ESHS/HSS Annual Meeting

Diagrammatic Computations and Their Symbolic Aspects (I)

Session Submission Type: Organized Session

English Abstract

Diagrams and their concomitant practices have been a focal point in the historiography of mathematics over the past couple decades, but most typically in the geometrical context. Here, we propose to approach diagrammatization from a different perspective, namely, computation and the forms of symbolism deployed in the carrying out of computations and algorithms. This symposium is intended to dovetail with an ongoing collective project, housed at The School of Mathematics in Edinburgh, to rethink the history of mathematical symbolism. In this endeavor, we have tried to move beyond a history of symbolism that begins with—or equally, that leads to—Viète’s algebraic notation and instead to develop an approach in which Viète figures as but one juncture in a much longer, and more global, history of symbolic practices. Within this broader framework, we wish to focus the symposium on those aspects of mathematical symbolisms that, in their form and use, make them closer to diagrams than to linguistic signs. In other words, we will explore how notations and inscriptions in computational work make use of diagrammatic reasoning independent of language. The symposium will consist of a series of three panels, with participants focusing on sources in Arabic, Chinese, Japanese, and Sanskrit.

Sub Unit

• Organized Session

Chair

• Célestin Xiaohan ZHOU, The Institute for the History of Natural Sciences, Chinese Academy of Sciences

Individual Presentations

• Diagrammatizing computations in Chinese and Arabic sources: From decimal place-value numeration systems to place-value notations for polynomials - Karine C. C. Chemla, University of Edinburgh and SPHERE, CNRS-UPC

• From Zhu Shijie to Seki Takakazu: transforming the calculating-rod notation into the side- writing notation - Stephen HUNG, SPHERE-CNRS, Université Paris Cité

• A Study on the Correlation Between the Symbolic System and Innovative Achievements of Japanese Mathematics - Rina Sa

Session Organizers

• Zehra Bilgin, University of Edinburgh & Istanbul Medeniyet University

• Alex Garnick, Harvard University