Britannica Sources used in this answer

How did Chinese mathematicians Jia Xian and Yang Hui study Pascal’s triangle before Blaise Pascal?

Created from Britannica articles using AI. AI can make mistakes, so verify using Britannica articles.

French philosopher Blaise Pascal — Blaise Pascal Blaise Pascal, oil painting by an anonymous artist, c. 1650; in the Musée Carnavalet–Histoire de Paris, Paris. Pascal laid the foundation for probability theory.

The triangular arrangement of numbers commonly known as Pascal’s triangle was studied in China centuries before Blaise Pascal.

In the 11th century, the mathematician Jia Xian devised this triangular representation to determine binomial coefficients for equations up to the sixth degree. He utilized this triangle in connection with his methods for extracting the roots of polynomials.12

In the 13th century, Yang Hui further studied and popularized Jia Xian’s work. In his 1261 treatise, Xiangjie jiuzhang suanfa, Yang Hui included a representation of the triangle, explicitly noting in the preface that he had copied it from Jia Xian’s earlier work. Because of Yang Hui's efforts to document and disseminate the method, the triangle is often referred to as the Yang Hui triangle in China. By the time it appeared in Zhu Shijie’s 1303 work, Siyuan yujian, the diagram was already referred to as the "Old Method," indicating its established place in Chinese mathematical tradition.13