7-2-49. H. Poincaré to Felix Klein, English translation

Caen, 22 June 1881

Sir,

I have not yet received the items you indicate and that will undoubtedly arrive before long at their destination. But I don’t want to wait until then to thank you for your promises, and for your letter, which I read with the greatest interest. No sooner had I received it, than I ran to the library to request Volume 70 of Borchardt; unfortunately the volume was on loan so I was unable to read Mr. Schwarz’s memoir. But I expect I’ll be able to reconstruct it based on what you tell me, and recognize therein certain results I’d found without suspecting they had been the object of prior investigations.

As I believe I understand, the Fuchsian functions determined by the investigations of Mr. Schwarz and yourself are those with which I have been occupied, in particular in my note of 23 May.11endnote: 1 Poincaré (1881a), reedited in Nörlund and Lebon (1916, 12–15). The particular group you speak of in your last letter appear to me to be of great interest, and I will request your permission to cite this passage of your letter in a communication I will deliver shortly to the Academy, and where I will seek to generalize your result.22endnote: 2 Poincaré (1881b), reedited in Nörlund and Lebon (1916, 19–22).

As far as the name Fuchsian functions is concerned, I will not change it. The respect I owe to Mr. Fuchs disallows it. Besides, if it is true that the standpoint of the knowledgeable Heidelberg geometer is entirely at odds with yours and mine, it is also certain that his work served as the starting point and the foundation of all that has been done subsequently in this theory. Thereby, It is only right that his name remain attached to the functions in which they play such an important role.

Please be assured, sir, of my respect,

Poincaré

ALS 3p. Nachlass Klein 11, 353, Niedersächsische Staats- und Universitätsbibliothek, Göttingen. Transcribed in Nörlund (1923, 103) and Dugac (1989, 94). Translated by S.A. Walter from the original French (§ 4-47-4), after that of R. Burns in Saint-Gervais (2016).

Time-stamp: "28.04.2021 00:03"

Notes

  • 1 Poincaré (1881a), reedited in Nörlund and Lebon (1916, 12–15).
  • 2 Poincaré (1881b), reedited in Nörlund and Lebon (1916, 19–22).

References

  • 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: 7-2-49. H. Poincaré to Felix Klein, English translation.
  • N. E. Nörlund and E. Lebon (Eds.) (1916) Œuvres d’Henri Poincaré, Volume 2. Gauthier-Villars, Paris. Link Cited by: endnote 1, endnote 2.
  • N. E. Nörlund (1923) Correspondance d’Henri Poincaré et de Felix Klein. Acta mathematica 39, pp. 94–132. Link Cited by: 7-2-49. H. Poincaré to Felix Klein, English translation.
  • H. Poincaré (1881a) Sur les fonctions fuchsiennes. Comptes rendus hebdomadaires des séances de l’Académie des sciences de Paris 92, pp. 1198–1200. Link Cited by: endnote 1.
  • H. Poincaré (1881b) Sur les fonctions fuchsiennes. Comptes rendus hebdomadaires des séances de l’Académie des sciences de Paris 92, pp. 1484–1487. Link Cited by: endnote 2.
  • H. P. d. Saint-Gervais (2016) Uniformization of Riemann Surfaces: Revisiting a Hundred-Year-Old Theorem. European Mathematical Society, Zurich. Link Cited by: 7-2-49. H. Poincaré to Felix Klein, English translation.