Li Shanlan

Li Shanlan

Li Shanlan ( Chinese  李善蘭  /  李善兰 , Pinyin Lǐ Shànlán ; age name ( zì ) Renshu , 壬 叔 , Rénshū ; stage name Qiuren , 秋 紉 , Qiūrèn ; * 1811 in Haining ; † 1882 in China ) was a Chinese mathematician. He is considered the most important Chinese mathematician of the 19th century.

Li Shanlan came from an educated, respected family and, like his brother Li Xinmei, who also became a mathematician, was taught by a private tutor, the well-known philologist Chen Huan (1786–1863). He became interested in mathematics through studying the classical Chinese mathematics book Nine Books on Mathematical Art ( Jiu Zhang Suanshu ). Soon afterwards he studied the elements of Euclid in Chinese translation and an algebra book by Li Ye (Li Zhi) and a trigonometry book by Dai Zhen (1724–1777). In order to continue his mathematical studies, he took a position as a private teacher in 1845. On the run from the turmoil of the Taiping uprising , he went to Shanghai in 1852 . There he met the British missionary Alexander Wylie , for whom he translated mathematical works into Chinese, for example an analysis textbook by Elias Loomis that appeared in 1859, the first analysis textbook in Chinese. He also translated the last nine chapters of Euclid's Elements with Wylie (the first books appeared as early as 1607 in the translation of Matteo Ricci and Xu Guangqi ). With the missionary Joseph Edkins (1823-1905) he translated a mechanics textbook by William Whewell (published 1867) and he also translated the algebra of Augustus De Morgan and the Outlines of Astronomy by John Herschel and a botany book.

Around 1860 he left Shanghai and worked for the governor of Jiangsu Province Xu Youren (1800-1860), who was a gifted amateur mathematician, and then for General Zeng Guofan and his brother, who were involved in the suppression of the Taiping uprising . With her support, Li's mathematical works were published in Nanjing in 1867 . From 1866 he was a lecturer at a state school for Western languages ​​in Beijing (Tongwen Guan) founded in 1863. In 1869 he was a professor of mathematics there. He not only taught Western mathematics there, but also based on the Chinese classics, and in his mathematical publications, for example on analysis (for example, infinite series, logarithms) and combinatorics, he took up the Chinese tradition. Many of the mathematical expressions used in China today come from him.

A formula of combinatorics (summation formula for binomial coefficients ) is named after him:

${\displaystyle \sum _{k=0}^{n}{n \choose k}^{2}{{m+2n-k} \choose {2n}}={{m+n} \choose n}^{2}}$.

It became known in the West through the Hungarian mathematician George Szekeres , when he was in Shanghai as a political refugee in 1937 and communicated this by letter to Pál Turán , who published a proof in 1954. The Chinese mathematician Zhang Yong (1911–1939), through whom Szekeres found out about the formula, published a proof in 1939.

literature

• Wann-Sheng Horng: Li Shanlan: The Impact of western mathematics in China during the late 19th Century , Dissertation, City University of New York 1991
• Jean-Claude Martzloff : Li Shanlan (1811-1882) and Chinese traditional mathematics , Mathematical Intelligencer, Volume 14, 1992, Issue 4, pp. 32-37 and his History of Chinese Mathematics , Springer, pp. 173ff.

Web links

• John J. O'Connor, Edmund F. Robertson :  Li Shanlan. In: MacTutor History of Mathematics archive .

Individual evidence

1. ↑ in western literature he was quoted under many different names and transcriptions, for example Li Jen-Shu
2. ^ Jean-Claude Martzloff History of Chinese Mathematics , Springer
3. ^ Jean-Claude Martzloff History of Chinese Mathematics , Springer, Chapter 18