## 4-21-19. Thomas Craig to H. Poincaré

Nov. 17/86

Athenaeum Club

Franklin & Charles Sts.

Dear M. Poincaré,

If it is not too much trouble for you I wish very much that you would give me information on the following two points.

I. What is the exact meaning of the word “monogène” used by
Weierstrass and by Mittag-Leffler in his memoir on uniform functions
(*Acta Math* Vol. IV, I think it is IV but am not sure at this
minute).^{1}^{1}endnote:
^{1}
Mittag-Leffler (1884). Mittag-Leffler wrote to Poincaré
concerning his ongoing research on monogenic functions in September,
1881 (§ 1-1-11). I thought
that I knew the meaning of the word in connection with the Theory of
Functions, but I do not understand the full significance of it as used
by Weierstrass and Mittag-Leffler.

II. Has anything been done on the general Theory of non-uniform functions? If so can you tell me where I can find it?

I shall feel deeply obliged to you if you will be kind enough to
answer these questions.
I have been much interested in reading your communications and those
of M. Picard to the Académie des Sciences in the transformations of
surfaces into themselves.^{2}^{2}endnote:
^{2}
Poincaré (1886). I have given to my class in Abelian
functions your generalization of Abel’s Theorem to gauche curves and to
surfaces. I think they got a clearer notion of what the theorem means
than they had when I only used a plane curve.

Hoping to hear from you very soon I remain my dear M. Poincaré,

Yours sincerely,

Thomas Craig

ALS 3p. Collection particulière, Paris 75017.

Time-stamp: "28.01.2021 13:47"

## References

- Sur la représentation analytique des fonctions monogènes uniformes d’une variable indépendante. Acta Mathematica 4, pp. 1–79. Link Cited by: endnote 1.
- Sur les transformations des surfaces en elles-mêmes. Comptes rendus hebdomadaires des séances de l’Académie des sciences de Paris 103, pp. 732–734. Link Cited by: endnote 2.