Evariste Galois

(1811 – 1832)

An examination of the lives of most prominent mathematicians of the eighteenth century reveals their generally quiet, conventional natures. In sharp contrast is the history of Evariste Galois. Brimming with political intrigue, rampant paranoia, imprisonment, and failed romance, Galois’s twenty years of life were as astonishingly productive as they were chaotic.

Born on October 25, 1811 in Bourg-la-Reine, a Parisian suburb, Galois was the son of Nicholas-Gabriel Galois and his wife, Adelaïde-Marie Demante. Evariste’s father was a charming, witty politician who served as mayor of Bourg-la-Reine and headed the town’s liberal, anti-royalist party. Evariste’s mother was a classicist who taught him at home until he reached the age of twelve. She imparted to her son her knowledge of Greek and Latin, as well as her fervent love of liberty and her mistrust of organized religion.

In 1823, Galois was enrolled in the Collège Royal de Louis-le-Grand, housed in a stark gray building with massive gates and barred windows. The boy’s initial impression, that the school more closely resembled a prison than a place of learning, was reinforced by the rigid discipline that reigned within. Galois’s liberal political convictions were strengthened by continued exposure to the school’s relentlessly conservative, royalist administration.

Galois was introduced to algebra during his fourth year at school. Impatient with the standard elementary texts, he turned instead to the original works of Legendre and Lagrange. By the age of sixteen, Galois recognized his genius as a mathematician.

Galois’s appreciation of his remarkable abilities led him to focus his attention almost exclusively on mathematics. He so neglected his study of the humanities that his teachers termed him “dissipated” and “bizarre.” Ignoring his instructors’ demands that he apply himself to subjects he considered trivial, Galois decided to apply for early admission to the famed Ècole Polytechnique. Apparently his preparation for the entrance exam was inadequate, for Galois was refused permission to matriculate. He reluctantly returned to Louis-le-Grand for yet another dismal year. When Galois was seventeen, he began to expand on the work of Lagrange with respect to the theory of equations, tackling difficult questions that had baffled many generations of mathematicians. Galois’s method of solving these problems led to an even more significant discovery: the theory of groups. Galois prepared a manuscript for the French Academy of Sciences in which he elucidated his research. The paper was assigned to the eminent mathematician Augustin Louis Cauchy for review. Apparently Cauchy misplaced the manuscript, just as he had previously lost one of Abel’s. Galois then submitted a second paper, which also disappeared. Galois began to see himself as persecuted by the established scientific community.

Nevertheless, Galois still hoped to pass the exam that would grant him admission to the Ècole Polytechnique. Since a candidate could take the test only twice, this second attemptwas crucial. Unfortunately, just before the test was to be administered, in the summer of 1829, Galois’s father committed suicide. Royalist forces in the town of Bourg-la-Reine had implicated the liberal Nicholas-Gabriel Galois in a crime of which he was entirely innocent; the elder Galois was unable to bear the resulting scandal. So grieved and distracted was Evariste Galois, that he failed the test a second time. These tragedies fueled Galois’s burning hatred of the conservative French hierarchy then in power.

In November 1829, Galois reluctantly enrolled in the less prestigious Ècole Préparatoire, which ironically was housed in the same Parisian building as his previous school, the hated Louisle-Grand. Galois’s burgeoning anger and frustration exploded in a furious article published in the Gazette des écoles, in which he blasted the Ècole Préparatorie’s conservative director. On December 8, 1830, Galois was expelled. He went home to live with his widowed mother, but his behavior was so erratic and disturbing that she fled, apparently in fear for her life.

Galois divided his time between the study of mathematics and the dissemination of republican propaganda. His political activities led to his arrest in May, 1831 for a crime of which he was soon acquitted and in July, 1831 for an act of defiance against the crown for which he spent eight months in prison. Just after his release in March 1832, Galois met Stéphanie-Félicie Poterin du Motel. It was apparently his relationship with her that led to his death.

Little is known of Galois’s affair with du Motel, except that for a short time they were lovers. They quarreled, then parted. Soon thereafter, Galois was challenged to a duel by two young men who, like him, were liberals. In a letter written just before his death, Galois confided to a friend, “I die the victim of an infamous coquette and her two dupes.” Why there was a duel at all is uncertain; nevertheless, Galois believed he had no choice but to accept the challenge, though he felt certain he would not survive.

Galois spent the night before his death editing the memoirs in which he revealed his most recent discoveries in analysis, including the algebraic solution of equations. He begged his friend Auguste Chevalier, to whom his papers were sent, to bring Galois’s work to the attention of the mathematicians Gauss and Jacobi. Galois expressed the fervent hope that one of these great men would agree to sort through the “mess” in his manuscripts, thus granting him some measure of immortality.

With the rising of the sun on the morning of May 30, 1832, Galois left his room and trudged to the appointed site on the banks of a nearby pond. There he was met by his adversary, probably Pescheux d’Herbinville, a fellow republican. D’Herbinville shot Galois once, in the abdomen. Galois’s pistol was never fired.

Galois died at about 10:00 a.m. the next morning, at the age of twenty. The publication of his manuscript a few years later ensured that he did not live in vain.

Links

http://www-history.mcs.st-andrews.ac.uk/Biographies/Galois.html
http://scienceworld.wolfram.com/biography/Galois.html

References

• Boyer, Carl B. A History of Mathematics. 2d ed., rev. Uta C. Merzbach. New York: John Wiley & Sons, Inc., 1991.
• Gillispie, Charles Coulston, ed. Dictionary of Scientific Biography. Vol. V. New York: Charles Scribner’s Sons, 1972.
• Rothman, Tony. “The Short Life of Evariste Galois.” In In Scientific Genius and Creativity, edited by Owen Gingerich, 50–60. New York: W.H. Freeman and Company, 1982.
• Struik, Dirk J. A Concise History of Mathematics. New York: Dover Publications, Inc., 1987.