Evariste Gallois was a 19thC French mathematician who had made major contributions to the theory of equations before he died at the age of 20, shot in a duel. Whatever the reasons behind the duel (the story says it was over a woman's honor), Galois 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, the famous letter to Auguste Chevalier outlining his ideas, and three attached manuscripts. That night he invented group theory--one of the most basic and important concepts of modem mathematics. Galois used his new concept to prove that equations of the fifth degree--quintics--and higher could never be solved. Because his ideas were so radical it took 150 years for mathematicians to work out their implications.
Hermann Weyl, one of the greatest mathematicians of the 20th century, said of this testament, "This letter, if judged by the novelty and profundity of ideas it contains, is perhaps the most substantial piece of writing in the whole literature of mankind."
Early in the morning of May 30, 1832, he was shot in the abdomen and died the following day in the Cochin hospital, Paris after refusing the offices of a priest.
His last words to his brother Alfred were: "Don't cry, Alfred! I need all my courage to die at twenty."
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