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Yang Hui

Chinese Mathematician and the "Pascal’s Triangle" Tradition

Yang Hui (c. 1238–1298) was a Chinese mathematician of the Southern Song dynasty, celebrated for his writings on combinatorics, magic squares, and algebra. His most famous contribution is the depiction of what is now called Yang Hui’s Triangle, known in the West as Pascal’s Triangle, though Yang’s systematic presentation predates Pascal by centuries.

The triangle provided coefficients for binomial expansions, a method written as: \[ (a + b)^n = \sum_{k=0}^{n} \binom{n}{k} a^{n-k} b^k \] This formulation allowed Chinese scholars to expand polynomials efficiently and explore properties of binomial coefficients, long before such techniques became standard in Europe.

Yang’s writings also include discussions of magic squares, permutations, and problems involving polynomial equations. He emphasized clear exposition, often criticizing earlier mathematicians for unnecessary obscurity, and sought to make advanced mathematics accessible to students.

His influence was lasting: Yang Hui’s triangle became a cornerstone of East Asian mathematics and was later transmitted to Japan and Korea. It remains one of the most recognizable mathematical tools in history, linking combinatorics, probability, and algebra across cultures.