Mathematical Study and Intellectual Transition in the Early and Mid-Qing

Abstract

��� The study of mathematics in the seventeenth century was part of the intellectual movement of practical (shixue), with statesmanship and scientific knowledge at its center, and mathematics its foundation. However, this program of learning was gradually narrowed by the evidential scholarship of the eighteenth century, and mathematical study was limited to rediscovering the lost mathematical astronomy of the past. Modern scholars have examined this intellectual shift from different perspectives. Yu Yingshi looks into the evolution of ideas from the mid-Ming to the Qing, contending that evidential scholarship was an inevitable result of the internal crisis in Ming-Qing classical learning.1 Yet Yu's explanation does not help us understand mathematical culture in the early and mid-Qing, and its relationship to this intellectual movement. Historians of Chinese science study the early and mid-Qing mathematical culture mainly from the perspective of its scientific progress, even though some discussions are concerned with the connections between mathematical study and classical learning.2 Jonathan Porter uses Ruan Yuan's Chouren zhuan (Biographies of Mathematicians and Astronomers) as a relatively complete population of specialists in the exact sciences, to explain China's characteristic pattern of scientific activity.3 However, his interpretation is too modernist to reveal the nature of chouren. Indeed, modern scholarship has not paid much attention to such questions as: Who were Qing chouren! How did they relate to each other? How did their activities in mathematical study connect formal education and the transformation of Qing scholarship? Based on the Chouren zhuan, this article will examine the change in the concept of chouren, and the characteristics