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Evariste Galois
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The story of Evariste Galois (Oct 25, 1811 to May 31, 1832) is a tragic one. He only lived 20 years, died in a duel. But he started a whole new branch of mathematics--group theory.
Evariste Galois was born to a well educated family near Paris. His father, Nicholas Gabriel Galois and his mother Adelaide Marie Demante were both well educated in philosophy, classical literature and religion. For the first twelve years, Evariste's mother served as his tutor. She taught him mathematics, Latin, Greek and religion.
At age sixteen (1827), he enrolled in his first mathematics class at Lycee of Louis-le-Grand. It turned out that this was a major turning point in his life. He immediately became absorbed in mathematics. His school report showed that he neglected all other subjects and concentrated on mathematics only. As his teacher put it "...[Galois] works only in the highest realms of mathematics. It is best for him to study nothing but mathematics. Otherwise he is wasting his time here."
In 1828, he took the entrance examination at Ecole Polytechnique, the best university at France at that time. However, the examiners failed to appreciate his talent because his methods were so innovative and advanced. What made matter worse was that he often calculated so many steps ahead in his head, leaving the examiners even more confused. Back to Louis-le-Grand, he studied mathematics under Louis Richard.
The prodigy soon outstripped the capacity of his teachers. He learned directly from the latest publications written by the masters (Legendre and Lagrange, to name a few) of his time and readily grasped the most complex concepts. By age seventeen (April 1829), he published his first paper on continued fractions in Annales de Gergonne.
The road ahead of Galois proved to be rough. When he took the examination for the second time at Ecole Polytechnique a year later, again the same thing happened, if not worse. This time, sensing that his talent was not going to be recognized and to be failed for the second time, he threw a chalk eraser at the examiner, Monsieur Dinet. Eventually he entered Ecole Normale a less prominent university than Ecole Polytechnique. He remained confident of his mathematical talent and continued his own research on quintic equations.
At age 19, Galois sent three papers on theory of equations to Augustin Louis Cauchy at the Academy of Science, who valued Galois' papers highly and recommended Galois revise them into one paper in order to be considered for the Grand Prize in Mathematics at the Academy. This genius was at the verge of being recognized. But it seemed that he was destined to be the contrary. In February 1830, he submitted his paper On the Condition that an Equation be Soluble by Radicals to Joseph Fourier, the secretary at the Academy. Unfortunately, Fourier had died in April 1830 before he could enter Galois' paper officially. His paper was never found again. He published two other papers in December 1830. And a letter in Gazette des Ecoles ( 2 January 1831) was his last publication. In January 1831, Galois submitted a third revision of his paper to Simeon Poisson at the Academy.
Meanwhile, Galois was also very active in the French Revolution. At the end of 1830, he was prisoned for threatening the King, Louis-Phillipe. Right after his release, he was arrested in July 1831 for wearing an illegal uniform and carrying a riffle. In prison, he received a rejection letter from Poisson stating "his [Galois'] argument is neither sufficiently clear nor sufficiently developed to allow us to judge its rigor".
He was released from prison in April 1832. Only more mishaps. He was involved in a romance with Stephanie-Felicie Poterine du Motel. A duel was arranged on May 30, 1832 with Pescheux d'Herbinville. The reason for the duel was not clear but definitely linked to Stephanie. The night before the duel, he scribbled down most of his mathematical ideas, knowing that his ideas were correct even though they were rejected by the Academy.
Galois was shot in the abdomen and died the next day, apparently from peritonitis. His last notes were organized by his brother and sent to Carl Gauss, Carl Jacobi and other mathematicians. Again, there was no recognition of Galois' work. In 1846, a copy reached Joseph Liouville who immediately recognized the ingeniousness. Liouville spent months trying to interpret its meaning and to fill the gaps Galois had calculated in his head. Liouville "...saw the complete correctness of the method by which Galois proves." In fact, Galois had formulated a complete understanding on how to find solutions to quintic equations. And behind his method was the essence of group theory. Liouville edited Galois' paper and published it in Journal de Mathematiques Pures et Appliques which received immediate and impressive responses from other mathematicians.
Galois only lived 20 years and 7 months. His complete works only filled 60 pages. Yet he will forever be remembered as the father of modern algebra. Some people think that Galois' story is one of stupidity (the duel) over genius. They may be correct. However, imagine you are fifteen or twenty years ahead of your time and nobody could understand you, what would you have done?