Philosophical Thought in Ancient Chinese Mathematics-- A Study of Confucianism in The Nine Chapters on the Mathematical Art and Liu Hui’s Commentary

This paper examines the ontological and epistemological ideas found in The Nine Chapters on the Mathematical Art (Jiuzhang suanshu) and Liu Hui’s Commentary, clarifying the fundamental principle of "action precedes knowledge" in ancient Chinese mathematical thought from the perspective of the philosophy of mathematics. The study further compares this Chinese mode of thinking with Western mathematical ontology, focusing on methods explored in Liu Hui’s Commentary, such as the "Jinyou Rule" and Liu Hui’s π algorithm . These approaches are contrasted with Western methods, including Archimedes' "double reductio ad absurdum," to illuminate the unique role of "action precedes knowledge" within Chinese ontological philosophy. Through this comparison, the paper highlights the distinct philosophical foundations underlying Eastern and Western approaches to mathematics.