The influence of Qing dynasty editorial work on the modern interpretation of mathematical sources: The case of Li Rui's edition of Li Ye's mathematical treatises

Argument Recent studies in Sinology have shown that Qing dynasty editors acted as philologists. This paper argues that the identification of their philological methods and editorial choices suggests that their choices were not totally neutral and may have significantly shaped the way modern historians interpreted specific works edited by mathematicians of that dynasty. A case study of the re-edition in 1798 of a Song dynasty treatise, the Yigu yanduan (1259), by a Qing dynasty mathematician will illustrate this point. At the end of the eighteenth century, Li Rui (1773-1817) was asked to prepare an edition of the mathematical works written by Li Ye (1192-1279) for a private collection. Li Rui was a talented mathematician, but he was also a meticulous editor and trained philologist. He adopted his editorial model from the preparation of the imperial encyclopaedia, the Siku quanshu, but Li Rui also made some corrections to the text in an effort to restore an older version of Li Ye's treatises that had been lost. Convinced of the Chinese origin of algebra, Li Rui used philological techniques to recover the lost materials and to restore the roots of Chinese mathematics. The Yigu yanduan contains two algebraic procedures to set up quadratic equations, one from the procedure of Celestial Source (tian yuan shu) and the other from the Section of Pieces [of Areas] (tiao duan). Curiously, the second procedure has not yet attracted the attention of scholars so far, although Li Rui's edition is the one typically used by twentieth-century historians of mathematics. Today, the Celestial Source characterizes Chinese algebra. However, the specific concerns of Li Rui about the procedure of Celestial Source, combined with his editorial methods, contributed to this perspective.