Research rooted in Chinese mathematics
Born in Haining, Zhejiang, Li studied the Nine Chapters and the first six books of Euclid’s Elements in the translation by Matteo Ricci and Xu Guangqi. He also read the Sea Mirror of Circle Measurements. Chinese equation methods, geometrical problems and techniques for finding areas and volumes provided resources for his own investigations.
His research covered logarithms, infinite series and combinatorial calculation. Fangyuan chanyou considered division and accumulation in finding areas and volumes; Duoji bilei examined finite summation relations. A collected edition of his mathematical writings appeared in 1867. This independent work accompanied, rather than being replaced by, his translation activity.
Collaborative translations of geometry and calculus
In Shanghai during the 1850s, Li collaborated with missionaries of the London Missionary Society. With Alexander Wylie he translated the remaining nine books of Euclid’s Elements and Elias Loomis’s textbook on analytic geometry and calculus. The latter appeared as Daiwei ji shiji in 1859. His collaborations also encompassed algebra, astronomy, mechanics and botany.
The calculus translation’s prefaces explain its educational sequence: symbolic methods lead toward differentiation and integration through increasingly difficult material. Li compared Chinese four-unknown techniques with Western algebra, then discussed constants, variables and changing geometrical quantities. The translators were also constructing a route through the subject for readers working in Chinese.
Choosing terminology and notation
Words such as weifen and jifen already appeared in older mathematical contexts. Li and Wylie gave them specialized meanings in calculus. Their book represented constants and variables with Chinese characters and adapted character components as operational signs, connecting terminology with actual written calculation.
Zhang Bisheng’s comparison of the translation with older texts distinguishes the mathematical meanings attached to similar words in different periods. Shared vocabulary alone does not establish identical theories. Li later taught mathematics at the Tongwen Guan in Beijing, bringing these fields into an educational setting as well as making them available through print.