Different clusters of text from ancient China, different mathematical ontologies

Abstract

Sources attesting to mathematical activities in ancient China form at least four distinct clusters of texts, bespeaking at least four different—though overlapping—ways of practicing mathematics. I will focus on two such sets of documents: the canons that in the seventh century constituted one of the two curricula taught in the Imperial “School of Mathematics,” and manuscripts recently excavated from tombs sealed in the last centuries BCE. I will argue that these two sets of documents testify to two different ways of practicing mathematics, which related to different material practices. Accordingly, we can perceive that mathematical objects were shaped and explored in different ways, with significant consequences for the knowledge produced.