Évariste Galois: Principles and applications

Abstract

Évariste Galois formulated his famous theory in 1831 in the first part of his Mémoire sur les conditions de résolubilité des équations par radicaux. It is titled Principes. Even though the theory is completely understood today, it is hard to follow Galois's original. The style is brief, almost aphoristic and the approach quite different from today's. The aim of this paper is to make Galois's Principes readable for contemporary mathematicians (Sections 1 and 2) and to give a survey of Galois's Applications concerning equations of prime degree, primitive equations, and the modular equation in the theory of elliptic functions (Section 3). Remarks show the relationship to the work of Lagrange and Gauss. © 2002 Elsevier Science (USA).