Ancient Chinese Mathematics in Action: Wu Wen-Tsun's Nationalist Historicism After the Cultural Revolution

Abstract

The article attempts to theoretically explain the origins of the nationalist and historicist turn of the Chinese mathematician Wu Wen-Tsun (born 1919). Wu returned to China from France in 1951 as an internationally recognized expert on algebraic topology, but his career was frustrated by political disruption and isolation from international research, especially during the Cultural Revolution (1966–76). After he studied ancient Chinese mathematics during the 1974 campaign against Confucianism (Pi Lin Pi Kong 批林批孔), he defended its relevance for modern mathematics and set out to demonstrate it in his own work. This coincided with Wu's reorientation from algebraic topology to mechanization of geometric proofs. Wu claimed that ancient Chinese mathematics inspired the method he developed, both by its general style and by specific techniques. His use of ancient Chinese mathematics was connected to his calls for an independent mathematical tradition in China. I argue that he turned to nationalism to protect himself from the “uneven development” of mathematics, in analogy to Ernest Gellner's theory of nationalism. The early success of his method of mechanization, however, resulted in more dependence on world mathematics, and a revival of ancient Chinese mathematics has not occurred.

Keywords:

• Wu Wen-Tsun (Wu Wenjun)
• mechanization of mathematics
• nationalism
• historicism
• Ernest Gellner

Acknowledgments

I wish to thank my supervisors, Dr. Eleanor Robson and Prof. Catherine Jami, for their devoted support during my research; Dr. Horumi Mizuno and the two reviewers for their suggestions to improve the manuscript; Dr. Leon Rocha for an insightful discussion of an earlier version of this paper presented in the Department of History and Philosophy of Science, University of Cambridge; and the Trustees of the Needham Research Institute for generous funding of my research trips to China.

Notes

¹ The name 吴文俊 should be transcribed “Wu Wenjun” in the official transcription pinyin. Wu has, however, consistently used older romanizations, either as “Wu Wen-Tsun” or “Wu Wen-Tsün.” I will use the former version, following his recent Selected Works (Wu 2008).

² “Ancient” gudai 古代 is used by Wu loosely for the entire period up to about the seventeenth century, when the impact of Jesuit translations of Western mathematical works transformed Chinese mathematics. On a few occasions, he also talked about “traditional” chuantong 传统 Chinese mathematics. This seems historically preferable, but for simplicity I will follow Wu's earlier wording, which he has never completely abandoned.

³ Sun Bin advised Tian Ji to match his best horse against his opponent's middle horse and his middle horse against the opponent's weakest horse, and to let his own weakest horse lose to the opponent's best horse, scoring two victories in a three-round race (Ssu-ma Ch'ien and Nienhauser 1994: 39–40).

⁴ The other pseudonymous author, “Shu Qun,” could be Yuan Xiangdong 袁向东 (b. 1942), who later specialized in the history of modern Chinese mathematics. Yuan's early interest was Zu Chongzhi's work on the Calendar of Great Clarity (Da Ming Li 大明历; interview with the author, 17 October 2008), which is precisely the focus of the Shu Qun article.

⁵ Wu Wen-Tsun has repeated since about 2001 that he understood the power of computers during his work in the First Beijing Wireless Telegraphy Factory (Beijing wuxiandian yi chang 北京无线电一厂), where he was dispatched to “engage in labor” in 1970 and 1971 (Hu and Shi 2002: 76, 138; Ke 2009: 93–94). According to a contemporary report, the “Telecommunications Factory in Peking” produced some simple, single-purpose production automation devices (Cheatham et al. 1973).

⁶ Neotraditionalist historicism in Chinese mathematics could be identified with the eighteenth-century belief in the “Chinese origins of Western learning.” Assimilationist historicism has dominated the last sixty years.