Men of Mathematics (71 page)

Two further disasters in his eighteenth year put the last touches to Galois' character. He presented himself a second time for the entrance examinations at the Polytechnique. Men who were not worthy to sharpen his pencils sat in judgment on him. The result was what might have been anticipated. Galois failed. It was his last chance; the doors of the Polytechnique were closed forever against him.

That examination has become a legend. Galois' habit of working almost entirely in his head put him at a serious disadvantage before a blackboard. Chalk and erasers embarrassed him—till he found a proper use for one of them. During the oral part of the examination one of the inquisitors ventured to argue a mathematical difficulty with Galois. The man was both wrong and obstinate. Seeing all his hopes and his whole life as a mathematician and polytechnic champion of democratic liberty slipping away from him, Galois lost all patience. He knew that he had officially failed. In a fit of rage and despair he hurled the eraser at his tormentor's face. It was a hit.

The final touch was the tragic death of Galois' father. As the mayor of Bourg-la-Reine the elder Galois was a target for the clerical intrigues of the times, especially as he had always championed the villagers against the priest. After the stormy elections of 1827 a resourceful young priest organized a scurrilous campaign against the mayor. Capitalizing the mayor's well-known gift for versifying, the ingenious priest composed a set of filthy and stupid verses against a member of the mayor's family, signed them with Mayor Galois' name, and circulated them freely among the citizens. The thoroughly decent mayor developed a persecution mania. During his wife's absence one day he slipped off to Paris and, in an apartment but a stone's throw
from the school where his son sat at his studies, committed suicide. At the funeral serious disorder broke out. Stones were hurled by the enraged citizens; a priest was gashed on the forehead. Galois saw his father's coffin lowered into the grave in the midst of an unseemly riot. Thereafter, suspecting everywhere the injustice which he hated, he could see no good in anything.

After his second failure at the Polytechnique, Galois returned to school to prepare for a teaching career. The school now had a new director, a timeserving, somewhat cowardly stoolpigeon for the royalists and clerics. This man's shilly-shally temporizing in the political upheaval which was presently to shake France to its foundations had a tragic influence on Galois' last years.

Still persecuted and maliciously misunderstood by his preceptors, Galois prepared himself for the final examinations. The comments of his examiners are interesting. In mathematics and physics he got “very good.” The final oral examination drew the following comments: “This pupil is sometimes obscure in expressing his ideas, but he is intelligent and shows a remarkable spirit of research. He has communicated to me some new results in applied analysis.” In literature: “This is the only student who has answered me poorly; he knows absolutely nothing. I was told that this student has an extraordinary capacity for mathematics. This astonishes me greatly; for, after his examination, I believed him to have but little intelligence. He succeeded in hiding such as he had from me. If this pupil is really what he has seemed to me to be, I seriously doubt whether he will ever make a good teacher.” To which Galois, remembering some of his own good teachers, might have replied, “God forbid.”

In February,
1830,
at the age of nineteen, Galois was definitely admitted to university standing. Again his sure knowledge of his own transcendent ability was reflected in a withering contempt for his plodding teachers and he continued to work in solitude on his own ideas. During this year he composed three papers in which he broke new ground. These papers contain some of his great work on the theory of algebraic equations. It was far in advance of anything that had been done, and Galois had hopefully submitted it all (with further results) in a memoir to the Academy of Sciences, in competition for the Grand Prize in Mathematics. This prize was still the blue ribbon in mathematical research; only the foremost mathematicians of the day could sensibly compete. Experts agree that Galois' memoir was
more than worthy of the prize. It was work of the highest originality. As Galois said with perfect justice, “I have carried out researches which will halt many savants in theirs.”

The manuscript reached the Secretary safely. The Secretary took it home with him for examination, but died before he had time to look at it. When his papers were searched after his death no trace of the manuscript was found, and that was the last Galois ever heard of it. He can scarcely be blamed for ascribing his misfortunes to something less uncertain than blind chance. After Cauchy's lapse a repetition of the same sort of thing looked too providential to be a mere accident. “Genius,” he said, “is condemned by a malicious social organization to an eternal denial of justice in favor of fawning mediocrity.” His hatred grew, and he flung himself into politics on the side of republicanism, then a forbidden radicalism.

*  *  *

The first shots of the revolution of 1830 filled Galois with joy. He tried to lead his fellow students into the fray, but they hung back, and the temporizing director put them on their honor not to quit the school. Galois refused to pledge his word, and the director begged him to stay in till the following day. In his speech the director displayed a singular lack of tact and a total absence of common sense. Enraged, Galois tried to escape during the night, but the wall was too high for him. Thereafter, all through “the glorious three days” while the heroic young Polytechnicians were out in the streets making history, the director prudently kept his charges under lock and key. Whichever way the cat should jump the director was prepared to jump with it. The revolt successfully accomplished, the astute director very generously placed his pupils at the disposal of the temporary government. This put the finishing touch to Galois' political creed. During the vacation he shocked his family and boyhood friends with his fierce championship of the rights of the masses.

