Observing mathematical practices as a key to mining our sources and conducting conceptual history. : Division in ancient China as a Case study

Une version révisée est parue dans Léna Soler, Sjoerd Zwart, Michael Lynch & Vincent Israël-Jost (eds.), Science after the Practice Turn in Philosophy, History, and the Social Studies of Science, Routledge (2014), p. 238-268.International audienceThrough a case study devoted to mathematical work done on operations in ancient China, we show how the description of practices can be essential to carry out conceptual history, in particular when we rely on sources that document theoretical work only indirectly. We first explain how the classic book The Nine Chapters on Mathematical Procedures (1st c. CE) bears witness to actors possessing at the time a quite complex and elaborate knowledge about a set of operations, in which division played the central part. To achieve this, we develop a close analysis of clues taken from actors' practices of terminology, practices of writing down texts for algorithms and practices of computing. Then, we derive, through a comparison with older texts, insight into the historical processes that led to the shaping of this knowledge. As a result, we show how The Nine Chapters bears witness to a radical shift in the understanding of, and practice with, the set of operations examined. At the end of the chapter, we offer some reflections on the part the study of practices can plan in conceptual history: far from being opposed to the results, practices can be considered as belonging to the knowledge produced in the framework of a knowledge activity