Wu Jing (mathematician)

Jiuzhang Suanfa Bilei Daquan originally contained nine chapters excluding the "table of contents" chapter. After a fire destroyed many printing woodblocks, Wu Jing's grandson Wu Ne (吳訥) added some materials as he prepared the manuscript for re-printing. Currently, there are at least four extant copies from the Ming dynasty, housed separately in four libraries in Beijing and Shanghai.^[3]

Every chapter begins with a topic from an "ancient" mathematical book, followed by Wu Jing's explanation of how real-life problems are solved with arithmetics.^[4] For example, in the first chapter, "Land" (方田), Wu described how to approximate land areas of different shapes and included 214 problems.^[5]

Because he was concerned with real-life problems, Wu Jing often preferred approximations over exact solutions.^[6] The Ming-period mathematician Cheng Dawei criticized Wu's work as "disorganized and containing numerous mistakes" in his Suanfa tongzong (1592). The Qing-period scholar Mei Wending, however, considered Wu's work superior to Suanfa tongzong.^[7]

Wu did not come up with new ways of solving older problems; he did, however, invent new methods of using the abacus.^[8] He also proposed using colors and visualization to solve math (especially geometric) problems, which may have influenced Chinese cartography.^[9]

The modern mathematician Qian Baocong noticed several identical arithmetic methods in Wu's work and the slightly later Treviso Arithmetic (1478).^[10]

• Lao Hansheng (劳汉生) (1999). "吴敬《九章算法比类大全》" [Wu Jing's Jiuzhang Suanfa Bilei Daquan]. In Li Di (李迪) (ed.). 中国数学史大系，第六卷：西夏金元明 [Compendium of the History of Chinese Mathematics, Volume Six: Western Xia, Jin, Yuan, and Ming] (in Chinese). Beijing Normal University Press. pp. 330–345. ISBN 7-303-04927-4.