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Visions of Antiquity

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Nine Chapters on Mathematical Modernity

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Abstract

The first of the present Nine Chapters analyses the nationalist and ideological aspects of some nineteenth- and twentieth-century self-assertive discourses that connect Chinese tradition and modernity with backwardness and progress in science. These historiographic snapshots reveal different ways of instrumentalizing research on China’s mathematical tradition, all of them in the context of the growing political and economic entanglements of China with the outside world after the Opium Wars. Whether for enriching the country, for preserving cultural identity or for patriotic education, the transmitted mathematical texts were selectively interpreted to serve a specific ideological purpose and were rarely read in view of developing new mathematical theories per se. The appeal of a radical scientific “modernity” outside of China nevertheless erased all efforts to revive China’s national tradition in contemporary mathematical research and conceptually and methodologically follow an alternative path to the West.

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Notes

  1. 1.

    Starting with Mehrtens (1990), the advent of mathematical modernity has been problematized by a number of historians of Western science. For a recent overview and discussion of definitions of modernity and modernism in mathematics, see Gray (2008) chapter 1.

  2. 2.

    Needham (1970) p. 397.

  3. 3.

    Pomeranz (2000).

  4. 4.

    Needham (1959).

  5. 5.

    As claimed in Hart (2013).

  6. 6.

    See Martzloff (1993).

  7. 7.

    Chinese translation of a Persian astronomical handbook with tables, a so-called zı̄j, prepared in 1383 and available at the Islamic Astronomical Bureau in Beijing. See Dalen (2002) p. 336–339.

  8. 8.

    618–807. The Nine Upholders Calendar was a calendrical system “adapted into Chinese from Indian sources at the beginning of the eighth century.” See Martzloff (2016) p. 109.

  9. 9.

    1279–1368. Based on Jamāl al-Dīn’s work, a Muslim astronomer from Bukhara. See Sivin (2009) p. 52 and Dalen (2002) p. 330.

  10. 10.

    1368–1398.

  11. 11.

    A legendary emperor, ca. 2300 BCE.

  12. 12.

    An East Shandong peninsula.

  13. 13.

    The south-eastern Asian region of Indochina.

  14. 14.

    In the extreme North, now Inner Mongolia.

  15. 15.

    Eleventh century—256 BCE.

  16. 16.

    Translated from Zhang et al. (1975, vol. 2, p. 544–545) scroll 31 卷三十一, Memoires 7 志第七, Calendrical Systems 1 曆一 , chap. “On Calendar Reform” (Lifa gaige 曆法沿革 ).

  17. 17.

    See, for example Tsu and Elman (2014) and Renn (2012).

  18. 18.

    See Tian (2005).

  19. 19.

    In particular, the first and integral translation of Li Shanlan’s Methods for Testing Primality (Kao shugen fa 考數根法, 1872) is provided in Appendix B.

  20. 20.

    See the editions in Qian (1963) vol. 1, p. 83–258, Guo (1990) and Li (1993). Annotated English translations of the text, including its commentaries, can be found in Shen et al. (1999) and Guo (2013); Chemla and Guo (2004) provide a French translation with commentaries and a Chinese edition of the text.

  21. 21.

    The long-lasting impact of the Nine Chapters was not limited to China, but spread to other Chinese-language based cultures. About the Nine Chapters in nineteenth-century Korea, for example, see Ying (2011).

  22. 22.

    Studying intermediaries, translations and networks has been proposed in Moyn and Sartori (2013) p. 9–16 as one possible framework for global intellectual history. See also Schaffer et al. (2009).

  23. 23.

    See the foundational articles Lan (1915, 1916).

  24. 24.

    See Wang (2002).

  25. 25.

    继兹以往. 代 兴于神州学术之林. 而为芸芸众生所托命者, 其唯科学乎, 其唯科学乎! Quoted from the editorial reproduced in Fan and Zhang (2002) p. 18.

  26. 26.

    A compound expression for building “a rich country and a strong army” (fuguo qiangbing 富國強 兵). On the emerging concept of nation in late nineteenth-century China, see Matten (2012).

  27. 27.

    See, for example, Yuan (1901) 凡例, p. 1A.

  28. 28.

    Quoted from Doleželová-Velingerová and Wagner (2014) p. 10.

  29. 29.

    Janku (2014) p. 333n13.

  30. 30.

