Xià Luánxiáng 夏鸞翔
Style name Zǐshēng 紫笙. Native of Qiántáng 錢塘 (modern Hángzhōu 杭州, Zhèjiāng). Born Dàoguāng 3 (1823); died Tóngzhì 3 (1864). CBDB c_personid 86133 confirms the lifedates.
A student of 項名達 Xiàng Míngdá in the Hángzhōu mathematical milieu and a junior contemporary of 戴煦 Dài Xù. His principal mathematical work is the Zhìqū shù / Zhìqū tújiě 致曲術 / 致曲圖解 (KR3fc076) — a treatise on the geometry and computation of higher-order curves (qū 曲 “curves”) going beyond the classical gōugǔ 勾股 (right-triangle) and húshǐ 弧矢 (circular-arc) problem-domains. The work extends the cyclotomic-series methods of the Míng Āntú / Xiàng Míngdá tradition to conic sections and other curves of higher degree.
Xià Luánxiáng worked in close mathematical correspondence with 李善蘭 Lǐ Shànlán in the 1850s, by which date Lǐ Shànlán had begun the major translation project of Wylie at the Mòhǎi Shūguǎn 墨海書館 in Shànghǎi. Xià’s late work shows the partial absorption of European-derived methods (series expansions of trigonometric functions and the like) into the indigenous Chinese cyclotomic-series framework.
His death in 1864 came in the aftermath of the Tàipíng Tiānguó war that devastated the Hángzhōu and Jiāngnán mathematical communities. With Xià Luánxiáng’s death and the wartime losses of 戴煦 Dài Xù (1860), 徐有壬 Xú Yǒurén (1860), and 羅士琳 Luó Shìlín (1853), the mid-century indigenous Chinese mathematical tradition was effectively brought to an end; the Tóng-zhì-to-Guāng-xù-era mathematical revival under 李善蘭 Lǐ Shànlán’s translation programme operated on a substantially different foundation.