Évariste Galois cracked a 350-year-old puzzle and died at twenty
Before turning 20, Évariste Galois found exactly which polynomial equations can be solved using roots, settling a question open for 350 years and founding group theory. He also twice failed the entrance exam for France's top mathematics school, spent months in prison for republican agitation, and died after a duel in 1832.
Born in 1811 in Bourg-la-Reine, where his father later became mayor, Galois was educated at home by his mother until 12. At the Lycée Louis-le-Grand he discovered mathematics around 14, reportedly devouring Legendre's geometry textbook in a single reading, and at 15 was studying Lagrange's papers on solving equations. Teachers nonetheless found his classwork dull and accused him of putting on airs. He failed the École Polytechnique exam in 1828, and again in 1829 just days after his father's death following a bitter feud with the village priest; accounts suggest he skipped too many steps and baffled the examiner.
His manuscripts suffered repeated misfortune. Augustin-Louis Cauchy refereed early papers and apparently urged him to merge them for the Academy's Grand Prize. Galois submitted to Joseph Fourier in February 1830, but Fourier died soon after and the memoir vanished; the prize went to Niels Henrik Abel, posthumously, and Carl Jacobi. Siméon Denis Poisson later called another version incomprehensible, though he encouraged publishing the complete work. Galois still managed three papers in 1830, including the first articulation of finite fields.
Politics consumed him. During the July Revolution his school director locked students in; Galois attacked the director in print and was expelled. At a May 1831 banquet attended by Alexandre Dumas, he raised a toast to King Louis Philippe while holding a dagger, was arrested, then acquitted after his lawyer claimed he had added the words if he betrays. On Bastille Day he led a protest heavily armed and wearing a disbanded artillery uniform, earning six months in prison.
Released on 29 April 1832, he fought a duel on 30 May, apparently tied to a broken romance, possibly with Stéphanie-Félicie Poterin du Motel, a physician's daughter at his lodging. His cousin said a supposed uncle and a supposed fiancé had both provoked it. He died the next day, 31 May.
Source: Évariste Galois
