Traditional Chinese Mathematics in the PRC


A review of You Fight Your Way, I Fight My Way: Wu Wen-Tsun and Traditional Chinese Mathematics, by Jiří Hudeček.

In this fascinating dissertation, Jiří Hudeček examines the academic endeavours of a French-trained Chinese mathematician Wu Wen-Tsun (born 1919) in algebraic topology, applied mathematics, as well as his turn to traditional Chinese mathematics and his internationally acclaimed work on the “mechanisation of mathematics” (computer proofs). Basing his study on Wu’s publications, unpublished materials from archives in China, and his personal interviews with Wu himself and other Chinese mathematicians, he confirms Wu’s claim that his method on the mechanisation of mathematics was mainly inspired by medieval Chinese algebra, and argues that Wu’s turn to the history of traditional Chinese mathematics was “a sophisticated response to political, institutional and ideological pressures on mathematics in post-1949 Maoist China” (p. vii).

Starting with one of Mao Zedong’s trademark slogans, “You fight your way, I fight my way”, Chapter 1 provides an introduction to the interesting nature of mathematical development in twentieth-century China in general, and the works of Wu Wen-Tsun in particular, in a context of the greater social and political atmosphere in the People’s Republic. Besides an innovative mathematician with international impact, the public images of Wu in China as “a paragon of independent innovation” (p. 3) and as “an example of the relevance of Chinese traditional knowledge” (p. 5) both respond to that slogan of Mao’s. According to the author, the problems of why and how Wu reoriented his research path in modern mathematics and linked it to traditional Chinese mathematics challenge the historian to re-examine Wu’s life and work.

Though not a full biography, Chapters 2 through 6 present a chronological narrative of Wu Wen-Tsun’s life and work until the present time, with the main focus on the source and process of his reorientation in the late 1970s. Chapter 2 summarises Wu’s early years, his topology training in France since 1947 to 1951, his first years as a topologist in China from 1952 to 1958, and his research in characteristic classes of sphere bundles (especially in Pontrjagin classes), imbedding and isotopy. The dissertation uses published peer reviews, mainly retrieved from MathSciNet, and also Jean Dieudonné, History of Algebraic and Differential Topology (Boston: Birkhäuser, 1989), to qualitatively discuss the impact of Wu’s work on modern mathematics. It also uses scientometric databases, including MathSciNet, Google Scholar and CKNI, to provide quantitative elements to the assessment of Wu’s work in this and later chapters.

Chapter 3 focuses on how the scholars in the Institute of Mathematics, Chinese Academy of Sciences (IMCAS), including Wu Wen-Tsun, coped with the external political demands in the period between 1953 and 1969. Instead of following two approaches of traditional historiography emphasising either the antagonistic division between intellectuals and the Communist Party of China, or on the competition between political and social capital, this chapter employs Richard P. Suttmeier’s theoretical framework (pp. 46-48) to understand how the form and contents of mathematics in the PRC was shaped by the social environment. For most of the 1950s, IMCAS was in what Suttmeier calls the “state of regularisation” in the Chinese research sector. It was run without much political intrusion. During the Great Leap Forward period in the late 1950s and early 1960s, IMCAS was moved into a “state of mobilisation”, when the research sector was required to “link theory with practice” (p. 65). The researchers of IMCAS were regrouped into new research sections oriented to practical applications of mathematics. Algebraists, number theorists and topologists, including Wu Wen-Tsun, were all assigned to the section of operation research. Wu turned his attention to game theory and gained fruitful results, which match the shared long-term goal of a planned growth of Chinese mathematics that the mathematicians wished to achieve despite the apparent fluctuation of policies.

Chapter 4 discusses the impact of the Cultural Revolution (CR) and later political campaigns on Wu Wen-Tsun’s continual search for a long-term research orientation, which, during this period, was mainly toward the fields of traditional Chinese mathematics and mechanical theorem proving. The relative difficulty of making international contacts caused by the political insecurity of the CR period, combined with Wu’s advanced age for a mathematician, are two reasons for Wu’s desire to pursue independent research in China. In 1974, the Anti-Lin Anti-Confucius campaign became “an umbrella for historical and philosophical studies” (p. 121), which was not acceptable during earlier stages of the CR. This, together with Wu’s wish to do research independently, shaped his new goal to draw lessons from traditional Chinese mathematics for modern mathematical practice, which was both an innovative idea and an elaboration on Mao’s policy of “independence and self-reliance” (p. 123).

Chapter 5 focuses on Wu’s approach to the history of mathematics. It shows that Wu argued that preferences for problem-solving, constructiveness and mechanisation are defining features of traditional Chinese mathematics, and he used them to refute certain Western historiographical bias to traditional Chinese mathematics mainly for not having axiomatisation and proofs. Wu put great emphasis on reconstructing demonstrations in ancient Chinese mathematics strictly with tools available to mathematicians in ancient China and on avoiding explanatory devices of Western mathematics such as parallel lines or modern algebraic symbols.

Chapter 6 presents Wu’s work after 1977, with a detailed explanation of his method on the “mechanisation of mathematics”. Wu’s work on this topic is highly cited in all databases the author surveyed. Wu believes that for certain levels, “with the development of computers, the laborious, patchy style of axiomatic-deductive reasoning would be superseded by algorithmic, mechanical methods” (p. 160), and the “mechanical methods” are exactly where the ancient Chinese used to be ahead of the world. This fits the ongoing agenda for independence, self-reliance and Wu’s personal patriotism. After the explanation of the theory and an example of Wu’s method, the author turns to the main sources of Wu’s method. By comparing it to the method of Four Unknowns in medieval Chinese algebra, the author presents a convincing structural affinity between this and Wu’s method, confirming Wu’s claim that his method was inspired by traditional Chinese mathematics. Joseph Fels Ritt’s theory also helped shape Wu’s method in the course of its development. In the concluding chapter 7, the author again cites the international recognition of Wu’s mathematical work throughout his career, his “cultural nationalism” (p. 191), and his historiography to “establish ancient Chinese mathematics’ close contacts with fundamental mathematical realities as understood by him, a twentieth-century mathematician” (p. 199).

Jiří Hudeček’s study makes an important contribution to the historiography of modern Chinese mathematics, which is generally lacking in the West in the research domain of history of science. By analysing the interactions between Chinese politics and the career orientations of Wu Wen-Tsun, the dissertation provides a convincing narrative for this twentieth-century Chinese mathematician, his rationale for studying traditional Chinese mathematics and its influence on his method for the mechanisation of mathematics.

Jia-Ming Ying
College of Humanities and Social Sciences
Taipei Medical University

Primary Sources

Wu Wen-Tsun’s publications (more than 90 articles and books)
Archival materials about IMCAS and ISSCAS, deposited in the Archives of CAS under volume numbers Z370 and Z373, respectively
The archives of the Academia Sinica, deposited in the Second Historical Archives of China in Nanjing
MathSciNet, Google Scholar and CKNI Databases

Dissertation Information

University of Cambridge. 2011. 235 pp. Primary Advisors: Catherine Jami, Eleanor Robson.


Image: Cover of Baike zhishi (Encyclopaedic Knowledge), 12 (1980).

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