Zhu Shijie

Zhu Shijie was a Chinese mathematician of the Yuan dynasty, known for Introduction to Mathematical Studies and Jade Mirror of the Four Unknowns. His work developed methods for solving polynomial equations and summing series.

Chinese mathematics: The mathematical traditions developed in China, including distinctive methods for arithmetic, algebra, geometry, and astronomy. Zhu's work belongs to a long tradition of Chinese problem-solving and computational methods.
Jade Mirror of the Four Unknowns: A mathematical treatise by Zhu Shijie that presents algebraic methods involving up to four unknown quantities. This is Zhu's best-known work and the main source for his advanced algebra.
Introduction to Mathematical Studies: A mathematical textbook by Zhu Shijie that introduces arithmetic methods and worked problems. This earlier treatise presents the instructional side of Zhu's mathematical writing.
Summation of series: The calculation of a finite or infinite sum from a sequence or a rule generating its terms. The Jade Mirror includes techniques for summing sequences and figurate-number patterns.
Chinese rod calculus: A positional arithmetic system using counting rods arranged on a counting board to represent numbers and perform calculations. Rod numerals provided the computational language behind the polynomial procedures associated with Zhu's work.
Four unknowns method: A method of representing four quantities as algebraic unknowns and deriving equations from their relationships. It is the distinctive procedure named in the Jade Mirror's title.
Yuan dynasty: A Chinese dynasty ruled by the Mongols from 1271 to 1368. Zhu's career and surviving works belong to the intellectual world of Yuan China.
Pascal's triangle: A triangular arrangement of binomial coefficients in which each interior number is the sum of the two above it. A version of this coefficient pattern appears in the mathematical tradition recorded by Zhu.
Polynomial: An algebraic expression formed from variables and coefficients using addition, subtraction, and nonnegative integer powers. The equations Zhu's methods solve are expressed as polynomials.
Polynomial equation: An equation in which a polynomial expression is set equal to another expression, often zero. Zhu's procedures reduce many problems to polynomial equations.

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Yang HuiRelated: His later scholarship shows the continued development of Chinese mathematics after Yang Hui's lifetime.