘classic’ Marxist historiography of science like the works of Hessen, Struik, or Needham and using the developed historiographical tradition of Eastern Marxist work (e.g. Wußing …), as well as the theoretical tools of a sophisticated and diversified Western Marxism, more intriguing results have turned up and may be expected” (Mehrtens Reference Mehrtens, Mehrtens, Bos and Schneider1981, 260).

Not being educated as a philosopher or theorist of science, I liked Mehrtens’ unprejudiced, self-declared unsystematic, philosophical approach, as revealed in the same methodological essay of 1981:

Further down in the essay, in a passage that also seemed to guarantee Mehrtens’ respect for the empirical side of historical research, he writes:

Mehrtens and I shared some common experiences with the “apolitical” ideologies of our leading mathematicians/scientists on each side of the political divide, which made them amenable to facile talk about science as a vehicle of “progress,” as promoter of “humanism,” and as a victim of “abuse” under oppressive regimes. In the East this talk was superficially and ostensibly complemented by declarations of the “social and political responsibility” of science and mathematics, apparently, in order to reach conformity with the leading ideology. As far as the history of mathematics and science during the Nazi period was concerned, one can safely say that this field of historical research was of no primary concern in the East and therefore not inviting for careers either.Footnote ⁵ The main reason for that was the grey zone of the political role and behavior of science and its practitioners in the NS period, in contrast to the political, economic and military developments that were most interesting for the official East German historiography of “fascist” Germany.Footnote ⁶ The various apparent and seeming parallels between the Nazi regime and the “socialist democracy” of the East, with their ruling parties in both cases, were further and obvious obstacles to critical historiography of NS in the German Democratic Republic (Siegmund-Schultze Reference Siegmund-Schultze, Macrakis and Hoffmann1999). There were, in addition, particular problems and phenomena such as “anti-Semitism” (in its difficult relationship to class-structure), nationalistic militarism in “humanistic scientists,” and the opposition of bourgeois scientists to the “bourgeois government” of the Weimar Republic.Footnote ⁷ These were difficult to handle within an historiographic tradition that stressed the underlying class-structure of the various and very different monarchist, parliamentarian, and dictatorial German societies between 1900 and 1945.

Under these political circumstances it is no wonder that I experienced Mehrtens’ approach as liberating. An important part of the picture was that closer collaboration had only become possible in the more relaxed political atmosphere between the East- and West Germany of the 1980s, in particular after “Glasnost” in the Soviet Union from 1985. Nevertheless, communication between Mehrtens’ and myself remained difficult, at least in technical terms, as long as the “Wall” (Mauer) which divided both Berlin and Germany as a whole was in existence. For the first five years, we maintained the distant “Sie” instead of the more informal “Du” in addressing each other in our communication, which was mostly by ordinary mail.

In January 1988, I sent an eight-page book proposal, “Mathematics in Fascist Germany—Studies, Theses, Documents” to my former doctoral advisor, Hans Wußing, at the Karl Sudhoff Institute in Leipzig. This was after learning that he, together with Erwin Hiebert (Harvard University), was planning a new series of publications on the history of science, in keeping with the zeitgeist of the gradual political opening between East and West. The new series was “Science Networks,” an East-West project undertaken by VEB Deutscher Verlag der Wissenschaften (Nationally owned German publisher of scientific books) and Birkhäuser-Verlag. The year before, I had defended my habilitation thesis at Humboldt University, which focused thematically on mathematical reviewing in the Third Reich. In the GDR, it was almost impossible to publish specialized scientific monographs that could not directly serve teaching purposes, especially if they also touched on sensitive political issues. I had already experienced this in 1979 with my doctoral thesis,Footnote ⁸ and therefore saw an opportunity in this new publication series, with its potentially larger readership in the German-speaking countries. This necessarily also put me in a certain competitive situation, at least as I felt it, with Mehrtens, who had not had to experience such restrictions.Footnote ⁹

To this day, I am not entirely clear whether Mehrtens had planned such a monograph in early 1988 or before. Wußing wrote me something at the time about an “earlier project” of Mehrtens’ for the same series, but it seems to me that the initiative at that earlier time had come from the publisher rather than from Mehrtens himself. In any case, after Wußing’s notice, I had no choice but to curb my personal ambition and propose a collaborative publication.

