Mathematics

The Mad Mathematician



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Evariste Galois was born on October 25, 1811 in Bourg-la-Reine, France twelve years after the end of the French Revolution. His father, Nicolas-Gabriel, was mayor of the village in which they lived and the headmaster of the local boarding school. Adelaide-Marie Demante, Galois' mother, was his teacher until the age of twelve. His parents taught him that liberty was the highest good and tyranny the opposite. E.T. Bell described Galois' father as “a relic of the Eighteenth century, cultivated, intellectual, saturated with philosophy, a passionate hater of royalty, and an ardent lover of liberty” and his mother as “a woman of strong character with a mind of her own, generous, with a marked vein of originality, quizzical, and, at times, inclined to be paradoxical” (Bell 362-363).

In 1823, when he was twelve years old, he attended his first school, the lycee of Louis-le-Grand in Paris. His school provisor wished to bring back the Jesuit order to the school and when the angry, young students became suspicious they refused to chant in chapel. The punishment he exacted for this was to expel any student he thought was not chanting without notifying their parents first. Galois either chanted or was not a suspect for he remained in school. However, he was outraged at the provisor's reaction. Bell tells us that he “gained something more lasting than any prize, the stubborn conviction, right or wrong, that neither fear nor the utmost severity of discipline can extinguish the sense of justice and fair dealing in young minds experiencing their first unselfish devotion” (Bell 363).

One year later, at the age of thirteen, Galois took another blow from fate. Because his genius in mathematics was already beginning to blossom, he became bored with his other courses and his grades began to suffer. The school administers decided to demote him. During this time he became aware of the work of Adrien Marie Legendre and the lectures of H.J. Vernier. After that he read the works of Legrange, then Abel “from cover to cover as easily as other boys read a pirate yarn (Bell 364). Two problems that Galois was having during this period was his boredom with dry and unimaginative algebraic texts and his inability to show his work to his teachers. Galois did all of his work in his head; he could not do any of his work on the blackboard. His professors gave him bad grades not for having the correct answer, but for not showing how he arrived at the solution.

At the age of sixteen he took the entrance exam for the Ecole Polytechnique, the best mathematics and science school in the country, if not in all of Europe. He failed. His examiners were so incompetent that they could not recognize the level at which Galois worked. Again, someone who could not do his work had passed a damning judgment upon him.

A year later he met Louis-Paul-Emile-Richard, a teacher at Louis-le-Grande. He wrote of Galois, “this pupil has a marked superiority above all his fellow students; he works only at the most advanced parts of mathematics” (Bell 368). March 1, 1829, Galois published his first paper on continued fractions at the age of eighteen. Galois applied for a second time to the Ecole Polytechnique and, again, they rejected him. Also that year, a slanderous political incident occurred between Galois' father and a young priest. Nicolas-Gabriel was persecuted and committed suicide in an apartment in Paris. Bell tells us after this that Galois “could see no good in anything” (Bell 370).

In 1830 he wrote three papers on his theory of algebraic equations and gave them to the secretary of the Academy of Sciences. He had hoped to win the Grand Prize in Mathematics. Guess how this ends? The secretary takes them home, but dies before he reads them. Later, Galois' papers can't be found. “Genius,” he said, “is condemned by a malicious social organization to a eternal denial of justice in favor of fawning mediocrity” (Bell 371).

Galois hated the political and educational systems so much that the revolution in 1830 “filled him with joy” (Bell 371). At the end of that year he wrote an article in the school newspaper blasting the administration. His students did not come to his defense and he was expelled. He wrote another letter saying “I ask nothing of you for myself, but speak out for your honor and according to your conscience” (Bell 372). Staying silent; it never goes out of fashion!

Also staying the same for centuries is not being allowed to threaten the leaders. May 1831 he threatened the life of the king and was imprisoned in Sainte-Pelagie. During his trial, Galois used the public forum to his advantage and ridiculed the entire legal system. Surprisingly, he made such an impact on the jury that he was found innocent within ten minutes of their deliberation. He was arrested again on July 14, 1831 as “precautionary measure” (Bell 373) because the authorities had heard there was going to be a republican rally. He was arrested for “illegally wearing a uniform” (Bell 374) since the military had previously been disbanded and sentenced to six months incarceration in Sainte-Pelagie. Galois was supposed to stay there until April 29, 1832, however the cholera epidemic of 1832 caused him to be transferred to an unnamed hospital on March 16. He was released on May 25.

The events that took place only four days after Galois gained his freedom are still very much uncertain. The most popular opinion is that after his release he ran into some political enemies. One of them challenged him to a duel and he accepted. That night Evariste Galois scribbled hastily on loose pieces of paper his last thoughts and theories on mathematics. E.T. Bell comments that “what he wrote in those desperate last hours before the dawn will keep generations of mathematicians busy for hundreds of years” (Bell 375).

He proved that higher-than-fourth-degree equations by radicals could not be solved. He discovered the conditions that an equation can be solved. Evariste's greatest contribution is today called Galois' Theorem. Abbot said, “the theorem also showed that if the highest power of x is prime, and if all other values of x can be found by taking only two values of x and combining them using only addition, subtraction, multiplication, and division, then the equation can be solved by using formulae similar in principle to the formula used in solving quadratic equations” (Abbott sec. G).

At dawn on May 30, 1832 Evariste met his opponent and stood with his back to him, flint-lock pistol in hand. They counted twenty-five paces together, turned and fired. He was shot in the intestines and left there bleeding. Later, a passerby took him to the Cochin Hospital where he refused the last rites offered to him by a priest. According to Bell, he tried to comfort his younger brother by telling him not to cry because he needed all of his courage to die at twenty. He did on May 31 at twenty-one years of age and was buried in a commoners grave. All in all, his collected works total sixty pages.


Works Cited

Abbot, David. Biographical Dictionary of Scientists, 1st ed. New York: Peter Bedrick Books, 1985

Bell, E.T.. Men of Mathematics, 15th ed. New York: Simon & Schuster, Inc., 1937


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