CAST Newsletter No.48 (Special Issue)

Commemoration of ancient Chinese mathematical master Liu Hui for his timeless influence on mathematics and civilizational exchange

Throughout history, numerous individuals have left marks, and Liu Hui, a 3rd-century Chinese mathematician, was one of the most influential in the field of classical Chinese mathematics. His study of the ancient classic Jiuzhang Suanshu (The Nine Chapters on the Mathematical Art) culminated in two landmark works: Jiuzhang Suanshu Zhu (Annotations on The Nine Chapters on the Mathematical Art) and Haidao Suanjing (Sea Island Mathematical Manual). These texts established the theoretical foundation of classical Chinese mathematics. Liu Hui’s contributions not only shaped Chinese mathematical history but also influenced mathematical development across East Asia and, indirectly, the wider world. In recognition of his extraordinary achievements, the UNESCO designated 2024-2025 the 1800th anniversary of Liu Hui’s birth. The commemoration celebrates his enduring legacy while showcasing the profound contributions of ancient Chinese science and culture to a global audience.

Emerging in the mid-1st century BC and preserved to the present day, Jiuzhang Suanshu contains numerous universal algorithms and mathematical problems. However, according to Zou Dahai, a research fellow at the Institute for the History of Natural Sciences, Chinese Academy of Sciences (CAS), who attended the commemoration event in Paris as an expert representative, the text lacks explanations for how these algorithms and formulas were derived, despite the rich content and academic achievements.

Liu Hui’s annotations, completed in 263, served as a crucial supplement to the original text by providing detailed demonstrations of its mathematical methods. “He also made original and significant contributions in various fields,” Zou explained, “including the concept of lü (ratio), the method of infinite division, volume theory, indirect surveying, the ratio of circumference to diameter, and decimals.”

Liu Hui defined the meaning of key mathematical vocabulary such as ratio, equation, positive and negative numbers, and square root, laying the groundwork for a unified framework of concepts. He introduced the concept of lü and Qi Tong (the principle of uniformity) to connect various algorithms. Building on the area formula for rectangles and the volume formula for rectangular prisms, he developed the out-in complementary principle, the principle of proportionality between opposite sides of right triangles, and the Liu Hui’s Principle (named by CAS member Wu Wenjun).

Using deductive reasoning, he rigorously proved the formulas in Jiuzhang Suanshu, creating an organic network of mathematical knowledge. He likened this system to a tree, with distinct branches all originating from a shared trunk.

“From land measurement to urban planning, from building houses to constructing levees, Liu Hui’s annotations not only introduce precise calculation methods but also provide rigorous mathematical proof,” said CAST Executive President He Junke in his speech at the launch ceremony. This creative journey serves as a reminder that advancing human well-being should be the ultimate value and goal of technological development.

For detailed information, please click here to download CAST Newsletter No. 48.

Tag: CAST Newsletter No. 48