A new perspective on Liu Hui's mathematical achievements

Liu Hui is a seminal figure in the history of Chinese mathematics. In 263 CE, he commented on The Nine Chapters on Mathematical Procedures ( Jiuzhang Suanshu 九章算术). Prior research has highlighted his contributions in formulating rigorous arguments for the correctness of mathematical procedures, employing logical reasoning through nearly infinite segmentation and systematizing Chinese mathematics. This article examines three other aspects of his work that have a profound impact on mathematics but have rarely been discussed before. First, it explores his discussion on the early development of mathematics, which profoundly influenced the cultural foundations of Chinese mathematics. Second, it analyzes his contributions to what is known as ‘geometrical algebra’, a precursor to the Confucian mathematical methods that emerged during the Southern and Northern dynasties (420–589 CE) and later evolved into the so-called Chinese algebra developed between the 11th and 13th centuries. Third, it examines his innovative concept and application of counting rods, which can be regarded as an early precursor to the textualization and symbolization of Chinese mathematics during the 13th century. Finally, the article argues that Liu Hui's achievements should also be understood in the context of his interactions with political power and his engagement with contemporary philosophical ideas.