# Did you know?

#### January 2021

Let ƒ be a holomorphic function in the unit disk of the complex plane fixing the origin with differential of modulus 1. The local inversion theorem guarantees that ƒ admits a holomorphic inverse *g* in a small disk of radius *r* > 0 centered at the origin. André Bloch showed that the maximum radius of existence of *g* is bounded below by an absolute constant *b* > 1/72.

This is André Bloch most famous theorem, which has been published in __1925__ in the *Annales de la Faculté des Sciences Toulouse*. The optimal absolute constant *b* is still unknown today, despite numerous works and steadyprogress (see e.g. Bonk, M. ; Eremenko, A. ; Covering properties of meromor-phic functions, negative curvature and spherical geometry. Ann. of Math. 2000, 152 , no. 2, 551-592).

André Bloch was an unusual mathematician. You’ll find some biographical information in this __article__ by H.Cartan and J.Ferrand.