Li Shan-lan 李善蘭 (T. 壬叔 H. 秋紉), 1810-1882, Dec. 9, mathematician, was a native of Hai-ning, Chekiang. From boyhood he was interested in mathematics. Though a licentiate of his district, he failed to obtain a higher degree. In 1845 he was engaged as tutor, or secretary, in the Lu-fei family (see under Lu-fei Ch'ih) and lived in Kashing for some years. During that time he wrote several mathematical works, including the 四元解 Ssŭ-yüan chieh, 3 chüan (completed in 1845), being explanations of the methods used in the Ssŭ-yüan yü-chien (see under Lo Shih-lin). In 1846 he wrote the 對數探源, Tui-shu t'an-yüan, "Principles of Logarithms", 2 chüan, which was printed in the collectanea Chih-hai (see under Chang Hai-p'êng). Alexander Wylie 威烈亞力 (1815-1887), commenting on this work some time later, said that Li "has here given us, as the result of four year's thought, a theorem, which in the days of Briggs and Napier would have been sufficient to raise him to distinction."
In 1852 Li Shan-lan went to Shanghai where for eight years he was engaged by missionaries of the London Missionary Society in translating Western scientific works into Chinese. As with the Catholic missionaries two centuries earlier, the thought in the original work was communicated orally and the Chinese scholar recorded it in the approved literary style. Li began with Wylie to translate Books 7-15 of Euclid's Elements, the first six books having been rendered into Chinese in 1606-08 and published in final form in 1611 under the title Chi-ho yüan-p ên (see under Hsü<> Kuang-ch'i). Li and Wylie completed their translation in three years (working in the mornings only) under the title 續幾何原本 Hsü<> Chi-ho yüan-p ên, 9 chüan. In the afternoons, during the same period, Li and another missionary, Joseph Edkins 艾約瑟 (T. 廸謹, 1823-1905), translated An Elementary Treatise on Mechanics (重學 Chung-hsüeh, 20 chüan) and Conic Sections (圓錐曲線 Yüan-chui ch'ü-hsien, 3 chüan), both by William Whewell 胡威立 (1794-1866). The printing blocks for these three works were carved in 1858, but were destroyed by fire after only a few copies were printed. The Hsü<> Chi-ho yüan-p ên was reprinted in 1865, together with the earlier 6 chüan. The Chung-hsüeh and the Yüan-chui ch'ü-hsien were reprinted in 1866. After 1855 Li and Wylie translated the following works, all printed in 1859: Outlines of Astronomy (1851 edition), by John F. W. Herschel 侯失勒 (1792-1871), under the title 談天 T'an-tien, 18 + 1 chüan ; Elements of Algebra, by Augustus de Morgan 棣麼甘 (1806-1871), under the title 代數學 Tai-shu hsüeh, 13 chüan ; Elements of Analytical Geometry and of Differential and Integral Calculus, by Elias Loomis 羅密士 (1811-1889), under the title 代微積拾級 Tai wei cHishih-chi, 18 chüan. The translation of Newton's Principia (奈端數理 Nai-tuan shu-li) was commenced but never finished. Li and Alexander Williamson 韋廉臣 (1829-1890) translated Lindley's Botany under the title 植物學 Chih-wu hsüeh, 8 chüan, printed in 1859. The last chüan was, in fact, translated by Li and Edkins, owing to Williamson's departure from Shanghai in 1857. In 1859 two of Li's own works were printed in the Hsü (續) I-hai chu-ch'ên (see under Mei Wên-ting), namely, the 方圓闡微 Fang-yüan shan-wei, 1 chüan, and the 弧矢啟祕 Hu-shih ch'i-mi-both on the measurement of the circle.
About the years 1859-60 Li Shan-lan joined the staff of the governor of Kiangsu, Hsü<> Yu-jên 徐有壬 (T. 君青, 鈞卿, posthumous name 莊愍, 1800-1860), and took up his residence in Soochow. Hsü<> was likewise a mathematician--nine titles representing his work in this field appear in the 白芙堂算學叢書 Pai fu-tang suan-hsüeh ts'ung-shu, printed about 1872-75 by Ting Ch'ü-chung 丁取忠, (T. 果臣 H. 雲梧) of Changsha. When Soochow fell to the Taiping army on June 1, 1860, Hsü<> was killed in action, and most of Li's printed books were burned, along with the governor's yamen. Li himself escaped to Shanghai where he remained several years. About 1863 he joined the famous staff of Tsêng Kuo-fan [q.v.], which was then stationed at Anking, but which after the recovery of Nan king (1864) was removed to that city. In 1865 Tsêng financed the reprinting of the Hsü<> Chi-ho yüan-pên as well as the Chi-ho yüan-pên ; and in the following year, Li Hung-chang [q.v.] financed the reprinting of the Chung-hsüeh. Thirteen of Li's own works, seven previously unpublished,  were printed in 1867 under the title 則古昔齋算學 Ts ê<> -k'u-hsi chai suan-hsüeh, in all, 24 chüan. In 1864 Li Shan-lan and another mathematician, Tsou Po-ch'i 鄒伯奇 (T. 一鶚 H. 特夫, 1819-1869) of Canton, were recommended by Kuo Sung-tao [q.v.] to be instructors in the T'ungWên kuan (see under Tung Hsün), or new school for interpreters, established in 1862. An edict was iSsŭed in 1866 summoning the two licentiates, but both declined on grounds of illness. In December 1866 plans were approved to expand the T'ung-wên kuan to a College, and to the classes in English, French and Russian was added a department of mathematics and astronomy. In 1867 some thirty-one students were enrolled in the new department and an edict was iSsŭed to hasten the coming of Li and Tsou to the capital. Li came in 1868, but Tsou again declined. In 1869 Li was appointed head of the Department of Mathematics and Astronomy and later in the same year W . A. P. Martin (see under Tung Hsün) was made President of the College. Li taught in the College for thirteen years (1869-82), being at first given the rank of a secretary of the Grand Secretariat, and later made a department director in the Board of Revenue, a secretary in the Tsungli Yamen, and an official of the fourth (third?) rank. He died in Peking and his remains were taken to Hai-yen, Chekiang.
Li Shan-lan was of corpulent physique. A gifted mathematician, he was the first Chinese to use Western algebra in the solution of the problem known as Ssŭ-yūan 四元 involving the solution of equations with more t han one unknown quantity, as introduced in the abovementioned Ssŭ-yüan yu-chien. Many of the scientific terms which Li established are still in use.
[ 1/512/24a; 2/69/72b; 6/43/3b; Li Shan-lan nienp'u (年譜) in Chung-suan-shih lun-ts'ung (see under Lo Shih-lin), Vol. ü, pp. 435-74; Martin, A Cycle of Cathay (1896) p. 312 (photograph of Li and his class in mathematics), pp. 368-70; Ch'ou- jên chuan (see under Jüan Yüan) 1935, pp. 810-15, 835-44, 846-56; Wylie, Memorials of Protestant Missionaries (1867), pp. 173-74, 187-88, 238-39; Portrait in 中華教育界 Chung-hua chiao-yü<> chieh, Vol. 23, No. 1 (July, 1935); Wylie, Chinese Researches, section on Science, pp. 193-94; Yoshio Mikami, The Development of Mathematics in China and Japan (1913), pp. 125-27.]