What kind of mathematical research activities took place in prisoner of war camps in Germany during the Second World War? And can one inspect such activities in order to re-examine, on the one hand, Herbert Mehrtens’ analysis of the modernism/counter-modernism divide of early twentieth-century mathematics, and on the other, his research on the instrumentalization of mathematics during the war? Closely examining the work carried out in the field of algebraic geometry by the French mathematician Bernard d’Orgeval, who was held in three of such camps between 1940 and 1945, the paper aims not only to unfold this unique episode in the history of mathematics, presenting it as an ephemeral configuration, but also to show the limitations of Mehrtens’ approach and the narrative of modern and counter-modern mathematics.

This essay takes inspiration from Herbert Mehrtens’ 1995 claim that the “history of mathematics is an integral part of intellectual history.” It asks why, despite the tremendous transformation the historiography of mathematics has undergone since the field began to professionalize in the 1970s, historians of mathematics repeatedly complain that their field has been marginalized. The answer, I suggest, is not due to the fact that mathematics is less amenable to the types of social, cultural, or material analysis that came to dominate the history of science in recent decades. Rather, at issue is that most historians have adopted mathematicians’ own definition of mathematics. The history of mathematics professionalized at a particular moment, one in which mathematicians were concerned about the limits and boundaries of their field. As such, they were invested in drawing boundaries around the “proper” confines of the field. Historians of mathematics have followed suit, and similarly restricted what did and did not belong in the history of mathematics. Following Mehrtens, however, and insisting that the history of mathematics is an integral part of broader intellectual history, a more capacious conception of the field is possible.

By breaking decisively with the predominantly apologetic and hagiographic literature on science during National Socialism and employing compelling terms such as “irresponsible purity” and “collaborative relations,” Herbert Mehrtens profoundly influenced both his contemporaries and the subsequent generation of historians working in this field.

Herbert Mehrtens‘ work and the implications of the historical ideas he advanced went beyond the history of any single discipline. The article therefore addresses three broad issues: (1) Mehrtens‘ reconceptualization of mathematical modernism, in his field-changing book Moderne—Sprache—Mathematik (1990) and other works, as an epistemic and cultural phenomenon in a way that could potentially reach across and also beyond the sciences and also link scientific and cultural modernisms; (2) the extension of his work to the history of modernity itself via the concept of “technocratic modernism”; (3) his seminal contributions to the historiography of the sciences and technology during the National Socialist period, focusing on his critique of claims that mathematics, the natural sciences and technology were morally or politically “neutral” during or after the Nazi era, and on his counter-claim that mathematicians and other scientists had in fact mobilized themselves and their knowledge in support of Nazism’s central political projects. Taken as a guide for understanding science-politics relations in general, Mehrtens‘ work was and remains a counterweight to the political abstinence adopted by many who have followed the “cultural turn” in history of science and technology. In the broadest sense, the article is a plea for the culturally relevant and politically engaged historiography of the sciences and humanities that Mehrtens himself pursued.