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Qin Jiushao

Medieval Chinese Polymath and Mathematician

Qin Jiushao (c. 1202–1261) was a remarkably versatile scholar of the Southern Song dynasty, excelling in mathematics, meteorology, invention, and administration. His masterwork, Shùshū Jiǔzhāng (“Mathematical Treatise in Nine Sections,” 1247), addresses high-degree polynomial equations (up to the 10th degree), surveying, military arithmetic, and calendrical science.

In the text, Qin describes a method equivalent to Horner’s method for finding roots iteratively. Notably, he also addressed a general form of the Chinese remainder theorem, using an algorithm known as Da yan shu to solve systems like: \[ x \equiv a_1 \pmod{n_1},\quad x \equiv a_2 \pmod{n_2},\dots \]

Qin also deduced a formula for triangle area analogous to Heron’s: \[ A = \sqrt{s(s - a)(s - b)(s - c)},\quad s = \tfrac12(a + b + c). \]

Beyond pure mathematics, he invented the Tianchi basin, an early rain gauge enabling systematic weather measurement—a significant stride in meteorology.

Legacy

Qin Jiushao’s treatise blends theoretical ingenuity with practical applications. His contributions foreshadow modern approaches to algebra and numerical analysis, and his inventions show deep interdisciplinary thinking—an extraordinary achievement in medieval science.