Id\'ees galoisiennes

TL;DR

This paper explores extending Galois theory beyond algebraic numbers to transcendental functions and quantities, highlighting recent ideas and results in this less traditional application.

Contribution

It discusses novel approaches and findings related to applying Galois theory to transcendental functions, expanding its classical scope.

Findings

Recent progress in Galois theory for transcendental functions

New methods for analyzing transcendental quantities

Potential applications in understanding transcendental algebraic structures

Abstract

Classical applications of Galois theory concern algebraic numbers and algebraic functions. Still, the night before his duel, Galois wrote that his last mathematical thoughts had been directed toward applying his "theory of ambiguity to transcendental functions and transcendental quantities". We outline some more or less recent ideas and results in this direction.