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MATHEMATICAL STUDY AND INTELLECTUAL TRANSITION IN THE EARLY AND MID-QING* Limin Bai The study of mathematics in the seventeenth century was part of the intellectual movement of "practical learning" (shixue), with statesmanship and scientific knowledge at its center, and mathematics as 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 *I would like to thank Mrs. Sheila Davies for her assistance in writing English. Thanks also go to Dr. Tom Fisher, Dr. Paul Rule, and Dr. Lotte Mulligan of La Trobe University, for their guidance in the course of research. In addition, I am indebted to two anonymous readers, whose comments on the first draft helped me reshape and improve this article. 1Yu Yingshi 1977:124-50. 2Such as Horng Wan-sheng 1991, 1993a, and 1993b. 3Porter 1982:530, 533. Late imperiai China. Vol. 16, No. 2 (December 1995): 23-61 23 24Limili Bai of chouren in the Kangxi reign (1662-1722) and the Qian-Jia period (17361820 ). From this specific analysis, the article attempts to throw light on the formation and change of the characteristic pattern of chouren against the background of the intellectual change from seventeenth-century practical learning to eighteenth-century evidential scholarship. The Concept of Chouren Chouren referred to people who were well versed in mathematics and astronomy . Between 1799 and 1898, Ruan Yuan (1764-1849) and other Qing scholars compiled and edited the Chouren zhuan, a collection of biographies of chouren throughout Chinese history.4 The title of the book had its origin in a sentence in the Shiji (Historical Records): "The descendants of the chouren were scattered."5 The term chouren here referred to special officials in the Zhou involved in astronomy and computing the calendar. This occupation was passed from generation to generation in a family. According to Tan Tan's textual research, the term chouren could refer to people: (1) who had a career in the astronomical or calendrical bureau which had been continued in their families for many generations ; (2) who were familiar with calendrical science, learning normally passed on from fathers to sons; (3) who were regarded as mathematicians;6 (4) who were employed by the government; (5) who were engaged in farming (because the root of the character chou is "peasants" or "farmers," and farming as a career in agricultural China was handed down from generation to generation); or (6) who were musicians.7 Tan T'ai's gloss of "chouren" indicates that the term appeared in historical documents in a very broad sense. However, the basic characteristics of chouren were that: (1) their occupations were handed down from generation to generation within the family; and (2) they earned a living by using skills. The concept of chouren underwent a significant change in the late Ming 4For a general introduction to the book, see Crossley and Lun 1987...

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