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. 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.

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.

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”.

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).