Évarist Galois He was born near Paris, in the village of Bourg la-Reine, where his father was mayor. At age 12 he showed little interest in Latin, Greek and Algebra but Legendre's geometry fascinated him. At the age of 16, judging himself to be fit, he sought entry into the Polytechnic School but was refused for lack of preparation and this marked his first failure. At the age of 17 he wrote an article where he expounded his fundamental discoveries and handed it to Cauchy to present at the Academy. Cauchy lost his job and with this came his second remarkable failure. He soon lost his father who, due to clerical intrigue, committed suicide. Disappointed, Gaiois entered the Normal School to prepare for teaching, always continuing his research.
In 1830 he wrote an article for the Academy Mathematics Contest delivering it to Fourier, who died soon after and the article was lost. With so many frustrations Galois eventually joined the causes of the 1830 revolution, was expelled from the NormaL School, and later joined the National Guard. Galois began his research with Lagrange's work on root permutations, which gave him the necessary and sufficient conditions to conclude that polynomial equations are radically soluble and, based on Abel's evidence, found that irreducible algebraic equations are radically soluble only. if the group of permutations on its roots is also resolvable. He provided an algorithm for finding these roots, as well as other postulates always focusing more on the algebraic structure than on specific cases, giving an arithmetic treatment to Algebra. In his works is implicit the concept of "body" that Dedekind would later explicitly define.
At the time Galois handed Poisson an article containing his theory and he called it "incomprehensible" but today what we call "Modern Mathematics" is nothing more than the ideas of Galois that are coming to us.
In 1832, getting involved with a woman, in the name of a code of honor, could not avoid a duel. Last night he spent his hours sketching notes for posterity in a letter to his friend. On the morning of May 30 he found his opponent receiving a fatal shot. Rescued by a peasant, he died in a hospital he was taken to at the age of 20.
Source: Fundamentals of Elementary Mathematics, Gelson Iezzi - Current Publisher