The paper is based on a hitherto unexplored document (audiotape of an interview accompanied by a German transcript) from 1953, located in the Freud Papers at the Library of Congress. It contributes to a better understanding of the impact of Freud and of Psychoanalysis on personalities from the exact sciences, here represented by the noted applied mathematicians Richard von Mises and Hilda Geiringer from Vienna. The detailed discussion of the interview sheds some new light on the different roles of Kraus and Freud in the Vienna culture, on the Vienna Jugendkulturbewegung (youth culture movement) during WWI in which Geiringer was involved, on Freud’s and Siegfried Bernfeld’s standing around 1930 among German philosophers and psychologists, and on Wilhelm Fließ’ theory of periodicity, which von Mises—based on his attitude as an applied mathematician—defended against superficial accusations. Finally, new biographical material is provided for von Mises and the remotely related Freud family, and for Geiringer’s and von Mises’ early lives. The interview, which was taken during the Cold War, also allows conclusions as to how politics influenced the memories and views of the participants. Part of the aim of the paper is historical documentation of unknown material (letters by Karl Kraus and Wolfgang Köhler, one book review by Wilhelm Ostwald, a file on Richard Pfennig), including some correction of erroneous information in the literature.

The Fourth Postulate of Euclid’s Elements states that all right angles are equal. This principle has always been considered problematic in the deductive economy of the treatise, and even the ancient interpreters were confused about its mathematical role and its epistemological status. The present essay reconsiders the ancient testimonies on the Fourth Postulate, showing that there is no certain evidence for its authenticity, nor for its spuriousness. The paper also considers modern mathematical interpretations of this postulate, pointing out various anachronisms. It further discusses the validity of the ancient proof by superposition of the Fourth Postulate. Finally, the article proposes an interpretation of the history of the concept of angle in Greek geometry between Euclid and Apollonius, and puts forward a conjecture on the interpolation of the Fourth Postulate in the Hellenistic age. The essay contributes to a general reassessment of the axiomatic foundations of ancient mathematics.

In this paper, we wish to explore the role that textual representations play in the creation of new mathematical objects. We do so by analyzing texts by Joseph-Louis Lagrange (1736–1813) and Évariste Galois (1811–1832), which are seen as central to the historical development of the mathematical concept of groups. In our analysis, we consider how the material features of representations relate to the changes in conceptualization that we see in the texts.

Against this backdrop, we discuss the idea that new mathematical concepts, in general, are increasingly abstract in the sense of being detached from material configurations. Our analysis supports the opposite view. We suggest that changes in the material aspects of textual representations (i.e., the actual graphic inscriptions) play an active and crucial role in conceptual change.

We employ an analytical framework adapted from Bruno Latour’s 1999 account of intertwined material and representational practices in the empirical sciences. This approach facilitates a foregrounding of the interconnection between the conceptual development of mathematics, and the construction, (re-)configuration, and manipulation of the materiality of representations. Our analysis suggests that, in mathematical practice, distinctions between the material and structural features of representations are not permanent and absolute. This problematizes the appropriateness of the distinction between concrete inscriptions and abstract relations in understanding the development of mathematical concepts.