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Applied Versus Pure Mathematics

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Abstract

This chapter is about the conflictual relations among pure and applied mathematical disciplines in the century from circa 1850 to 1950. It shows the historical variations associated with the ways in which boundaries were drawn in this period, and how, often under the influence of the political orientations of China in a global context, the focus upon one or the other aspect of mathematics was shifted. A first section describes the official debates about the nature of mathematics as it evolved into a discipline in the decades leading up to the early twentieth century. However, it would be anachronistic to attempt a historicization of the relationship between what we now consider as “pure” or “applied” mathematics in China at the turn of the twentieth century. Adopting a China-centred approach, this chapter applies instead a distinction between what in Chinese terms are the “fundamental principles” (ti 體) and “applications” (yong 用) in the mathematical sciences. In a second part, the example of statistics is used to illustrate how this pure-applied paradigm was instrumentalized in scientific and political discourses from the 1930s to the early 1950s, when statistical actors began to develop diverse strategies to find consensus with the hostile Communist state, oscillating between complementary and at times conflictual approaches to statistics.

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Notes

  1. 1.

    He obtained his doctorate there in 1929 with his thesis Recherches sur les fonctions entières quasi exceptionnelles et les fonctions méromorphes quasi exceptionnelles. Lyon: Bosc Frères & Riou, 1929. See Li and Martzloff (1998) p. 189–190.

  2. 2.

    Fan (1937) p. 1.

  3. 3.

    Fan later wrote a treatise on Rational Mechanics (Fan 1944).

  4. 4.

    Fan (1937) p. 9.

  5. 5.

    The only exception was during the Sui and Tang dynasty when a School for Computation was founded and functioned (with interruptions) for approximately 100 years. See Keller and Volkov (2014) p. 59–63 and Bréard and Horiuchi (2014) p. 159–166.

  6. 6.

    Zhao et al. (1981) 志一百二十二, 藝文三, 子部, 天文算法類, 算書, esp. p. 4343–4347.

  7. 7.

    Ibid. p. 4348.

  8. 8.

    Ruan and Luo (1882) scroll 31, p. 16A.

  9. 9.

    Quoted from Martzloff (1993) p. 160.

  10. 10.

    See Ding and Chen (1995) and Levenson (1968) vol. 1, p. 59–78.

  11. 11.

    See Fairbank (1978) chap. 10 “Self-Strengthening: The pursuit of Western Technology.”

  12. 12.

    See idem p. 528–530.

  13. 13.

    See Bréard (2001).

  14. 14.

    Li was affiliated with the Interpreter’s College from 1868 to his death in 1882.

  15. 15.

    Whewell (1859) “Preface”, p. 1A.

  16. 16.

    Idem.

  17. 17.

    Table adapted from Guo (2003). For an analysis of the exam problems of other late Qing schools where mathematics were taught, see Li (2012).

  18. 18.

    See Chap. 4, p. 89.

  19. 19.

    Measures of length, where 1 chi = 10 cun.

  20. 20.

    Translated from Xi and Gui (1880) scroll 2, p. 59A–59B.

  21. 21.

    On problems of pursuit in the Chinese mathematical tradition and their possible astronomical significance, see Bréard (2002).

  22. 22.

    Cai, after graduation from the Interpreter’s College, worked as a translator for the China-based news agency of the Associated Press. From 1893 to 1897 he headed the New School for Self-Strengthening (Ziqiang xuetang 自强 學堂), Wuhan University’s precursor.

  23. 23.

    On the concept of lü, see p. 43.

  24. 24.

    The values of the common logarithms of 2 and 16 given here are indicated qualitatively, their values are log2 = 0.301… and log1016 = 1.204… respectively.

  25. 25.

    Translated from Xi and Gui (1880) scroll 2, p. 59A-59B, original text shown in Fig. 8.2.

  26. 26.

    See Elman (2005) p. 409–410 and Li (1995) p. 105–107.

  27. 27.

    Shen (1901).

  28. 28.

    Two units of length.

  29. 29.

    Memorial dated 15 March 1909. Translated from XTXF (1911) no 2 (1910), p. 2B. For an integral translation of the Memorial, see Bréard (2008) Appendix A.5, p. 179–186.

