Évariste Galois

Lore & Background

Galois was born on 25 October 1811 to Nicolas-Gabriel Galois and Adélaïde-Marie. His father was a Republican and mayor of Bourg-la-Reine. His mother, fluent in Latin and classical literature, educated him for his first twelve years. In October 1823, he entered the Lycée Louis-le-Grand, where his teacher Louis Paul Émile Richard recognized his brilliance. At 14, he began serious study of mathematics, reading Legendre's Éléments de Géométrie like a novel and later the original papers of Joseph-Louis Lagrange. Despite his talent, his classwork was uninspired and teachers accused him of putting on the airs of a genius.

In 1828, Galois failed the entrance examination for the École Polytechnique and entered the École Normale. His first paper, on simple continued fractions, was published in 1829. He submitted two papers on polynomial equations to the Academy of Sciences; Augustin-Louis Cauchy refereed them but refused publication, though he likely recognized their importance and suggested combining them for the Grand Prize. After his father's suicide on 28 July 1829, Galois failed his second attempt at the Polytechnique. He passed the Baccalaureate on 29 December 1829. His memoir on equation theory was lost after Joseph Fourier died, and the prize went to Niels Henrik Abel and Carl Gustav Jacob Jacobi. He published three papers that year, including one laying foundations for Galois theory and one first articulating the concept of a finite field.

Galois was a staunch Republican involved in the 1830 Revolution. Locked in at the École Normale during the July Revolution, he wrote a blistering letter criticizing the director and was expelled. He joined the artillery unit of the National Guard, which was soon disbanded. In May 1831, he proposed a toast to Louis Philippe with a dagger above his cup, was arrested, but acquitted. On 14 July 1831, he was arrested again for wearing the uniform of the disbanded artillery while heavily armed. He was sentenced to six months in prison. While imprisoned, he attempted suicide and continued mathematical work. After release on 29 April 1832, he fought in a duel and died of his wounds on 31 May 1832.

Reader's Guide

Évariste Galois's significance lies in his foundational contributions to abstract algebra, specifically Galois theory and group theory, which he developed as a teenager. By determining a necessary and sufficient condition for a polynomial to be solvable by radicals, he resolved a 350-year-old problem. His work, though largely unpublished in his lifetime, later became central to modern mathematics. Galois's life was marked by political activism as a staunch Republican during the French Revolution of 1830, leading to repeated arrests and imprisonment. His death at age 20 from a duel, the reasons for which remain obscure, cut short a brilliant career. Despite the loss of his key memoir and rejection by the Academy, his published papers laid the groundwork for two major branches of algebra. His legacy endures in the concepts of Galois theory, group theory, and finite fields, influencing fields from number theory to cryptography.

Did You Know?

• Galois read Adrien-Marie Legendre's Éléments de Géométrie 'like a novel' and mastered it at the first reading at age 14.
• He first articulated the concept of a finite field in a number theory paper published in 1830.
• While in prison, Galois attempted suicide but was stopped by fellow inmates.
• His memoir on equation theory was lost after Academy secretary Joseph Fourier died.

Notable Quotes (Wikiquote)

"letter to Auguste Chevalier (May 25, 1832) as quoted by George Sarton, "Evariste Galois" (Oct 10, 1921) The Scientific Monthly Vol. 13, p.371." — Évariste Galois "... un auteur ne nuit jamais tant à ses lecteurs que quand il dissimule une difficulté." — Évariste Galois "... an author never does more damage to his readers than when he hides a difficulty." — Évariste Galois "in the preface of Deux mémoires d'Analyse pure, October 8, 1831, edited by Jules Tannery (1908). Manuscrits de Évariste Galois. Gauthier-Villars. p. 27." — Évariste Galois