7-2-57. H. Poincaré to Felix Klein, English translation

Paris, 17 December 1881

rue Gay-Lussac 66


I have the honor of sending you the little work in question; I have not described succinctly my proof methods, as you were asking me to.11endnote: 1 Poincaré (1882). I would not have been able to do so without substantially exceeding the limits you imposed.

I realize that these limits were not absolute. However, from another standpoint I don’t believe that a proof can be summarized; one cannot shorten it without depriving it of its rigor and a proof without rigor is no proof at all. I would prefer, therefore, to send you from time to time a series of short letters in which I would give successive proofs of the stated results or at least the main ones. You may dispose of these letters as you see fit.

I do indeed live in Paris; I am an associate professor in the Faculty of Science.

Here is Picard’s address: Adjunct Professor in the Faculty of Science, 13 rue Michelet, Paris.

Here also is Appell’s: Associate Professor at the École Normale Supérieure, 22 rue Soufflot, Paris.

Please be assured, Monsieur, of my highest regard.


PTrL. Translated by S.A. Walter from the original French (§ 4-47-13). Previously translated by R. Burns in Saint-Gervais (2016).

Time-stamp: "30.04.2021 14:07"



  • H. Poincaré (1882) Sur les fonctions uniformes qui se reproduisent par des substitutions linéaires. Mathematische Annalen 19, pp. 553–564. Link Cited by: endnote 1.
  • H. P. d. Saint-Gervais (2016) Uniformization of Riemann Surfaces: Revisiting a Hundred-Year-Old Theorem. European Mathematical Society, Zurich. Link Cited by: 7-2-57. H. Poincaré to Felix Klein, English translation.