  30. 30.

    The Yu gong 禹貢, a chapter in the Book of Documents (Shang shu 尚書), which is the most authoritative ancient Chinese terrestrial description. Its authorship is attributed to Yu the Great (5th–3rd cent. BCE), the legendary founder of the Xia dynasty. The claim that he was the first Chinese statistician can be traced back to at least as early as to the French Jesuit missionary Antoine Gaubil (1689–1759). See Simon (1970) and Richthofen (1877).

  31. 31.

    Ca. 145–ca. 86 BCE. Author of the first Chinese history, the Records of the Grand Historian (Shiji 史記).

  32. 32.

    See Article (tiao 條) 1: Xianzheng bianchaguan you zou ding tongji biaoshi zongli 憲政編查館又奏定統計表式總例 (The Commission for Drawing up Regulations for Constitutional Government further memorializes to fix general rules for the design of statistical tables) in XTXF (1911) no 2 (1910) p. 2A.

  33. 33.

    Later in the text, on p. 105, Meng Sen explains this expression in relation to mass observations (dashu guancha 大數觀察) :

    The expression “large numbers” has the meaning of what I call an extreme that is not made of instances (Dashu yu zhe ji wu suo wei ji bu xuyu zhi yi 大數云者即吾所謂極不須臾之義).

  34. 34.

    Meng (1907) p. 103.

  35. 35.

    See Chap. 7, p. 70.

  36. 36.

    See Bréard (2006).

  37. 37.

    Meng (1909) p. 70.

  38. 38.

    See Fu and Hua (1896). The expression jueyi chosen by the translators for “probability” existed earlier in classical Chinese, literally meaning “dispelling doubt” or “to resolve questions that are difficult to decide” (jiejue yihuo 解決疑惑).

  39. 39.

    Galloway (1796–1851) was a Scottish mathematician working as an actuary at the Amicable Life Assurance Office. His most famous paper “On the Proper Motion of the Solar System” won a Royal Medal in 1848 for his application of probability theory to determining the proper motion of the solar system. See Galloway (1843) and Obituary (1852).

  40. 40.

    Galloway (1839).

  41. 41.

    Bennett (1967) p. 80.

  42. 42.

    Yan (1990) for example states wrongly that the original of John Fryer’s and Hua Hengfang’s translation was Augustus De Morgan’s work.

  43. 43.

    Galloway (1839) Preface p. xi. For a detailed discussion of the mathematical content of the book, see Guo (1989) and Wang (2007).

  44. 44.

    Reference to Kameichi (1899). Translated from Meng (1909) p. 270–273.

  45. 45.

    In Yang (1910) p. 6A–6B.

  46. 46.

    For example, Shen was in close contact with Xue Fucheng 薛福成 (1838–1894), who, like Shen, was a native of Wuxi, Jiangsu province, and for whose diary, written during his diplomatic mission to Great Britain, France, Italy and Belgium from GX 17/3/1 to GX 20/5/20, Shen wrote a postface. See Lü (1995) p. 57.

  47. 47.

    See the Book Register (Shuji ce 書籍冊) from 1911, Archives of the Commission for Constitutional Reform, No 1 Historical Archives, Beijing, showing two copies each of Anonymous (high official investigating governments) (1907) and Meng (1909).

  48. 48.

    For a more detailed account of Shen’s CV, see his Record of Conduct reprinted in Qin et al. (1996) 8:581 and translated in Bréard (2008) Appendix A.6, p. 186–188.

  49. 49.

    The Gnomon of Zhou (Zhou bi suan jing 周 髀算經) and Master Sun’s Mathematical Classic (Sunzi suan jing 孫子算經) respectively.

  50. 50.

    Shen and Li (1908) scroll 5, p. 2B.

  51. 51.

    Gu (1910) based on Merriman (1884) and Gu (1913) based on Yule (1911).

  52. 52.

    Gu (1913) Preface p. 2.

  53. 53.

