Grothendieck's vision provides inspiration today for several developments in mathematics such as the extension and generalization of Galois theory, which is currently being extended based on his original proposal.
The proposal was not successful, but Grothendieck obtained a special position where, while keeping his affiliation at the University of Montpellier, he was paid by the CNRS and released of his teaching obligations.
[6] The outlines of dessins d'enfants, or "children's drawings", and "anabelian geometry", that are contained in this manuscript continue to inspire research; thus, "Anabelian geometry is a proposed theory in mathematics, describing the way the algebraic fundamental group G of an algebraic variety V, or some related geometric object, determines how V can be mapped into another geometric object W, under the assumption that G is not an abelian group, in the sense of being strongly noncommutative.
The idea of anabelian (an alpha privative an- before abelian), first introduced in Letter to Faltings (June 27, 1983),[7] is developed in Esquisse d'un Programme.
While the work of Grothendieck was for many years unpublished, and unavailable through the traditional formal scholarly channels, the formulation and predictions of the proposed theory received much attention, and some alterations, at the hands of a number of mathematicians.