The letter from Mehrtens describes his ambivalent situation and mood at that time, and should probably have been a warning to me.

In the same letter, however, there is already a two-page rough conception of a joint book.Footnote ¹⁴ This begins with: “1. Initial Situation: Mathematics in the Weimar Republic – Structures, Conflicts, Tendencies.” This seemed to me a more natural “first chapter of a book on Math in German Fascism,” than Mehrtens’ habilitation thesis, which was focusing on “the period 1890-1914.”Footnote ¹⁵

On November 22, 1988 Mehrtens sent me a more detailed ten-page conception. By this time we had changed to the “Du.” In his November letter, Mehrtens reacted to my original book proposal for Wußing from January 1988:

The outline (here essentially in its main headings) was:

[More in detail:]

One must add that even in the subchapters, not given here in detail, terms are missing, such as “Mathematics as a Social System,” “Market and Legitimation of Mathematics,” “Foreign and Domestic Politics of Mathematicians,”Footnote ¹⁷ “Self-Mobilization of Mathematics in War,”Footnote ¹⁸ which Mehrtens used in parallel works such as the more general and sociological one on “The Social System of Mathematics and National Socialism” (Mehrtens Reference Mehrtens1987a). The word “anti-modernism” appears only once in a subchapter to “Prologue: Mathematics during the Weimar Republic.” Mehrtens had agreed with “intended completeness,” which I aimed at, and even argued against the somewhat more problem-oriented structure of my January 1988 draft: “I am sure that a more chronological order makes better sense for both publisher and reader…. I would rather stick to the narrative style.”

Even less do topics occur in Mehrtens’ conception that were later to play a central role in his habilitation and in his book on modernity in mathematics, such as “language of mathematics,” “number as an act of creation,” “counter-modernity,” [Gegen-Moderne] or “feminism in mathematics.” It is also striking that Mehrtens had no problem using terminology cultivated in GDR historiography, such as the concept of fascism.Footnote ¹⁹ In any case, he had been using the word fascism, applied also to the German case, for years in his own papers.

To me, at least in retrospect, it looks as if Mehrtens was actually no longer very interested in empirical research (“facts”) back in 1988, according to his earlier letter to me of August 12, although he had sufficiently demonstrated his aptitude for this kind of historical work in his studies on the political coordination of the German Mathematicians’ Association (DMV) (MehrtensReference Mehrtens1989a), on Bieberbach, and on war research. Nevertheless, Mehrtens apparently considered a chronologically structured and fact-oriented book on mathematics during NS as quite useful at that time. Apparently, he hoped that I would above all provide the necessary help for empirical work and for assessing some mathematical developments. He wrote to me on November 22: “I am now leaning very much toward YES and am quite willing to compromise.”

