Liu Hui, the founder of the theoretical system of classical mathematics in China

This article reviews how historians of mathematics in China during the 1980s and 1990s overcame the preconceptions that ‘the history of mathematics in China has been fully studied’ and ‘it is an unproductive field’. It critically examines several major issues in the Nine Chapters on the Art of Mathematics (hereafter Nine Chapters ) and Liu Hui's commentary that were either unsolved or incorrectly solved by previous scholars, thereby sparking a wave of research on the Nine Chapters and Liu Hui, both within China and internationally. The article argues that the Nine Chapters , compiled by Zhang Cang and Geng Shouchang in the Western Han Dynasty, established the foundational framework of classical mathematics in China but had limitations, such as the absence of mathematical definitions and derivations of mathematical formulas. In the 3rd century, under the influence of the vibrant academic debate during the Wei-Jin period, Liu Hui defined several mathematical concepts, comprehensively demonstrated the validity of the algorithms in the Nine Chapters , and further established the theoretical system of classical mathematics in China. Liu Hui's contributions still hold practical significance in the modern era.