Knowing Number: Mathematics, Astronomy, and the Changing Culture of Learning in Middle-Period China, 1100-1300

Abstract

This dissertation seeks to integrate the history of mathematical knowledge in middle-period China with the history of its learned culture. It challenges the traditional historiographic image of Chinese mathematics and astronomy as socially and epistemically isolated enterprises, and argues that their significant development in the twelfth and thirteenth centuries was in deep connection with the primary programs of learning for the literati and for those who aspired to become one of them – reading texts and comprehending tradition. In so doing, the study stresses the overlapping ventures of knowledge making under the broad rubric of “number” (shu 數) and the communication between divergent intellectual groups in a time when the hierarchy of “learning” (xue 學) was flexible and contestable.

This dissertation is divided into two parts, each in turn consisting of two chapters in the form of case studies. Part I mainly focuses on mathematics in the Southern Song (1127-1279), highlighting the connected endeavors of mathematicians and literati in the making and application of numerical knowledge largely outside of state sponsorship or control. Part II turns to Chinese mathematical astronomy under the Mongol Empire (1206-1259) and the early Yuan dynasty (1271-1368), featuring a stronger presence of political power as well as cross-cultural elements.

In the first part, chapter 1 analyzes and compares three Southern Song publishers of mathematical books, who belonged to divergent social groups of literati and practitioners but displayed parallel efforts to make mathematical knowledge more accessible through printed texts. Chapter 2 discusses literati scholars’ and mathematicians’ shared engagement with numerical problems related to milfoil divination and the Classic of Changes (Yijing 易經).

In the second part, chapter 3 looks into the uses of textual investigations in the calendar reform of the Yuan around 1280, highlighting the astronomers’ precise choice of hermeneutical stance and its relation with contemporary classical scholarship. Chapter 4 examines the Chinese study of meridian differences in the Eurasian context and shows how contacts with Islamic knowledge brought about a new spatial as well as cultural awareness in the Chinese conception of astronomical knowledge.