ESHS/HSS Annual Meeting

Reconsidering the Qilüshu (其率術) Problems in Early Chinese Classical Mathematics: Focusing on Recently Unearthed Qin and Han Bamboo Manuscripts (秦漢簡牘算書)

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

English Abstract

In early Chinese classical mathematics, there is an algorithm known as the Qilvshu 其率術 (rule of its rate), recorded in the Sumi 粟米 chapter of the transmitted mathematical classic九章算術 Jiuzhang sunashu (Nine Chapters on the Art of Mathematics). Scholars have long debated the mathematical nature of the Qilvshu problem, particularly whether it represents an indeterminate equation (不定方程). In recent years, several previously unknown mathematical texts on bamboo slips have been unearthed, including the Suan shu B (算書乙種 among the Peking University Qin manuscripts (北大秦簡) and the Arithmetic (算術) text from the Shuihudi Han manuscripts (睡虎地漢簡), which contain content directly related to the Qilvshu problem.Building upon earlier research, this study reexamines Qilvshu by integrating these newly discovered sources with the corresponding section of The Nine Chapters, offering new insights into its algorithmic structure and mathematical reasoning. It further explores the possibility of interpreting Qilvshu as a specific form of indeterminate equation. Moreover, based on these Qin and Han mathematical manuscripts collectively, this paper conducts a preliminary comparative analysis with Diophantine equations (丟番圖方程) in ancient Greek mathematics, aiming to illuminate distinctive modes of mathematical thought and problem-solving strategies in early civilizations from a cross-cultural perspective in the history of mathematics.

Author

• Qingzhuo XIA, Institute of Mathematics, Chinese Academy of Sciences, Beijing, PRC