Four Great Mathematical-Masters during Song and Yuan Dynasties
2 min readChinese maths in Song and Yuan dynasties was a highlight of al the disciplines of science. In addition, it was also the summit in the history of Chinese ancient maths as well as a most splendid page in the world’s medieval history of maths.
Four mathematicians, Qin Jiushao, Li Ye, Yang Hui and Zhu Shijie were representatives during Song and Yuan dynasties, known as the four great mathematical masters of the time.
Qin Jiushao (1202-1261), or Qin Gudao in his courtesy name, was born in Sichuan. He was proficient inastronomy, maths, music and architecture. His great works include Mathematical Treatise in Nine Chapters (1247) in 18 volumes, classified in 9 major categories with the calculation method for each category being explained in nine examples. His prominent accomplishments lie in his initial solutions to high-order algebraic equations and general method of Chinese remainder theorem. The former techniques of the solution were about 600 years earlier than the West and the latter,500 years earlier.
Li Ye(1192-1279), originally named Li Zhi, or Li Renqing by his courtesy name, was a native of Zhending (present-day Zhengding) of Hebei province. He was summoned to the presence of Kublai Khan, founder of Yang Hui（living around the mid 13th century），also Yang Qianguang in his courtesy name，was a native of Hangzhou.His mathematical works include Detailed Explanation for the Calculation Solutions in Nine Chapters on Mathematic Art（1261，now incomplete），Practical Calculation Solutions（1262，now incomplete），and Yang Hui’s Triangle（1274-1275）.In his books he introduced quite a few mathematical problems and solutions，such as “root extraction by additional multiplication”and“the origin of the solution by root extraction””.
Zhu Shijie（living during the end of the 13th century and the beginning of 14th century），also called ZhuHanqing by his courtesy name，was a native of Hebei province. He was the author of the mathematical works A First Introduction to Arithmetic(1299) and Precious Mirror of the Four Elements (1303). The former was a mathematical reading primer with a complete introduction to general mathematical problems ranging from multiplication and division, root extraction to solution to the “celestial unknown”, explaining profound problems in a simple way. The latter work initiated “removal solutions to quadruple unknown equations by a vertical and horizontal matrix”, which was unknown in the West until 1779,470 years later. Coincidently, his formula for higher-order arithmetic progression was the same in all respects as theone created by the British scientist Isaac Newton some 370 years later.