On December 4, 1988, I reported to Mehrtens about a conference on the history of mathematics at the Mathematical Research Institute [Mathematisches Forschungsinstitut] Oberwolfach in early December, which I had been able to attend even before the fall of the Berlin Wall (November 1989) due to the political thaw. There, among other things, I had unsuccessfully tried to obtain access from the director of the institute, Martin Barner (1921–2020) to the estate he administered of the chairman (Vorsitzende) of the DMV, Wilhelm Süss (1895-1968), who had been influential during the Nazi period. Research on mathematics under the Nazi regime tended to be hampered, even in the 1980s and 1990s, by German mathematicians, especially if their teachers could potentially be the subject of historiography and if historians wanted to do more than just look at the production of “apolitical and pure” mathematics.Footnote ²⁰ Several applications for funding of the topic “Mathematics in the NS,” in particular one that David Rowe submitted to the German Research Foundation in 1996 on my behalf, were rejected by mathematical reviewers. As late as 1997, interested historians (Kneser, Epple, and Speck Reference Kneser, Epple and Speck1997) could not retrieve important files concerning Süss, which several years before had been temporarily accessible for a historical contribution to the centenary volume of the DMV (Schappacher and Kneser Reference Schappacher, Kneser, Fischer, Hirzebruch, Scharlau and Törnig1990). It was not until the late 1990s that younger historians of mathematics, especially Moritz Epple and Volker Remmert (Remmert Reference Remmert, Hoffmann and Walker2012), succeeded in obtaining access for historians to the DMV files and to the Süss Nachlass. These files are now in the archives of the University of Freiburg/Breisgau, Süss’ place of work, near which the Oberwolfach Institute, founded in 1944 under Nazi rule, is located.

At the Oberwolfach meeting in December 1988, there had also been a discussion with the prospective publisher about our book project. An impression of the reluctance to discuss political topics in the history of mathematics, even among publishing house employees, is given by a letter that Hans Wußing sent to Mehrtens on December 9. In this letter, Wußing was responding to a positive reaction from Mehrtens on November 12 regarding the book project, and then wrote:

I then sent Wußing the preliminary table of contents of the book on January 13, 1989, and wrote:

With the new year 1989, the cooperation between Mehrtens and myself became more intense, despite the still existing division of Germany. Questions of interpretation came more to the fore in our discussion. In addition to Mehrtens’ empirical work, his more interpretive work also became important to me. I certainly did not want to restrict my part of the project to a pure collection of “facts.” I was impressed by Mehrtens’ 1984 article, published only in German, and entitled “Anschauungswelt und Papierwelt” (World of Intuition versus World on Paper) (Mehrtens Reference Mehrtens, Poser and Schütt1984). Here he pursued the ideological-historical dimension in the transition of mathematics to the Third Reich. The paper contains a reinterpretation of the dispute on the foundations of mathematics (Grundlagenstreit) between intuitionism and formalism, and was a nucleus of Mehrtens’ future book on modernity in mathematics (Mehrtens Reference Mehrtens1990). I was particularly impressed by how Mehrtens—when discussing pre-Fascist ideologies or ideological continuities in general—always spoke in a nuanced manner of historical “possibilities” and “potentials,” and dismissed the idea of necessary connections. In the book and partly already in the 1984 paper, Mehrtens would interpret the anti-Semitism in Bieberbach’s racist “German Mathematics” within the broader framework of the alienation from “Anschauung” and the abandonment of the ontological binding of mathematical objects brought about by modernism. I still feel today that several aspects of the 1984 article, in particular the discussion of the well-known “Forman thesis” about the influence of Weimar culture on physics and mathematics (1971), could have been used with profit for Mehrtens’ book on modernity as well, and would thus have connected the latter more closely to the topic of mathematics under NS.

When preparing our book, Mehrtens and I discussed Bieberbach’s role intensely, and from various angles, in particular his ambiguous and changing position vis-à-vis mathematical axiomatics, and its relation to his seemingly sudden conversion to National Socialism in 1933. In my habilitation thesis (1987), I had discussed the policies and strategies of the classical German reviewing journal Jahrbuch über die Fortschritte der Mathematik (1987), which was heavily influenced by Bieberbach at the Academy of Sciences in Berlin. When looking at the competition between the Jahrbuch and the more modern Zentralblatt from 1931, I found that Bieberbach, and some other more conservative German mathematicians, saw a subliminal connection between the systematic, collecting function of the Jahrbuch and the foundational, rigor-assuring function of mathematical axiomatics. Bieberbach approved of the latter function of axiomatics, but he was suspicious of the creative, expansive functions of axiomatics, as well as of uncontrolled and unsystematic mathematical reviewing. Again, more on the empirical side, I was impressed by Mehrtens’ finding that Bieberbach’s racist and partly intuitionistic “Deutsche Mathematik” lost support within the regime in the second half of the 1930s, once it had fulfilled its function of giving a rationale for the expulsions of Jewish mathematicians, and once pragmatic mathematical work was needed in preparation for the war (Mehrtens Reference Mehrtens and Esther1987b).Footnote ²¹ All this would have found a place in our book.

