Translations and interpretations of mathematical works in ancient China: A case study of Liu Hui's commentaries on <i>The Nine Chapters</i>

This paper explores the translation and interpretation of ancient Chinese mathematical texts, with a focus on Liu Hui's commentary on The Nine Chapters on Mathematical Procedures (hereafter The Nine Chapters ). Since the mid-19th century, European missionaries and sinologists have gradually introduced Chinese mathematical texts to Europe through various translations, a process that attracted increasing scholarly attention in the 20th century. The Nine Chapters , along with Liu Hui's commentary, has been one of the most translated and studied works, although in-depth research and translations of Liu Hui's work began to increase gradually only after the 1970s. The paper examines the challenges of translating ancient mathematical terms and concepts, highlighting the importance of maintaining terminological consistency to reflect the original mathematical ideas. Various translation strategies are discussed, each revealing differing scholarly approaches and perspectives. Examples of different translations of Liu Hui's terminology and his explanations illustrate how translators made their choice between historical accuracy and modern understanding. Through detailed analysis of specific mathematical problems and their translations, the paper underscores the richness and complexity of the meanings implied in Chinese mathematical text and the challenges of faithfully translating the subtle ideas. Ultimately, the paper argues that translations that try to carefully preserve the terminological features and textual structure can serve as valuable research tools, deepening our understanding of the algorithms and proofs in ancient Chinese mathematical texts.