ESHS/HSS Annual Meeting

Two Perspectives, Two Interpretations: Sea Mirror in the Complete Library and in Li Rui’s Edition

• In Event: Diagrammatic Computations and Their Symbolic Aspects (II)

English Abstract

Within the Chinese scholarly tradition, later generations of scholars produced
commentaries on earlier mathematical treatises that incorporated both their interpretations of
the original text and their own mathematical analyses.
Sea Mirror of the Circle Measurements 測圓海鏡 (Ce yuan hai jing, 1248, hereafter
Sea Mirror) is the earliest known text to record the “procedure of the celestial source” (天元
術, tian yuan shu). This procedure entails computing in a diagrammatic way with polynomials
to establish algebraic equations, the root of which is an unknown sought. The procedure is
today considered an important breakthrough in the history of mathematics in ancient China.
However, its meaning was lost after the 13th century. In the 1770s, a national program was
launched with the objective of collecting, collating and annotating ancient works of the past.
This enormous undertaking, known as the Complete Library of the Four Treasuries (四庫全
書, si ku quan shu, hereafter Four Treasuries), included Sea Mirror. Later, in 1798, a new
collated edition of Sea Mirror, conducted by the mathematician Li Rui 李銳 (1769–1817),
was published, and soon became the standard reference for subsequent scholarship.
The differences between these two editions reveal distinct understandings of the long-
lost mathematical procedure, in particular in its diagrammatic features. This case thus
illustrates how differing perspectives can generate divergent interpretations of the same
mathematical work, and how mathematical knowledge may become contested in the process.

Author

• Rui YUAN, SPHERE-Université Paris Cité