ESHS/HSS Annual Meeting

Between Greek Tradition and Indo-Arabic Innovation: Reassessing Byzantine Algorithmic Culture

• In Event: Pluralizing the Heritage: Ancient Authors Between Transmission, Contestation, and Reinvention

English Abstract

This paper examines Byzantine algorithmic practices through a case study focused on the partial and selective reception of Indo-Arabic numerals and calculation methods in Byzantium following their introduction in the thirteenth century, notably by Maximos Planudes. Often described as a mere “delay” in comparison with the Latin West, the adoption of algorismic calculation in the Byzantine world has long been interpreted within a teleological narrative of mathematical progress. Yet a close analysis of the manuscripts reveals a far more complex landscape, in which coexistence, hybridization, and epistemic resistance play a central role.
In his treatise, Planudes presents the “Indian numerals” and the rules of positional decimal calculation, but situates them within an intellectual horizon still dominated by the Greek mathematical tradition. The text suggests a theoretical appropriation of the new techniques rather than a widespread practical adoption: Planudes’s detailed explanation of the Indo-Arabic system contrasts with the near absence of evidence for its effective use in Byzantine administrative or commercial contexts. This case study invites us to reconsider the Byzantine reception of algorism not as an “incomplete” stage, but as a space of negotiation between multiple worlds of knowledge. It highlights the ways in which Byzantine mathematical culture resists homogeneous narratives of technical progress and shows how necessary a change of perspective is for understanding the plural and often contested forms of medieval scientific transmission.
The paper offers an examination of this plurality through the study of manuscripts copied between the thirteenth and fifteenth centuries. It presents hybrid layouts combining algorismic columns with Greek numerical signs, local adaptations of multiplication rules, and marginal glosses in vernacular Greek that reshape procedures to meet specific pedagogical needs. These traces allow us to recover the contributions of scribes, teachers, and anonymous calculators whose situated practices have long been rendered invisible by canonical readings focused on a handful of authors.

Author

• Carole Hofstetter, SPHERE, CNRS, Université Paris Cité