Although, as described at the beginning, I was looking for new interpretations, and, in particular, had left behind the idealizing and anthropocentric view of science as a “humanistic pursuit of knowledge,” I could not follow Mehrtens in all directions. On December 11, 1988, for example, I wrote to him:

Mehrtens answered me on January 2, 1989, among other things with the following:

Partly reacting to a discussion paper (Mehrtens Reference Mehrtens1988) which Mehrtens had sent me attached to his letter, I ventured a few more objections in a response on January 13, which today, shortly after the Corona pandemic, may again sound reasonable and at the same time once again appear like a futile appeal:

Passages in Mehrtens’ discussion paper like the following had been hard for me to swallow:

But I conceded:

The latter resentment was perhaps related on the fact that the emancipation of women in the GDR was more advanced than in West Germany. I felt myself to be a spontaneous and matter of course “feminist”Footnote ²² and probably for that reason could not quite understand the call for “feminist theory,” although my mother’s experiences had sensitized me to the inequalities that remained in the East as well.

2. Mehrtens’ habilitation thesis on mathematics and modernity and the decline of our project

On June 26, 1989, Mehrtens fulfilled his warning from August of the previous year and sent me the draft of his approximately 400-page habilitation thesis. On September 24, in a first remark on it, I wrote to him along the lines of my previous reservations: “Of course I do not understand the ‘phallic One’ [phallische Eins] and related topics.”Footnote ²³ Previously, on September 15, 1989, I had sent Mehrtens four pages of notes on his manuscript, which was to be published a year later as his book on Modernity in Mathematics.Footnote ²⁴ Among other things, I wrote to him:

It seems to me today that I had partly misunderstood or interpreted Mehrtens too narrowly here, especially with regard to his notion of counter-modernism. Mehrtens himself explained in a later article:

But I presume that some readers understood even less than I did when they read Mehrtens’ Reference Mehrtens1990 book.

With the publication of this book, the collaboration between Mehrtens and myself was essentially over. I should have taken his August 1988 warning more seriously. As late as 2006, he said the following in an interview about the priority he had given to his modernity book:

The remark about historians of mathematics is perhaps somewhat unfair and, at the same time, somewhat at odds with Mehrtens’ own earlier empirical work. The passage in the interview, which should perhaps be taken more as a spontaneous utterance, also contradicts his own vacillation between our project and his habilitation in the late 1980s. But the interview probably does reflect Mehrtens’ gradual alienation from mathematics and the history of mathematics, which had been fostered by some experiences, especially conferences in Oberwolfach.

On December 19, 1999, Mehrtens congratulated me—now by email, of course—on my appointment to Kristiansand in Norway. He then referred to a workshop planned for the end of January/beginning of February 2000 in Oberwolfach, with the title “The History of Mathematics of the 20th Century”: “See you then in O’w’ach. I can’t quite get away from the subject, I keep getting talked into doing something. Well…”

In the discussion, several mathematicians and historians were very critical of this lecture, and regretted the lack of reference to mathematical research work or teaching in the NS, (i.e. any specific reference to “the mathematical” as they understood it). I was no support for Mehrtens in the discussion either. I had a bit of a guilty conscience afterwards and therefore wrote to him one day after the end of the workshop on February 6, 2000:

Mehrtens replied immediately on February 7, 2000:

3. Epilogue

I have been in occasional contact with Mehrtens—from Norway—in the years after 2000. He invited me to a German conference on the history of science in Wittenberg in 2002. There I lectured on the Marxist Dutch-American mathematician and historian of mathematics Dirk Jan Struik (1894-2000), whom we both admired, and whom I had interviewed in Boston in the 1990s.

