The motivation, methods and ideological origins behind the formulation and demonstration of Liu Hui's Principle

Liu Hui's Principle is the cornerstone of volume theory in ancient China. The proposal and demonstration of the principle resulted from Liu Hui's strong pursuit of mathematical demonstration in the specific social and cultural environment of the 3rd century CE. Liu Hui's demonstration can be divided into two stages. The first stage is a mathematical process involving finite steps. Liu Hui used blocks to perform the division and recombination of geometrical solids, employing the out-in principle, the concept of solid similarity and the method of cyclic recurrence—all of which originated from the early ancient Chinese mathematical tradition focused on algorithms. The second stage involves an infinite process. Liu Hui drew on the ideological methods of the Taoist and Mohist schools, and in particular used the thought of connecting ‘Being’ and ‘Nonbeing’ from the ‘Autumn Flood’ chapter of Zhuang Zi to handle the infinite process and its results, reflecting the application value of the Chinese philosophical tradition in mathematics. The demonstration of this principle indicates that the mathematical tradition and philosophical tradition in ancient China can be effectively combined. Among the many factors leading to this achievement, the most crucial are Liu Hui's personal abilities and qualities, while other factors such as the existing mathematical and philosophical traditions, as well as the social environment and cultural trends of Liu Hui's time, are also indispensable.