Michael Friedman

The use of AI-based technologies is reshaping mathematics in ways that extend but also strain the classic Big Science analogy. As in Big Science, the new AI-based mathematical work relies on concentrated computation, specialized and hierarchical teams, sociopolitical justification, and large-scale collaboration. But AI also changes how epistemic labor is distributed and attributed: Systems now generate constructions, explore proof spaces, and formalize arguments, prompting mathematicians to renegotiate how credit, authority, and accountability are assigned across hybrid human–machine assemblages. This reconfiguration redistributes epistemic authority toward corporate labs and elite hubs that control models, data, compute, and narrative, thereby gating which problems appear tractable and legitimate. Analyzing four dimensions (resource concentration, division of labor, political embedding, and collaboration), and examining recent cases, we argue that AI-based mathematics constitutes a novel sociotechnical regime we call ‘Big AI Mathematics’, in which truth claims are increasingly mediated by opaque pipelines and institutional power, making the future of mathematical knowledge as much a governance problem as an epistemic one.

During the seventeenth century there was an increased interest in artisanal practices on behalf of European natural philosophers, which manifested itself also in examining textiles and textile-related practices mathematically. Were these reflections only an attempt to record artisanal knowledge, or rather to extract from it mathematical reasoning that the practitioners did not know how to formulate? The paper will examine the manuscripts of Daniel Krüger and Gottfried Wilhelm Leibniz, dealing with arithmetical calculations done in the course of yarn winding and warping. While these texts had different aims and their writings appeared against different social and economical backgrounds, both scholars aimed not only to show explicitly the arithmetical rules governing the practices of winding and spinning, but also to prompt the externalization of such artisanal knowledge.

Which metaphors can be employed to account for a crisis of sexuality? And how is mathematics even related to such a crisis? At the end of the 18th century, Rousseau viewed mathematics as a “safe place” which should be protected from such crises of sexuality. At the beginning of the 20th century, Freud highlighted the contrary, presenting mathematics as a “treacherous space” where such crises could very well erupt. To analyse this metaphorical transition, I will turn to Hans Blumenberg, whose theory reveals Rousseau’s and Freud’s works as background metaphors, which also operated in 19th century mathematical discourse. Blumenberg himself reflects on this transition via the shipwreck metaphor, which was also adopted by Freud and Rousseau, albeit in other frameworks.

One of the well-known medieval mathematical treatises written in Hebrew is Rabbi Abrahambar Ḥiyya’s Ḥibbur ha-Meshiḥah ve-ha-Tishboret, composed between 1116 and 1145. The Ḥibbursurvives in (at least) eight manuscript copies, produced between the fourteenth and the sixteenthcenturies, as well as in a Latin translation titled Liber embadorum, made in 1145 by Plato of Tivoli.Of the latter, five extant copies from the fifteenth and the sixteenth centuries are known. While theLatin translation adheres to the general structure of the Ḥibbur, it also exhibits specific changesthat are indicative of the historical development of both the Hebrew and the Latin texts. By focusingexclusively on the extant manuscripts – rather than on any endeavor to (re)construct a history ofthe Urtext, whether in Hebrew or Latin – one can observe not only various omissions, comments,and notes added to the various copies, but also that such changes modify the character of the text,rendering it less or more practice- or theory-oriented.What do these additions and omissions reveal about how mathematical texts were regarded in thefourteenth to sixteenth centuries? Can we draw conclusions about how these texts were read, copiedand used? To answer these questions, this paper examines three sections of the Ḥibbur and Liberembadorum, all of which concern the study of the division of geometric figures. I argue that a refinedtypology of the additions, omissions, added notes, comments and diagrams can help us to see thesemanuscripts not as ‘copies’ of an ‘original text’, but as complex mathematical written artefacts intheir own right, each with unique characteristics.

What was Leibniz’s approach to artisanal knowledge? And how did he consider it with respect to mathematical, and more concretely, to geometrical knowledge? On the one hand, Leibniz emphasizes several times in his writings that one should extract “secrets and inventions” from the artisans. On the other hand, Leibniz points out that such artisans cannot formulate by themselves the geometric principles at the base of their machines. In this paper, we examine these intricate relations between Leibniz’s reflections on artisans, especially clockmakers and textile workers, as well as his thoughts on mechanical and geometric knowledge. Leibniz’s considerations of various artisanal machines, like clocks and looms, lead us to discuss his wish to expand geometry, presenting these machines as embodying a “secret,” “hidden,” or even “deeper” or “more profound” geometry.

How can metaphors account for the formation of mathematical concepts, for changes in mathematical practices, or for the handling of mathematical problems? Following Hans Blumenberg’s thought, this paper aims to unfold a possible answer to these questions by viewing the metaphorical frameworks accompanying these changes as essential for an understanding of how changes in mathematical practices have been accounted for. I will focus especially on cases in which these changes were caused by encounters with a mathematical object which did not yet have a well-defined concept, but also show that such indeterminacy remains with the mathematical concept even after it is considered ‘well-defined’. As the paper will show, this ‘forefield’ [Vorfeld] of the concept is addressed by Blumenberg’s account of metaphorology on the one hand, and accompanied by his later account of nonconceptuality [Unbegrifflichkeit] on the other hand. While Blumenberg himself did not develop a full-fledged philosophy of mathematics or of mathematical practices, I aim to show that one can nevertheless extract from his writings a unique position concerning the role metaphors play in mathematics. To this end, Blumenberg’s account of nautical and oceanic metaphors and Alexandre Grothendieck’s philosophy of mathematical practice provide fruitful starting points.