4-47. Felix Klein

Felix Klein (1849–1925) and Henri Poincaré exchanged numerous letters, mostly during the period from 12 June 1881 to 22 September 1882, which was one of intense mathematical activity for both men, in the new field of automorphic functions, and on the uniformization theorem. The letters from this period were edited in 1923 by N. E. Nörlund (1923), and reedited by Pierre Dugac, with French translations of Klein’s letters (Dugac, 1989).11endnote: 1 The twenty-six letters of the early Poincaré-Klein exchange were translated from French to English by Robert Burns; see Saint-Gervais (2016). An overview of this celebrated exchange is provided in Klein (1926, 374–381), Klein (1923, 577–586), Dieudonné (1982), Gray and Walter (1997b), Gray (2000), Gray (2013, chap. 3), and Rowe (2018, chap. 11). On Klein’s life and work, see the detailed biography by Tobies (2019).

During the two decades following their early exchange, Klein and Poincaré collaborated on an international project to index scientific publications. They exchanged several letters on this topic, and both participated in a meeting held in London in August, 1899 (Armstrong et al., 1899). Another, even more ambitious project was launched by Klein in the closing years of the nineteenth century: the Encyclopedia of Mathematical Sciences Including Applications. A French-language version of the encyclopedia was planned, led by Jules Molk, and several volumes were published.22endnote: 2 Molk’s death in 1914, and the subsequent outbreak of the First World War put a strain on the collaborative project, and after 1916, the French version of the encyclopedia was abandoned. For a comparison of the two versions of the encyclopedia, see Gispert (2001). Molk sollicited a contribution from Poincaré (§ 4-59-1) in 1901, but nothing came of it.

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Notes

  • 1 The twenty-six letters of the early Poincaré-Klein exchange were translated from French to English by Robert Burns; see Saint-Gervais (2016).
  • 2 Molk’s death in 1914, and the subsequent outbreak of the First World War put a strain on the collaborative project, and after 1916, the French version of the encyclopedia was abandoned. For a comparison of the two versions of the encyclopedia, see Gispert (2001).

References

  • H. E. Armstrong, M. Foster, F. Klein, Th. P. Köppen, H. Poincaré, A. W. Rücker, B. Schwalbe, and E. Weiss (1899) International catalogue of scientific literature: Report of the Provisional International Committee. Science 10 (249), pp. 482–487. Link Cited by: 4-47. Felix Klein.
  • Congrès du Groupement des mathématiciens d’expression latine (Ed.) (1982) Actes du VIe congrès du regroupement des mathématiciens d’expression latine, Luxembourg, 7–12 septembre 1981. Gauthier-Villars, Paris. Cited by: J. Dieudonné (1982).
  • J. Dieudonné (1982) La découverte des fonctions fuchsiennes. See Actes du VIe congrès du regroupement des mathématiciens d’expression latine, Luxembourg, 7–12 septembre 1981, Congrès du Groupement des mathématiciens d’expression latine, pp. 3–23. Cited by: 4-47. Felix Klein.
  • P. Dugac (1989) Henri Poincaré, la correspondance avec des mathématiciens (de J à Z). Cahiers du séminaire d’histoire des mathématiques 10, pp. 83–229. Link Cited by: 4-47. Felix Klein.
  • H. Gispert (2001) The German and French editions of the Klein-Molk Encyclopedia: contrasted images. In Changing Images in Mathematics: From the French Revolution to the New Millennium, U. Bottazzini and A. Dahan Dalmedico (Eds.), Studies in the History of Science, Technology and Medicine, Vol. 13, pp. 93–112. Cited by: endnote 2.
  • J. Gray and S. A. Walter (Eds.) (1997a) Henri Poincaré: Trois suppléments sur la découverte des fonctions fuchsiennes. Akademie-Verlag, Berlin. Link Cited by: J. Gray and S. A. Walter (1997b).
  • J. Gray and S. A. Walter (1997b) Introduction. See Henri Poincaré: Trois suppléments sur la découverte des fonctions fuchsiennes, Gray and Walter, pp. 1–25. Link Cited by: 4-47. Felix Klein.
  • J. Gray (2000) Linear Differential Equations and Group Theory from Riemann to Poincaré. Birkhäuser, Boston. Cited by: 4-47. Felix Klein.
  • J. Gray (2013) Henri Poincaré: A Scientific Biography. Princeton University Press, Princeton. Cited by: 4-47. Felix Klein.
  • F. Klein (1923) Gesammelte mathematische Abhandlungen, Volume 3. Springer, Berlin. Link Cited by: 4-47. Felix Klein.
  • F. Klein (1926) Vorlesungen über die Entwicklung der Mathematik im 19. Jahrhundert, Volume 1. Julius Springer, Berlin. Link Cited by: 4-47. Felix Klein.
  • N. E. Nörlund (1923) Correspondance d’Henri Poincaré et de Felix Klein. Acta mathematica 39, pp. 94–132. Link Cited by: 4-47. Felix Klein.
  • D. E. Rowe (2018) A Richer Picture of Mathematics: the Göttingen Tradition and Beyond. Springer, Cham. Cited by: 4-47. Felix Klein.
  • H. P. d. Saint-Gervais (2016) Uniformization of Riemann Surfaces: Revisiting a Hundred-Year-Old Theorem. European Mathematical Society, Zurich. Link Cited by: endnote 1.
  • R. Tobies (2019) Felix Klein: Visionen für Mathematik, Anwendungen und Unterricht. Springer, Berlin. Cited by: 4-47. Felix Klein.