In 1828, while still a teenager, Évariste Galois solved the long-standing problem of determining the condition for a polynomial to be solvable by radicals. He produced a memoir that was submitted several times to the Academy of Sciences but never published in his lifetime. His first attempt was refused by Cauchy. He re-submitted it to Fourier, the Academy's secretary, but Fourier died soon after and the memoir was lost. Simeon Poisson asked him to again submit his work, but found it incomprehensible, declaring that

"Galois' argument is neither sufficiently clear nor sufficiently developed to allow us to judge its rigor."

Galois reacted violently to the rejection letter and decided to publish his papers privately. While in prison for political activism, he polished his ideas. Set for a duel after his release, and convinced of his impending death, he stayed up all night composing what would become his mathematical testament. On May 30th, 1832, at age 21, he was shot and died. Galois' mathematical contributions were published in full in 1843. His work led to what is now called Galois field theory, with direct applications in coding and cryptography.