Lǐ Shànlán 李善蘭
Style names Qiūrèn 秋紉 and Rénshū 壬叔. Native of Hǎiníng 海寧 (Hángzhōu prefecture, Zhèjiāng). Born Jiāqìng 15 (1810); died Guāngxù 8 (1882). CBDB c_personid 65735 records the birth year 1810; the conventional death year 1882 is given here (CBDB has 1884; the discrepancy is documented in the standard biographies — Horng 1991 prefers 1882, on the basis of the documented memorial activities).
The principal Chinese mathematician of the mid-to-late nineteenth century, and the central figure in the late-Qīng translation programme that introduced systematic European symbolic algebra, calculus, analytical geometry, and projective geometry to China. Lǐ Shànlán’s career has three phases:
(1) Indigenous mathematical period (1830s–1851): Self-taught in the indigenous SòngYuán mathematical tradition (the Cèyuán hǎijìng and Sìyuán yùjiàn) and the cyclotomic-series tradition (Míng Āntú, Xiàng Míngdá, Dài Xù). His Fāngyuán chǎn yōu 方圓闡幽, Húshǐ qǐ mì 弧矢啓秘, and Duī duǒ bǐlèi 垛積比類 belong to this period and represent the high indigenous-tradition synthesis. The Duī duǒ bǐlèi in particular contains an independent rediscovery of what is now called the “Lǐ Shànlán identity” — a binomial-coefficient identity discovered independently from the European literature.
(2) Mòhǎi Shūguǎn translation period (1852–1860): From 1852 Lǐ Shànlán worked at the London Missionary Society Press (Mòhǎi Shūguǎn 墨海書館) in Shànghǎi, collaborating with Alexander Wylie (偉烈亞力 Wěilièyàlì) on translations of European mathematical and scientific works. The principal translations include: Euclid’s Elements Books VII–XV (completing Ricci–Xú’s 1607 translation of Books I–VI); A. De Morgan, Elements of Algebra (1859); Elias Loomis, Elements of Analytical Geometry and of the Differential and Integral Calculus (1859 — the first Chinese-language calculus textbook); Herschel, Outlines of Astronomy; Whewell, Elementary Treatise on Mechanics. The translation programme is the foundational moment of modern Chinese mathematics and science.
(3) Tóngwén Guǎn period (1868–1882): From 1868 Lǐ Shànlán was Professor of Mathematics at the Tóngwén Guǎn 同文館 (“School of Combined Learning”) in Běijīng — the first professorial chair of mathematics in modern Chinese higher education. His Zégǔxī zhāi suànxué 則古昔齋算學 (KR3fc078) collects his indigenous-period mathematical works in 25 juàn (= “13 kinds” shísān zhǒng 十三種) and remained the principal Chinese-language advanced-mathematics text of the late-Qīng curriculum.
Lǐ Shànlán’s mathematical vocabulary — the Chinese terms for function, limit, differential, integral, series, and the like — was established in his Mòhǎi translations and remains the basis of modern Chinese mathematical Chinese to this day. He is the principal individual figure of the Xīxué dōngjiàn 西學東漸 (“eastward-coming of Western learning”) movement in mathematics.