Qin Jiushao

Qin Jiushao was a 13th-century Chinese mathematician whose Shùshū Jiǔzhāng presented methods for solving polynomial equations and simultaneous congruences.

Chinese mathematics: The mathematical traditions developed in China, including distinctive work in arithmetic, algebra, and computation. Qin’s work belongs to a long tradition of practical computation and algorithmic mathematics.
Qin Jiushao's method: A procedure for solving systems of congruences by successively combining their modular conditions. This is Qin’s signature algorithm for simultaneous congruences.
Shushu Jiuzhang: A mathematical treatise by Qin Jiushao, completed in 1247 and organized into nine sections of problems and methods. It is the principal surviving source for Qin’s mathematics.
Chinese remainder theorem in China: The development of methods for solving simultaneous congruences in Chinese mathematics, from early texts through Qin Jiushao. Qin gave the method a particularly systematic treatment in his 13th-century work.
Chinese remainder theorem: A theorem describing when simultaneous congruences have solutions and how to determine them. It names the class of problems Qin’s systematic method solves.
Horner's method: An algorithm for evaluating a polynomial efficiently and approximating its roots through successive transformations. Qin’s root-finding procedure uses a related pattern of successive approximation.
Southern Song dynasty: The Chinese dynasty that ruled south of the Huai River from 1127 to 1279. Qin lived and worked during this period of his mathematical career.
Polynomial algebra in China: The study of polynomial equations in Chinese mathematics, including numerical root-finding methods. Qin’s procedures advanced a distinctive tradition of computational algebra.
Polynomial equation: An equation in which a polynomial expression is set equal to zero or another expression. Qin developed numerical procedures for finding roots of polynomial equations.
Remainder (arithmetic): The quantity left after one integer is divided by another. His congruence calculations reduce numbers to remainders under several moduli.

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