Sur les traces d'Évariste Galois

"Cursed mathematician", "romantic genius", "the Rimbaud of mathematics", "the Mozart of algebra", "misunderstood mind"... These are not the expressions that are lacking to qualify the short life of Évariste Galois, a young mathematician who died at 20 in an obscure duel. The mystery surrounding certain passages of his life, as well as the depth of his ideas, add to the legend of an icon whose personality and scientific legacy we are far from having fully understood!

At the time when Galois began to take an interest in mathematics, polynomials had long been studied, and substitutions and permutation groups had already been introduced by Lagrange and studied by Cauchy. Ruffini and Abel had previously proven that it is generally impossible to solve polynomial equations of degree 5 or higher algebraically. So what is Galois's contribution? Beyond solving a problem, he opened a new field of mathematics by showing how much a group could encode the fundamental properties of a polynomial.

In addition to some of his mathematical works, we have received several documents that inform us about the thinking of young Galois: fragments of texts found in his notes, protest articles that denounce the functioning of the school institution, notebooks that present his first research… This is also the case with his school work: some have only been studied recently, and others remain unpublished!