You are here

Mathematical Treasure: Zhu Shijie’s Introduction to Mathematical Studies

Frank J. Swetz (The Pennsylvania State University)

Zhu Shijie (1249-1314) of the Yuan dynasty was one of the greatest algebraists of traditional China. In his Suan xue qi yuan (Introduction to Mathematical Studies, or Primer of Mathematics) of 1299, he presented his tianyuan (celestial) technique of solving algebraic equations. As with many Chinese mathematical classics, the book was lost over time in China; however, it was still known and studied in Korea and Japan. When in the 19th century, the scholar Luo Shilin (1774-1853) resurrected mathematical studies in China, he obtained a Korean copy, which he translated into Chinese for the use of his students. This is a later Chinese copy.

Figure 1. Title page and preface of the Suan xue qi yuan of Zhu Shijie

Figure 2. Example of tianyuan method. Note the columns of numerical coefficients. For a more complete description of this technique, see pp. 347-365 of the sourcebook referenced below.

See images from another copy of this text in MAA Convergence.


Joseph Dauben. “Chinese Mathematics” in The Mathematics of Egypt, Mesopotamia, China, India and Islam: A Sourcebook (Victor Katz, ed.). Princeton University Press, 2007.

Primer of Mathematics, World Digital Library:


The images above were obtained through the courtesy of the World Digital Library (WDL) and the assistance of the digital imaging staff at the United States Library of Congress. All items can be viewed in full at the WDL website.

Frank J. Swetz (The Pennsylvania State University), "Mathematical Treasure: Zhu Shijie’s Introduction to Mathematical Studies," Convergence (January 2014)