2026 Theses Doctoral

Polygons and Polyphony: Traditions of Arabic Mathematics across the Post-Classical World

Tomasson, Julia C.

This dissertation asks how the textual polyphony in post-classical Arabic mathematical texts—so evident in the archive and the materiality of these texts—was gradually taken to be a chorus of Greek mathematics, and what that process reveals about the making of claims to universality itself. Drawing upon new directions in post-classical intellectual history that seek to move beyond “decline” narratives, this dissertation examines manuscripts of post-classical commentaries on Euclidean (and non-Euclidean) geometry that have previously been largely read for Greek mathematics (or classical Arabic innovations on Greek mathematics) or as evidence of pedagogy rather than research.

Rather than focusing on who got what proof, where, when, and how, I instead focus on the epistemological practices embedded in these texts and their use, and on how we might trace divergent ideas of logos and non-logocentrism in mathematics. I argue that in the post-classical period (as opposed to the classical period), Arabic mathematics continued to evolve enmeshed in distinctly non-Greek (post-Avicennan) epistemologies of mathematics with shared epistemic and discursive practices with the Islamic “rational” sciences (i.e., rational theology, jurisprudence, dialectic, logic, etc.). These were dynamic, generative, and polyphonic traditions of knowledge that were nonetheless productive on their own terms.

This polyphony was obscured and ultimately (trans)muted into a monophonic history of mathematics through the reception of these texts by early modern European scholars, who read them through the lens of their own emerging ideas about proof, texts, and history that have shaped our understandings to this day. Arabic mathematical manuscripts were feverishly collected by early modern European scholars and fruitfully misread as they reconfigured notions of antiquity and mathematical progress that were “universal” but culturally European in the process. The material-textual processes by which these manuscripts became illegible led to their eventual omissions from the history of mathematics. Ultimately, mathematical innovations from the Islamic world were appropriated without attribution by European scholars, while they adopted new ideals of things like mathematical “genius” that excluded their Islamic predecessors.