On September 26, 2011, shortly after his retirement from Braunschweig and resettlement in Berlin, Mehrtens responded to the draft of my biographical essay on the East German historian of mathematics Hans Wußing, who had just died, in the following way:

In this epilogue, I will conclude by saying something about the stimuli that Mehrtens’ theory-driven and empirical historical work of the 1980s—not so much his modernity book, which I may never have properly understood—gave me. In part, I will quote from articles of mine. In one I wrote about Mehrtens’ article, “The Social System of Mathematics and National Socialism” (Mehrtens Reference Mehrtens1987a):

The scientists’ amoral quest for social legitimacy of their research and the rulers’ ruthless search for scientific competence led to alliances that were also visible in the reconstruction of the science system in East Germany after the war, as I stated in an article which was certainly influenced by Mehrtens’ work on the social system of mathematics. There I wrote about a leading German number theorist and his behavior under the NS and in the GDR:

This was also connected to Mehrtens’ discussion of the alleged and self-declared “resistance” of scientists in the Third Reich, by which they meant their rejection of ideological intrusions like Bieberbach’s “Deutsche Mathematik” (Mehrtens Reference Mehrtens and Esther1987b), while in reality they served the system in many ways, particularly during the war (Mehrtens Reference Mehrtens1996a).

Mehrtens and I were convinced that membership in the Nazi party was in itself no real criterion of guilt (though it had been misconstrued as such both in East and Western Germany after the war), and that younger scientists were often forced into formal political loyalty in order not to ruin their careers. This again invited comparisons to science in East Germany:

Mehrtens would approve of careful comparisons between NS and GDR, even given the dangers of anti-communist simplifications as within the theories of “totalitarianism.” He wrote: “The comparison of the GDR and the Nazi state is necessary and meaningful, and a comparison made with awareness shows the differences as well as the similarities, and above all it is aware of the limits of comparability” (Mehrtens Reference Mehrtens1994, 14). I tried to use a nuanced concept of political engagement of scientists, for instance in my biographical studies on Helmut Grunsky, B. L. Van der Waerden, and others who had been one-sidedly accused by other historians and mathematicians of strong involvement in Nazi policies. As far as the international relations of German mathematicians during the NS are concerned, I profited much from Mehrtens’ article on the “Gleichschaltung” (toeing the line) of the DMV, where he showed that “Gleichschaltung” was delayed due to necessary regard for the international relations of German mathematicians (Mehrtens Reference Mehrtens1989a).

On the other hand, existing international contacts of dissenting mathematicians could be used by the Nazis as political arguments against them. Most importantly, international relations were misused to pursue strategies of a German dominance in European mathematics. My own contributions in continuation of our failed project went to a large extent into the direction of an analysis of the international dimension of German mathematics, culminating in my books on refugee mathematicians from NS-Germany (1998, 2009), on Rockefeller and the Internationalization of mathematics (2001), and on the International Congress of Mathematicians in Oslo 1936 (2020).

These are only a few of many inspirations and stimuli which I and other historians gained from Herbert Mehrtens’ research during the 1980s. I leave it to other, more competent writers to analyze the importance and influence of his book on mathematics and modernity. A comprehensive book on mathematics under the NS regime in all its aspects has not been written yet. The valuable book by Segal (Reference Segal2003), which is very much based on previous German publications, focuses on individual mathematicians and less so on institutions, general policies, and mathematical developments. Maybe in the future there will be a renewed effort for such a synthesis, using the work of a younger generation of historians that has since appeared. Personally, I feel safe to say that our, ultimately unsuccessful, project for a book on mathematics during the NS regime helped to prepare the ground for critical studies of the social and political history of mathematics during a difficult and crucial period for Germany and the world.