Comparison of treatises written/published in the 16th and 17th century brings to light a drastic change of writing styles in traditional Chinese mathematics. Though historians of Chinese mathematics generally agree that such transformation is in part a Chinese response to the introduction of Jesuit mathematics into China, in particular the translation and publication of the first six books off Euclid’s Elements as Jihe yuanben 幾何原本, explication of such a grand transformation is needed to better understand its impact on the development of Chinese mathematics since the beginning of the 17th century.

In this paper, we examine the role of explanation in the mathematical treatises in 17th-century China using Mei Wending’s (1633-1721) Fangcheng lun 方程論 as a case study. Mei broke away with the textual tradition and adopted an approach that resembles “written oral instruction.” In his effort to explain, he categorized all the Fangcheng problems into four kinds and applied appropriate procedures accordingly, counter to the mainstream practice of the day. Mei’s explanation appeals to suanli (computational principles) to justify itself as a true heir to “antiquity.” Consequently, Mei’s detailed narratives of procedures and their underlying principles not only make his texts more accessible to general readers, but also justify his approach as coming from ancient orthodoxy. Mei’s approach later became the mainstream practice either through his persuasion or through its inclusion as the approach to solving Fangcheng problems in Shuli jingyun (數理精蘊), the imperially produced mathematical compendium.