Evariste Galois (October 25, 1811-May 31, 1832) was a French mathematician born in Bourg-la-Reine. While still in his teens, he was able to determine a necessary and sufficient condition for a polynomial to be solvable by radicals, thereby solving a long-standing problem. He died in a duel at the age of twenty.
He was the first to use the word "group" as a technical term in mathematics to represent a group of permutations. His work on equation theory was submitted to the Academy and was reviewed by Simeon Denis Poisson, who did not understand it. It was resubmitted again in shorter form. The truth and importance of the work were not confirmed during his lifetime. His work laid the fundamental foundations for Galois theory, a major branch of abstract algebra and of pseudorandom sequence (PN) and error-correction coding applications.
Galois was a staunch Republican, famous for having toasted Louis-Philippe with a dagger above his cup, which leads some to believe that his death in a duel was set-up by the secret police.
The night before the duel, supposedly fought in order to defend the honor of a woman, he was so convinced of his impending death that he stayed up all night writing letters to his Republican friends and composing what would become his mathematical testament. In his final papers he outlined the rough edges of some work he had been doing in analysis and annotated a copy of the manuscript submitted to the academy. On the 30th of May 1832, early in the morning, he was shot in the abdomen and died the following day at ten in the Cochin hospital (probably of peritonitis) after refusing the offices of a priest.
His last words to his brother Alfred were: "Don't cry! I need all my courage to die at twenty."
His work was not understood until 1843 when Liouville reviewed his manuscript and declared that he had indeed solved the problem first proposed by Abel. The manuscript was finally published in the October-November 1846 issue of the Journal des mathématiques pures et appliquées.