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Visions of Modernity

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Nine Chapters on Mathematical Modernity

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Abstract

The last of the present Nine Chapters analyses the nationalist and ideological aspects of some twentieth-century self-assertive discourses that connect Chinese tradition and modernity with backwardness and progress in science. It shows what persists of China’s efforts to revive its scientific past today and problematizes the notion of “modernity” and its relevance to the history of mathematics in China. This final discussion is introduced by asking what it means today to be a global modern mathematician, relating a recent event that has raised many questions about the possible cultural specificity of a Chinese-born American mathematician’s pathbreaking approach to number theory.

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Notes

  1. 1.

    See Zhang (2012), online summary at: http://hbylzx.vicp.net/ReadNews.asp?NewsID=8865 consulted 27 January, 2017.

  2. 2.

    Chen (2011).

  3. 3.

    Cai (2013) p. 93.

  4. 4.

    See Zhao (2015) p. 7: “Sinology education is an important part of ideological education in colleges and universities” (Guoxue jiaoyu shi dangdai daxuesheng sixiang jiaoyu de zhongyao zucheng bufen 国学 教育 是当代 大学 生思 想 教育 的重要 组 成部 分 ).

  5. 5.

    For an overview of the curricula, see Zhao (2015) p. 9.

  6. 6.

    The first of these conferences was held in Qingdao in 2013. For a summary, see Yu (2013).

  7. 7.

    See Kang Kuanying’s 亢宽 盈 contribution on “The system of Natural National Studies considered from the characteristics of China’s traditional mathematics” (Cong Zhongguo chuantong shuxue de tezheng kan ziran guoxue tixi 从 中国传 统 数学 的特征看自然国学 体系 ) in Zhang et al. (2002) p. 8–9.

  8. 8.

    See Tu (2011).

  9. 9.

    See page 15.

  10. 10.

    Translated from Zhang and Tong (2015) p. 93.

  11. 11.

    Chen was named director of the newly founded National Studies Department of Beijing University in 1995.

  12. 12.

    Yu (2013) p. 91.

  13. 13.

    Zhang (2014).

  14. 14.

    Stating that there are an infinite number of pairs of twin primes, i.e. two consecutive primes where p n+1 = p n + 2.

  15. 15.

    Every even integer greater than 2 can be expressed as the sum of two primes.

  16. 16.

    See Chap. 1 p. 7.

  17. 17.

    Norbert Wiener (1894–1964), professor of mathematics at MIT who visited the Departments of Electrical Engineering and Mathematics at Qinghua University in Beijing (Fall, 1935–Summer, 1936) “provided a vivid description of how many of the Chinese faculty carried the distinct styles of the country in which they were trained.” Wang (2002) p. 306n51. See Wiener (1956) p. 186 and Wei (1996).

  18. 18.

    See for example http://news.xinhuanet.com/local/2015-08/25/c_1116370665.htm, consulted on January 25, 2017. See also Wilkinson (2015) and the film documentary Counting from infinity by George Csicsery, Zala Films 2015 http://www.zalafilms.com/films/countingindex.html.

  19. 19.

    First published by the Shanghai-based Juvenile and Children’s Publishing House (Shaonian ertong chubanshe 少 年兒童 出版社 ) in 1962.

  20. 20.

    See Riemann (1859). The hypothesis concerns the location of zeros to the Riemann zeta function, defined as the absolutely convergent infinite series:

    $$\displaystyle \begin{aligned}\zeta(s) = 1 + 2^{-s}+3^{-s}+4^{-s}+\cdots\end{aligned}$$

    or, in more compact notation:

    $$\displaystyle \begin{aligned}\zeta(s)=\sum^{\infty}_{n=1}\frac{1}{n^s}\end{aligned}$$

    where s is a fixed complex number with a real part greater than 1.

  21. 21.

    The entry on the Goldbach conjecture, for example, was written by the number theorist Wang Yuan 王元 (b. 1930). Former president of the Chinese Mathematical Society, he works as a member of the Chinese Academy of Sciences at the Institute of Mathematics. In the attempt to solve the Goldbach conjecture, Wang’s research focuses on the sieve method and its applications, Diophantine approximations and equations and applications of number theory.

  22. 22.

    After the Cultural Revolution, Xia obtained his professorship at Fudan University in 1978 and went to the United States in 1984. He mainly focused on operator theory and algebraic topology.

  23. 23.

    Chapter 2, “Research on π by Chinese mathematicians in the past” (Wo guo gudai shuxuejia guanyu π de yanjiu 我 国 古代 数 学 家 关 于π的研 究 ) in Xia (1964) p. 10–17.

  24. 24.

    Idem p. 17.

  25. 25.

    Page 2 of Shaonian ertong chubanshe 少 年儿童 出版社 , 1962 ed.

  26. 26.

    As in Wootton (2015).

  27. 27.

    See Mehrtens (1990) p. 7.

  28. 28.

    Translated from Chern (1948) p. 11.

  29. 29.

    Cao (1963). The “Four Modernizations” concerned agriculture, industry, science and technology, and national defence.

  30. 30.

    Private communication with Prof. Juan Alvarez-Paiva.

  31. 31.

    On the “Chinese way” of learning mathematics today, see Fan et al. (2004) and the critical review (Bréard 2012) of the collection of papers written by a group of educators and researchers interested in the culture-specific kind of mathematics education in China today.

  32. 32.

    Such valorization of ethnoepistemology can equally be observed in India, where “Vedic mathematics,” a set of versified calculation tricks presumably as old as the Vedas, has been introduced in the school curriculum. See (Michaels 2015).

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  1. Faculté des Sciences d’Orsay, Université Paris-Sud, Orsay, France

    Andrea Bréard

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Bréard, A. (2019). Visions of Modernity. In: Nine Chapters on Mathematical Modernity. Transcultural Research – Heidelberg Studies on Asia and Europe in a Global Context. Springer, Cham. https://doi.org/10.1007/978-3-319-93695-6_9

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