ESHS/HSS Annual Meeting

Diagrammatisation of computations in the Bakhshālī manuscript: some reflections on formalism, symbolical notations, and proofs.

• In Event: Diagrammatic Computations and Their Symbolic Aspects (III)

English Abstract

South Asian medieval Sanskrit mathematical commentaries— which were transmitted by continuous copy— testify to the use of ephemeral numerical tables representing the executing of different arithmetical and algebraical computations. How formal were these executions? What kind of inscriptions and notations did they use? Can these diagrammatized computations be considered as a kind of mathematical symbolism? This presentation will raise these questions in a specific case study. The Bakhshālī Manuscript is an exceptional mathematical text for South Asia, because it was excavated in 1881, in what is now the North East of Pakistan. This birch-bark manuscript is approximatively dated—with some controversy— from the 8th to the 10th century. It is written in “middle-indic”, a variation of classical Sanskrit. It has many modes of representing computations. It contains multiple proofs (pratyaya). It uses tabular variations as a form of explanation. In this presentation these early testimonies of practices of diagrammatized computations in South Asia will be analyzed questioning whether they can be understood as a kind of mathematical symbolism.

Author

• Agathe Keller, LTE, HSA, CNRS & Observatoire de Paris