The 數 Shu (Mathematics): a Qin-dynasty work on bamboo and wooden slips from ancient China—transcription and English translation with commentary

Abstract

In 2007, a trove of bamboo and wooden slips clandestinely smuggled out of China was sold to the Yuelu Academy of Hunan University by a Hong Kong cultural relics dealer. The following year, another small number of slips that later proved to belong to the same group were also donated to the Academy. These slips are believed to date from no later than 212 bce. Among the documents conveyed to the Yuelu Academy is a mathematical text, the 數 Shu (Mathematics), a character that appears on the verso of slip 01(0956) and generally regarded as the title of this work. The problems in the Shu can be divided into eleven distinctive types, namely: areas, fractions, military encampments, norms, grain conversions, proportional distributions, shao-guang ([method for] slightly [increasing] widths), volumes, excess and deficiency, right triangles (gou-gu), and taxation. The original collators of the Shu published photographs of a majority of the Shu slips along with transcriptions and notes concerning their contents in 2011; the rest appeared in 2022. In the course of the research presented here, each character on the Shu slips has been individually examined, special scribal marks have been identified, and their functions are explained. Also, each Chinese sentence has been carefully punctuated, resulting in a more readable version of the Chinese text. In what follows, the Shu is translated into English for the first time, with corresponding notes to help readers better understand the context of the Shu as well as many of the paleographic, philological, and various technical details necessary for a correct understanding of the translation. This work serves as a window into the evolution and development of Chinese mathematics during the pre-Qin and Qin periods, and thereby reflects the state of ancient Chinese mathematics at that time.