ESHS/HSS Annual Meeting

Early Chinese Mathematical Achievements Reflected in the Unearthed Arithmetical Books of the Qin and Han Dynasties

• In Event: Recent Archaeological Excavations: New Light on Ancient Chinese Mathematics 2

English Abstract

Mathematics was the most developed basic discipline in ancient China, and arithmetical books served as crucial carriers and direct records of the early history of mathematics. Among the arithmetical documents from the Pre-Qin, Qin, and Han periods, only The Nine Chapters on Mathematical Procedures (Jiuzhang suanshu 九章算術) has been handed down to the present day. In recent years, there has been a spurt of discoveries of unearthed arithmetical documents, propelling research on the early history of Chinese mathematics into a new stage. The complete set of unearthed arithmetical books includes: Suan shu shu 算數書 on the Han Dynasty bamboo slips from Zhangjiashan 張家山, Shu 數 on the Qin Dynasty bamboo slips in the collection of Yuelu Academy 岳麓書院, Suan shu 算書 on the Qin Dynasty bamboo slips in the collection of Peking University 北大, and Suan shu 算術on the Han Dynasty bamboo slips from Shuihudi 睡虎地. The first three have been fully published, while more than half of the Suan Shu (Arithmetic) has been released, and a complete report will be officially published soon. Taking several specific algorithms commonly found in these arithmetical books—such as the Li tian shu 里田術, lü 率-related arithmetic problems, and the circumference ratio (pi)—as examples, this paper explains the characteristics of Qin and Han arithmetical algorithms, including empirical algorithms, trial algorithms, and mechanical algorithms, and demonstrates that early Chinese mathematics possessed both a high level of theory and practical attributes.

Author

• Jingnan TAN, Jianghan University, Wuhan,. PRC