Évariste Galois had soon followed his initial…

Évariste Galois had soon followed his initial paper with one dealing with the impossibility of solving the general quintic (fifth-degree) equation by algebraic means alone; his work lays the fundamental foundations for Galois theory, a major branch of abstract algebra, and the subfield of Galois connections.

He is the first to use the word "group" (French: groupe) as a technical term in mathematics to represent a group of permutations.

While their counterparts at Polytechnique were making history in the streets during the les Trois Glorieuses, Galois and all the other students at the École Normale had been locked in by the school's director.

Galois, incensed, writes a blistering letter criticizing the director that he submits to the Gazette des Écoles, signing the letter with his full name.

Despite the fact that the Gazette's editor redacts the signature for publication, Galois is, predictably, expelled for it.