    After the Boxer Rebellion, 15 million US dollars were available for educational purposes from the remissions of the Boxer Indemnity Fund. This allowed Chinese students to study in the United States after 1908. Although by then many more students went to Japanese universities with government or personal funding, the United States, followed by Europe, was the preferred destination for pursuing advanced degrees in pure and applied mathematics, or science and engineering, subjects in which many Chinese students obtained PhDs from the 1920s on. Jiang Lifu 姜立夫 (1890–1978) for example, left China in 1910 to study mathematics at the University of California, Berkeley and obtained his PhD from Harvard in 1919 on The Geometry of Non-Euclidean Line Sphere Transformation. Upon his return to China he was the only mathematics professor in Nankai University in Tianjin, where he founded the Mathematics Department in 1920. Among his many students was the later famous geometer S. S. (Shiing-Shen) Chern 陳省身(1911–2004). See Xu (2002).

  54. 54.

    Shen (1933). Talk given in 1933 at the Mathematics Department of The Great China University (Daxia daxue 大夏大學) in Shanghai. Later, in 1940, Shen obtained a PhD in Japan from the Tohoku Imperial University 東北帝國大學.

  55. 55.

    On Tang Qingzeng’s life and thought, see Borokh (2013).

  56. 56.

    Tang (1931) p. 136.

  57. 57.

    See Tang (1931) p. 135:

    As for economic statistics, they particularly record the facts (shishi 事實) of wealth and industry and commerce, based on the accuracy of mathematical methods, they arrange and put in order with the purpose of deciding upon an accurate plan, they make comparisons in order to gain all sorts of knowledge, they use inductive methods in order to obtain all sorts of experimental laws. These laws, which should rely upon the statistics which have determined them, can only be applied to a specific time and place. […] The Italian statistician Gabaglio says: “Statistics do choose and analyse economic realities, they represent the material of these realities, arranged and in order in a critical and comparative mode. Accomplished statistics provide for the study of economy a kind of material that is based on experience, and thus complements what cannot be achieved from abstract theories and proofs.” etc. These words are true indeed.

  58. 58.

    See, for example, the article “Reasons why China has not developed statistical science and Zheng Qiao’s theory of illustrated registers” (Wo guo tongjixue bu fada zhi yuanyin yu Zheng Qiao zhi tupu xueshuo 我國統計學不發達之原因與 鄭樵之圖 譜學說) by Wei Jun 盛俊, one of the co-founders of the China Statistical Society (Zhongguo tongji xueshe 中國統計學社), in Chen (1934) p. 95–99.

  59. 59.

    Qin (1934) p. 2.

  60. 60.

    Liu adds translations of the Chinese terms into German or/and English for most of the technical statistical vocabulary used in Liu (1942). I have reflected these in Fig. 8.5, adding quotation marks to the German terms.

  61. 61.

    Liu (1942) p. 14.

  62. 62.

    See Liang (1922). On Liang’s ideas about applying statistics in historical research, see Song (2006).

  63. 63.

    Garnaut (2013) p. 238. I discuss in more detail the conflicts between mathematical and political approaches to statistical concepts in twentieth-century China in an article currently in preparation for publication in the journal Historia Mathematica.

  64. 64.

    See the tables of content in Figs. 8.7 and 8.8 from Chen (1934) and (Zhonghua quanguo zong gonghui tongji chu 1950) respectively.

  65. 65.

    Chen (1925).

  66. 66.

    Beizuofu (1957).

  67. 67.

    Detailed biographies of many important Chinese statisticians can be found in Gong (2000). For Jin Guobao, see also Ghosh (2014) p. 103–110.

  68. 68.

    See Fig. 8.9 for his complete bibliography.

  69. 69.

    我要尽我的余年, 把我的一切力量, 贡献给党和人民 . See Jin Guobao’s speech when attending the Second Plenary Conference of the Second National Committee of the Political Consultative Conference 政治协商会议第二届全国委员会第二次全体会议 , published in the journal People’s Daily (Renmin ribao 人民日報) 1956.02.10.

  70. 70.

    The summaries of the interventions were published 1958 in Caijing yanjiu 财经研究 (3) p. 57–62 & 65.

  71. 71.

    Ibid., p. 65.

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    Andrea Bréard

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Bréard, A. (2019). Applied Versus Pure Mathematics. 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_8

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