The interplay between textual procedures and material operations from the viewpoint of Chinese mathematical texts

For more than 2,000 years, counting rods were the main tool used in Chinese mathematics. However, direct evidence for their use is lacking. The current evidence is primarily derived from two sources: procedural texts in ancient mathematical writings and counting diagrams drawn with rod signs in thirteenth-century writings. This study analyzes the procedural texts in two ancient Chinese mathematical books: 1) The Nine Chapters on Mathematical Procedures, completed by approximately 100 BCE or 100 CE, and 2) the Mathematical Canon by Master Sun, completed by approximately 400 CE. This article argues that the differences between the texts insufficiently explain the fundamental differences in the operations that could be performed with mathematical rods. Further, by examining two mathematical books from the thirteenth century, namely the Mathematical Book in Nine Chapters written by Qin Jiushao in 1247 and Fast Methods on Various Categories of Multiplication and Division of Areas of Fields written by Yang Hui in , this article argues that the relationships between counting diagrams and their accompanying text vary depending on the author, thereby highlighting authors' different epistemological perspectives. Examining the historical context is essential for understanding the relationship between procedural texts and material operations and for developing new methods to investigate the use of counting rods.