Galois, Evariste, << gah lwah, ay vah reest >> (1811-1832), a French mathematician, was one of the originators of a branch of abstract algebra known as group theory. His analysis of the solvability of algebraic equations is now called Galois theory. His work and contribution to mathematics is widely recognized today, but the mathematical establishment of his time did not recognize the full significance of his work.
Galois was born on Oct. 25, 1811, in Bourg-la-Reine, near Paris. In 1829, while still a student at the school of Louis-le-Grand, he had his first mathematical paper published. But in the same year, he failed his entrance to the Ecole Polytechnique in Paris. Instead, he entered the Ecole Normale Superieure. On three separate occasions—in 1829, 1830, and 1831—Galois submitted papers to the French Academy of Sciences but the authorities lost or rejected his work.
Galois’s most famous contribution to mathematics concerns the solution of equations. In an equation such as x + 3 = 7, the quantity x is known as a variable. A root of an equation is a quantity which, when substituted for the variable, satisfies the equation. So in this example, 4 is a root, because 4 + 3 = 7. More general equations may contain the square, cube, or higher powers of the variable and will have a number of roots. Mathematicians had found general solutions to equations containing powers up to the fourth. But they had not been able to establish a theory on the solvability of equations containing fifth powers and higher. Galois examined the collection of roots to an equation and analyzed the set of permutations (rearrangements) of the roots. He showed that the permutations form a mathematical structure known as a group. His fundamental result shows that the solvability of the original equation is related to the structure of the associated group.
Politically, Galois was active in his support of the republicans (opponents of the royal family). In 1830, Galois wrote a criticism of the director of the Ecole Normale Superieure, who had prevented students from taking part in a republican demonstration. As a result, Galois was expelled. In 1831, the authorities arrested Galois for taking part in a demonstration and sentenced him to several months’ imprisonment. He left prison in April 1832. On May 30, Galois fought a duel with Pecheux d’Herbinville. Historians have been unable to determine the reasons for the duel. Galois died from his wounds the following day. He was only 20 years old. On the night before the duel, he wrote a letter summarizing his mathematical investigations. In 1846, the mathematician Joseph Liouville published Galois’s papers.
See also Algebra (Statements and equations) ; Root .
