7-2-61. H. Poincaré to Felix Klein, English translation

Paris, 28 March 1882

Monsieur,

You appended a note to my article ‘‘Sur les Fonctions Uniformes qui se reproduisent par des substitutions linéaires’’, in which you reveal the reasons underlying your rejection of my terminology.11endnote: 1 Poincaré (1882a): “On the single-valued functions that replicate themselves under linear substitutions”; Klein (1882a). You were good enough to send me the page proofs and to ask me if I wanted any changes made. I am grateful to you for the discretion of your approach, which I could not abuse, however, by asking you to silence half of what you think.

You will understand, then, that I cannot leave the readers of the Annales with the impression that I have committed an injustice. That is why I wrote, as you recall perhaps, that I requested no change to your note, but that I would request permission to write you a few lines justifying my terminology.22endnote: 2 See Poincaré’s previous letter to Klein (§ 4-47-15).

Here, then, are those lines; perhaps you will judge them suitable for insertion. In turn, I will ask you if you wish me to make any changes to the text of this little note. I stand ready to make any changes that would not alter my meaning.33endnote: 3 Poincaré’s response to Klein’s footnote appeared in Volume 20 of the Mathematische Annalen (Poincaré, 1882b). The letter has been reedited (§ 4-47-17), and translated to English (§ 7-2-62).

Please excuse my importunity and pardon this bit of pro domo advocacy.

Please rest assured, Monsieur, of my greatest regard,

Poincaré

I would be obliged if you could give me the address of Mr. Hurwitz, to whom I would like to pay homage with an offprint of my work.

I would also be very grateful if you were able to indicate the general features of the proof by means of which you establish the theorem stated in your latest work: “Ueber eindeutige Funktionen mit linearen Transformation in sich”.44endnote: 4 Klein (1882b).

PTrL. Translated by S.A. Walter from the original French (§ 4-47-16). Previously translated by R. Burns in Saint-Gervais (2016).

Time-stamp: " 1.05.2021 14:12"

Notes

  • 1 Poincaré (1882a): “On the single-valued functions that replicate themselves under linear substitutions”; Klein (1882a).
  • 2 See Poincaré’s previous letter to Klein (§ 4-47-15).
  • 3 Poincaré’s response to Klein’s footnote appeared in Volume 20 of the Mathematische Annalen (Poincaré, 1882b). The letter has been reedited (§ 4-47-17), and translated to English (§ 7-2-62).
  • 4 Klein (1882b).

References

  • F. Klein (1882a) Editorial note to Poincaré, ‘Sur les fonctions uniformes qui se reproduisent par des substitutions linéaires’. Mathematische Annalen 19 (4), pp. 564. Link Cited by: endnote 1.
  • F. Klein (1882b) Ueber eindeutige Functionen mit linearen Transformationen in sich. Mathematische Annalen 19, pp. 565–568. Link Cited by: endnote 4.
  • H. Poincaré (1882a) Sur les fonctions uniformes qui se reproduisent par des substitutions linéaires. Mathematische Annalen 19, pp. 553–564. Link Cited by: endnote 1.
  • H. Poincaré (1882b) Sur les fonctions uniformes qui se reproduisent par des substitutions linéaires. Mathematische Annalen 20, pp. 52–53. Link Cited by: endnote 3.
  • H. P. d. Saint-Gervais (2016) Uniformization of Riemann Surfaces: Revisiting a Hundred-Year-Old Theorem. European Mathematical Society, Zurich. Link Cited by: 7-2-61. H. Poincaré to Felix Klein, English translation.