Esquisse d'un Programme

"Esquisse d'un Programme" is a famous proposal for long-term mathematical research made by the German-born, French mathematician Alexander Grothendieck in 1984. He pursued the sequence of logically linked ideas in his important project proposal from 1984 until 1988, but his proposed research continues to date to be of major interest in several branches of advanced mathematics. 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.

Submitted in 1984, the Esquisse d'un Programme was a proposal submitted by Alexander Grothendieck for a position at the Centre National de la Recherche Scientifique. 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. Grothendieck held this position from 1984 till 1988. This proposal was not formally published until 1997, because the author "could not be found, much less his permission requested". 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 word anabelian (an alpha privative an- before abelian) was introduced 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 While the work of Grothendieck was for many years unpublished, and unavailable through the traditional formal scholarly channels, the formulation and predictions of the proposed theory received much attention, and some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. Those who have researched in this area have obtained some expected and related results, and in the 21st century the beginnings of such a theory started to be available."

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