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Mathematics

Advances in polynomial algebra were made by mathematicians during the Yuan era. The mathematician Zhu Shijie (1249–1314) solved simultaneous equations with up to four unknowns using a rectangular array of coefficients, equivalent to modern matrices. Zhu used a method of elimination to reduce the simultaneous equations to a single equation with only one unknown. His method is described in the Jade Mirror of the Four Unknowns, written in 1303. The opening pages contain a diagram of Pascal's triangle. The summation of a finite arithmetic series is also covered in the book.

Guo Shoujing applied mathematics to the construction of calendars. He was one of the first mathematicians in China to work on spherical trigonometry. Gou derived a cubic interpolation formula for his astronomical calculations. His calendar, the Shoushi Li (授時暦; ' Time Granting Calendar' '), was disseminated in 1281 as the official calendar of the Yuan dynasty. The calendar may have been influenced solely by the work of Song dynasty astronomer Shen Kuo or possibly by the work of Arab astronomers. There are no explicit signs of Muslim influences in the Shoushi calendar, but Mongol rulers were known to be interested in Muslim calendars. Mathematical knowledge from the Middle East was introduced to China under the Mongols, and Muslim astronomers brought Arabic numerals to China in the 13th century.