Galois, Évariste

Born Oct. 26, 1811, in Bourg-la-Reine, near Paris; died May 30, 1832, in Paris. French mathematician whose research had an exceptionally strong influence on the development of algebra.

Galois studied in the Lycée Louis le Grand, and by the time he graduated he was already doing original work in mathematics. In 1830 he entered the Ecole Normale and was expelled from it in 1831 for political reasons. The beginning of Galois’s political activities dates to this period: he belonged to the secret republican society Friends of the People. He was imprisoned twice for public action against the royal regime. Almost immediately after his release, at the age of 20, he was killed in a duel, which from all appearances was provoked by his political enemies.

Galois’s mathematical legacy comprises a small number of very concisely written works that were not understood by his contemporaries. Galois, in effect, constructed the entire theory of finite fields (today called Galois fields). In a letter to a friend, written on the eve of the duel, Galois formulated the basic theorems on integrals of algebraic functions, which were rediscovered much later in the works of B. Riemann. Galois’s principal contribution was the formulation of a complex of ideas, which he arrived at as a result of continuing the research on the solvability of algebraic equations by radicals begun by J. Lagrange, N. Abel, and other mathematicians. The Galois theory constructed as a result of this, by establishing the description of extensions of fields in terms of groups resembling a description of the symmetries of a polyhedron, reduces questions concerning fields to questions of the theory of groups (which originated with this development).