Changing Mathematical Cultures, Conceptual History, and the Circulation of Knowledge: A Case Study Based on Mathematical Sources from Ancient China

This chapter is devoted to the conceptual history of “quadratic equation” in China between the first and the eleventh centuries. It argues that conceptual history must rely on a description of how practitioners worked with various elements in their mathematical activity—here mainly problems, algorithms, computational tools, and diagrams. The uses of these elements establish connections among them, forming complexes of practices to which the author refers as “mathematical cultures.” She argues that describing the mathematical cultures in the context in which practitioners actually operated provides essential tools for interpreting sources. The author identifies different mathematical cultures in China during the time span considered that display both continuities and transformations in mathematical practice. In each of these contexts, the concept of equation identified correlates with both computational tools and ways of working with diagrams. This approach highlights material dimensions of conceptual history.