    Zhang (1896) contained twelve titles on mathematics (Suanxue 算學) of which only two are translations: 勾股六術一卷 (by Xiang Mingda 項名達), 九數外錄一卷 (by Gu Guanguang 顧觀光), 算式集要四卷 (original by Charles Haynes Haswell 哈司韋, transl. by John Fryer 傅蘭雅 and Jiang Heng 江衡), 衍元要義一卷 (by Xie Jiahe 謝家禾), 弧田問率一卷 (by Xie Jiahe), 直積 囘求一 卷 (by Xie Jiahe), 割圜連比例 術圖解三卷 淸 (by Dong Youcheng 董祐誠), 撱圜求周 術一 卷 (by Dong Youcheng), 斜弧三邊求角補術一卷 (by Dong Youcheng), 堆垛求積術一卷 (by Dong Youcheng), 三統術衍補一卷 (by Dong Youcheng), 器象顯眞四卷 圖一卷 (The Engineer and Machinists Drawing Book by V. Lebland and J. Armengaud, transl. by John Fryer and Xu Jianyin 徐建寅).

  31. 31.

    For example, two mice digging under a wall from opposite directions, or two plants growing at different speed, as explained by Cui Chaoqing 崔朝慶 in the two titles Pu guan bing sheng cao 蒲莞並生草 and Liang shu chuan yuan cao 兩鼠穿垣草 in Yuan (1901).

  32. 32.

    Wu Cheng’s 呉 誠 Detailed Explanations of Algebra (Daishu shu xiangjie 代 數術詳解) discuss the Chinese translation of Wallace (1853) in Fu and Hua (1873).

  33. 33.

    Jiao Xun’s Explanation of the One Celestial Element (Tianyuan yi shi 天元一釋), 2 vols. already compiled a century earlier in 1800.

  34. 34.

    Li and Edkins (1898), see p. 30.

  35. 35.

    Teng and Fairbank (1979) p. 76.

  36. 36.

    Idem p. 78.

  37. 37.

    Lit. Lifa 曆法 . The expression does not only refer to the calendar, but also to the computational system underlying astronomy more generally. See Martzloff (2016) p. 16–19 on the technical meaning of the term li.

  38. 38.

    See Anonymous (1907) and Amelung (2014) p. 52.

  39. 39.

    Amelung (2014) p. 52.

  40. 40.

    Due to the critiques of the National Studies movement, the notion of National Studies was conceptualized in various ways and evolved over time. It reemerged in 1993, a point that I will return to in the final Chap. 9. On the diverse facets of guoxue over the last century, see the collection of articles in the journal Perspectives Chinoises No. 2011/1. Online edition at: https://perspectiveschinoises.revues.org/5723. See also the programmatic article (Zheng 1929) defending the idea that scientific knowledge and methodology is necessary to pursue National Studies.

  41. 41.

    See Wylie (1897), Mikami (1912) and the correspondence between D. E. Smith and Li Yan in Xu (2015). The collaboration between the latter two ended abruptly in 1917 because Smith was unsatisfied with the many historical imprecisions in Li’s writings and the little he could learn from Li Yan.

  42. 42.

    Li (1917) p. 238.

  43. 43.

    “One of China’s foremost physicists,” who “in his youth published several articles on the history of mathematics.” Amelung (2014) p. 53.

  44. 44.

    See Ye (1916) p. 59.

  45. 45.

    Idem.

  46. 46.

    See, for example, the introduction to the Eighth Section: A Primer of the History of Mathematics in China (第八門 數學小史內篇之部) in Zhao (1923) p. 721.

  47. 47.

    Liu (1936) p. 325–326.

  48. 48.

    Formulas for the summation of infinite trigonometric series brought to China by the French Jesuit Pierre Jartoux (1669–1720). See also chap. 2, p. 23.

  49. 49.

    Mao Yisheng (1896–1989) is regarded as the founder of modern bridge engineering in China. He obtained his master’s degree from Cornell University and was the first ever to obtain a PhD in engineering at the Carnegie Institute of Technology in 1919.

  50. 50.

    See Yan (1936) p. 37, translated partly to German in Amelung (2014) p. 54.

  51. 51.

    See Renmin ribao 人民日報 (People’s Daily) (1951.08.16).

  52. 52.

    Qian (1951) p. 1043.

  53. 53.

    Translated from Hua (1951) in Wang and Shiu (1999) p. 162 and quoted in Amelung (2003) p. 254–255 .

  54. 54.

    On Wu Wen-Tsun’s politically motivated change in research orientation, see Hudecek (2012) and the excellent biography (Hudecek 2014).

  55. 55.

    I shall come back to the problem of “modernity” in the last chapter of this book.

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    Andrea Bréard

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Bréard, A. (2019). Visions of Antiquity. 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_1

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