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Mathematical Treasure: Zhu Shijie’s New Arithmetic

Frank J. Swetz (The Pennsylvania State University)

In the early part of the 19th century, the Chinese Empire undertook a series of educational reforms, modernizing its curriculum and strengthening studies in mathematics and the sciences. To support this effort, foreign texts were imported and translated into Chinese and a series of traditional mathematics classics were revised and republished. Among these revised classics was the Xin bian suan xue qi meng, or New Arithmetic Enlightenment (1299), of Zhu Shijie (c. 1260-1320). Since no original Chinese version of this text existed, a Korean copy was secured and republished in the Chinese form. The scholar Luo Shilin (1774-1853) undertook this task and published his new version in 1839. The images below are from the text written by Luo.

Figure 1. Title page and preface of the Xin bian suan xue qi meng of Zhu Shijie, as recreated by Luo Shilin

Figure 2. Examples of numerical operations

See images from the 1660 Korean copy of this text in MAA Convergence.

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.

Index to Mathematical Treasures

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