Évariste Galois

Lore & Background

Évariste Galois was a French mathematician and political activist, born in 1811. He was a staunch Republican, deeply engaged in the political upheaval following the French Revolution of 1830. His political activism led to multiple arrests and a jail sentence of several months. Shortly after his release, he died from wounds suffered in a duel, the reasons for which remain obscure. Galois’s defining achievement came in his teens: he determined the necessary and sufficient condition for a polynomial to be solvable by radicals, solving a problem open for 350 years. This work founded Galois theory and group theory, major branches of abstract algebra. He attended the Lycée Louis-le-Grand, where his teacher recognized his brilliance. At fourteen, he began serious mathematical study, reading Legendre’s geometry “like a novel” and mastering it at first reading. At fifteen, he studied Lagrange’s original papers. He twice failed the entrance exam for the École Polytechnique, once due to lack of preparation and later due to unclear circumstances, possibly involving an incompetent examiner and the recent suicide of his father. He instead entered the École Normale. His first paper, on continued fractions, was published in 1829. He submitted foundational work on equation theory to the Academy of Sciences; Augustin-Louis Cauchy reviewed it but refused publication, likely suggesting it be combined for a prize competition. After Cauchy’s suggestion, Galois submitted the memoir for the Grand Prix, but it was lost upon the death of secretary Joseph Fourier. Despite this, he published three papers that year, one laying the foundations for Galois theory, another on numerical equation solving, and a third articulating the concept of a finite field.

Reader's Guide

Galois was born on 25 October 1811 to Nicolas-Gabriel Galois and Adélaïde-Marie (née Demante). His father was a Republican and mayor of Bourg-la-Reine. His mother educated him for his first twelve years. In October 1823, he entered Lycée Louis-le-Grand. At 14, he began serious interest in mathematics, reading Legendre's Éléments de Géométrie and Lagrange's original papers. In 1828, he failed the entrance exam for the École Polytechnique and entered the École Normale (then l'École préparatoire). His first paper, on 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 for unclear reasons, though he recognized their importance and suggested combining them for the Grand Prize. On 28 July 1829, Galois's father died by suicide after a political dispute. Galois failed his second attempt at the Polytechnique; accounts differ on why. He passed the Baccalaureate on 29 December 1829. He submitted his memoir on equation theory several times; it was never published in his lifetime. After Cauchy's suggestion, he submitted it to Joseph Fourier for the Grand Prix, but Fourier died and the memoir was lost. The prize went to Niels Henrik Abel posthumously and Carl Gustav Jacob Jacobi. Galois published three papers in 1830: one laid foundations for Galois theory, one on numerical resolution of equations, and one in number theory first articulating the concept of a finite field. After the July Revolution, Galois was expelled from the École Normale for criticizing the director. He joined the Republican artillery unit of the National Guard, which was disbanded on 31 December 1830. In May 1831, at a banquet, he proposed a toast to Louis Philippe with a dagger above his cup; he was arrested and acquitted on 15 June. On 14 July 1831, he was arrested again for wearing a uniform and carrying weapons. While in prison, he drank alcohol for the first time at the goading of fellow inmates; one inmate recorded Galois saying he would die in a duel over a coquette. Galois was sentenced on 23 October to six months for illegally wearing a uniform. He was released on 29 April 1832.

Did You Know?

• Galois read Legendre's Éléments de Géométrie 'like a novel' and mastered it at the first reading.
• His father died by suicide after a bitter political dispute with the village priest.
• Galois's memoir on equation theory was lost after Joseph Fourier died.
• He was expelled from the École Normale for writing a blistering letter criticizing the school's director.

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