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Early Twentieth-Century Visitors and the Development of Modern Mathematics in China

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Notes

  1. In both [24] and [26], Yuen-Ren Chao is not listed as a mathematics PhD. However, according to [20, p. 295], Chao studied mathematical logic under the supervision of Henry M. Sheffer.

  2. In Chinese culture, the surname is written before the given name. In this paper, however, we adopt the convention of writing the surname last. Regarding romanization—the transliteration from Chinese characters into the Latin alphabet—there was at first no official system, resulting in a variety of spellings. Since 1978, however, Chinese government regulations have mandated the use of the pinyin system, which has become the international standard. As a result, many older Chinese names have two romanized forms. For example, with the arrival of pinyin, the capital city Peking became Beijing, and the name Yuen-Ren Chao became Yuanren Zhao. In what follows, I use both traditional and pinyin names where applicable.

  3. For more social and institutional background, we refer to [16, 29].

  4. For what follows in this section, compare [7, 22].

  5. Chiang’s Harvard thesis was titled “The Geometry of a Non-Euclidean Line–Sphere Transformation” and was written under the supervision of Julian Coolidge.

  6. On November 1, 1897, two German missionaries, Franciscus Nies and Richard Henle, were murdered in Juye county in the Shandong Province of China. Thirteen days later, seven hundred German soldiers landed in the province’s Jiaozhou Bay and occupied the area, which from 1898 to 1914 included the German colony of Qingdao.

  7. On Knopp in China, see [14, p. 109] and [27].

  8. For more on this visit, see [14, pp. 111–113] and [24, p. 62].

  9. Unfortunately, Borel gave no mathematical lectures during the visit.

  10. For these and other details of this visit, see [14, p. 110], [21], and [24, p. 63].

  11. For an account of the whole tour, see Blaschke’s book Reden und Reisen eines Geometers [4, pp. 87–90].

  12. Blaschke’s visit is treated in [14, pp. 114–115] and [24, p. 63].

  13. Emanuel Sperner obtained his PhD in 1928 under the supervision of Otto Schreier and Wilhelm Blaschke. For more on Sperner’s life, see [1].

  14. For more on Birkhoff’s life and work, see [2, 17, pp. 56–85], and [25].

  15. On Osgood’s life, see [2, 10, 17, pp. 32–55], and [25].

  16. On Osgood’s time in China, see [8] and [14, pp. 117–118].

  17. On Wiener’s time in China and its import, see [14, pp. 118–129] and [24, pp. 125–130].

  18. On Wiener’s life, see his autobiography [19].

  19. That Wiener and Hua remained close is clearly evidenced in [11] and [23].

  20. For more on Hadamard’s Chinese sojourn, see [12] and [18].

  21. Both Hadamard’s biography [15, pp. 221–226] and Wiener’s autobiography [19, Chapter 10] provide accounts of their Beijing experiences.

  22. Recall that in 1896, Hadamard had proved, independently of Charles-Jean de la Vallée Poussin, the prime number theorem, which describes the asymptotic distribution of the primes among the positive integers.

  23. For a detailed description of the early papers published in Acta Mathematica Sinica, see [6, pp. 278–280].

  24. See, for example, [11, 14, 18], and [23].

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Acknowledgments

This work was supported by the National Natural Science Foundation of China (NSFC11921001) and the National Key Research and Development Program of China (2018YFA0704701). The author is grateful to Professors Richard Gardner and John Ewing as well as to a referee for comments and suggestions on earlier versions of this paper. Its quality has been substantially improved as a result. I also thank Professor Karen Hunger Parshall for her kind help in improving the English and the Mathematisches Forschungsinstitut Oberwolfach for permission to use the photos of Blaschke, Knopp, and Sperner from the Oberwolfach photo collection. The photos of Russell, Osgood, Wiener, and Hadamard are in the public domain, and all other photos were created by the author.

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    Chuanming Zong

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Zong, C. Early Twentieth-Century Visitors and the Development of Modern Mathematics in China. Math Intelligencer 44, 137–149 (2022). https://doi.org/10.1007/s00283-021-10117-2

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