Li Shanlan: The impact of Western mathematics in China during the late 19th century

Li Shanlan (1811-1882) played a crucial and significant role in the transition from traditional to modern mathematics in China. His important place in the history of modern Chinese mathematics can best be appreciated in terms of his roles first as traditional mathematician, then translator of Western mathematics and science, and finally instructor at the Tong Wen Guan (the Imperial College at Beijing). These three roles were assumed by Li Shanlan during three distinct periods of his career, the "Ze Gu Xi" period (1845-1852), the "Mo Hai Shu Guan" (the London Missionary Society Press at Shanghai) period (1852-1860), and the Tong Wen Guan period (1868-1882).; In the first period, Li Shanlan's contributions to infinite series expansions for trigonometric, inverse-trigonometric and logarithmic functions served to establish him as a clear leader of the Chinese mathematical community in the middle of the 19th century. Thus prepared, Li Shanlan went on to become a very successful translator at the Mo Hai Shu Guan. His translations, in collaboration with Alexander Wylie and Joseph Edkins, of texts on Western mathematics and science paved the way for Chinese traditional mathematics to merge into the mainstream of modern mathematics. In 1868, Li Shanlan began to teach mathematics at the Tong Wen Guan in Beijing. Here he was to play a significant role in helping to promote the institutionalization and professionalization of mathematics as a serious academic discipline in China.; Li Shanlan's life spanned two important periods of late Qing intellectual history. One is the period (1736-1820) during which the Qian-Jia school was predominant. The other is the period (1860-1890) when the Qing government was forced to Westernize or modernize in response to the Self-strengthening Movement. Each of these served to provide a favorable intellectual context and a suitable institutional basis for mathematics. In the rapid modernization of mathematics in China during the 19th century, Li Shanlan proved to be a critical figure at a crucial juncture in Chinese history.