c. 1202-c. 1261

Chinese Mathematician

The work of Ch'in Chiu-shao represents the culmination of Chinese studies in indeterminate analysis. His principal writing was Shushu chiu chang (1247), variously translated as Mathematical Treatise in Nine Sections and The Nine Sections of Mathematics.

According to the modern system for spellings of Chinese names, Ch'in's would be rendered as Qin Jiushao. As was typical of scholars in his country, he adopted a literary name, in his case Hao Tao-ku. He was born in the town of P'uchou, Szechuan Province, and in 1219 joined the army, serving as captain in a volunteer unit who put down a local rebellion against the Sung Dynasty. Afterward he went on to a number of positions within the Sung state, becoming governor of Ch'iung-chou Province, now part of Hainan.

In 1247, Ch'in published his Nine Sections, which discussed a range of subjects that included simultaneous integer congruencies, linear simultaneous equations, algebraic equations, the areas of geometrical figures, and what became known as the Chinese Remainder Theorem. As was typical of Chinese mathematical texts, the book was heavily concerned with practical applications crucial to the administration of a Confucian bureaucracy, including matters relating to calendars and finances.

Though it remained unpublished except in manuscript form for many years and has never been fully translated, the Nine Sections would remain an influential text in Chinese mathematics for the next four centuries. Later Johann Karl Friedrich Gauss (1777-1855) and other mathematicians would delve into the questions of congruencies investigated by Ch'in.

In addition to his work in mathematics, Ch'in was recognized for his knowledge of the arts including poetry, music, and architecture, as well as his martial talents which included fencing, archery, and riding. In 1258 he lost his position as governor amid charges of corruption and died about three years later in Mei-chou, Kwangtung Province.