The last months of 1830 were as turbulent as is usual after a thorough political stir-up. The dregs sank to the bottom, the scum rose to the top, and suspended between the two the moderate element of the population hung in indecision. Galois, back at college, contrasted the timeserving vacillations of the director and the wishy-washy loyalty of the students with their exact opposites at the Polytechnique. Unable to endure the humiliation of inaction longer he wrote a blistering letter to the
Gazette des Écoles
in which he let both
students and director have what he thought was their due. The students could have saved him. But they lacked backbone, and Galois was expelled. Incensed, Galois wrote a second letter to the
Gazette,
addressed to the students. “I ask nothing of you for myself,” he wrote; “but speak out for your honor and according to your conscience.” The letter was unanswered, for the apparent reason that those to whom Galois appealed had neither honor nor conscience.

Footloose now, Galois announced a private class in higher algebra, to meet once a week. Here he was at nineteen, a creative mathematician of the very first rank, peddling lessons to no takers. The course was to have included “a new theory of imaginaries [what is now known as the theory of 'Galois Imaginaries/ of great importance in algebra and the theory of numbers]; the theory of the solution of equations by radicals, and the theory of numbers and elliptic functions treated by pure algebra”—all his own work.

Finding no students, Galois temporarily abandoned mathematics and joined the artillery of the National Guard, two of whose four battalions were composed almost wholly of the liberal group calling themselves “Friends of the People.” He had not yet given up mathematics entirely. In one last desperate effort to gain recognition, encouraged by Poisson, he had sent a memoir on the general solution of equations—now called the “Galois theory”—to the Academy of Sciences. Poisson, whose name is remembered wherever the mathematical theories of gravitation, electricity, and magnetism are studied, was the referee. He submitted a perfunctory report. The memoir, he said was “incomprehensible,” but he did not state how long it had taken him to reach his remarkable conclusion. This was the last straw. Galois devoted all his energies to revolutionary politics. “If a carcase is needed to stir up the people,” he wrote, “I will donate mine.”

The ninth of May, 1831, marked the beginning of the end. About two hundred young republicans held a banquet to protest against the royal order disbanding the artillery which Galois had joined. Toasts were drunk to the Revolutions of 1789 and 1793, to Robespierre, and to the Revolution of 1830. The whole atmosphere of the gathering was revolutionary and defiant. Galois rose to propose a toast, his glass in one hand, his open pocket knife in the other: “To Louis Philippe”—the King. His companions misunderstood the purpose of the toast and whistled him down. Then they saw the open knife. Interpreting this as a threat against the life of the King they howled
their approval. A friend of Galois, seeing the great Alexander Dumas and other notables passing by the open windows, implored Galois to sit down, but the uproar continued. Galois was the hero of the moment, and the artillerists adjourned to the street to celebrate their exuberance by dancing all night. The following day Galois was arrested at his mother's house and thrown into the prison of Sainte-Pélagie.

A clever lawyer, with the help of Galois' loyal friends, devised an ingenious defence, to the effect that Galois had really said: “To Louis Philippe,
if he turns traitor.”
The open knife was easily explained; Galois had been using it to cut his chicken. This was the fact. The saving clause in his toast, according to his friends who swore they had heard it, was drowned by the whistling, and only those close to the speaker caught what was said. Galois would not claim the saving clause.

During the trial Galois' demeanor was one of haughty contempt for the court and his accusers. Caring nothing for the outcome, he launched into an impassioned tirade against all the forces of political injustice. The judge was a human being with children of his own. He warned the accused that he was not helping his own case and sharply silenced him. The prosecution quibbled over the point whether the restaurant where the incident occurred was or was not a “public place” when used for a semiprivate banquet. On this nice point of law hung the liberty of Galois. But it was evident that both court and jury were moved by the youth of the accused. After only ten minutes' deliberation the jury returned a verdict of not guilty. Galois picked up his knife from the evidence table, closed it, slipped it in his pocket, and left the courtroom without a word.

He did not keep his freedom long. In less than a month, on July 14, 1831, he was arrested again, this time as a precautionary measure. The republicans were about to hold a celebration, and Galois, being a “dangerous radical” in the eyes of the authorities, was locked up
on no charge whatever.
The government papers of all France played up this brilliant coup of the police. They now had “the dangerous
republican,
Évariste Galois,” where he could not possibly start a revolution. But they were hard put to it to find a legal accusation under which he could be brought to trial. True, he had been armed to the teeth when arrested, but he had not resisted arrest. Galois was no fool. Should they accuse him of plotting against the government? Too strong; it wouldn't go; no jury would convict. Ah! After two months
of incessant thought they succeeded in trumping up a charge. When arrested Galois had been wearing his artillery uniform. But the artillery had been disbanded. Therefore Galois was guilty of illegally wearing a uniform. This time they convicted him. A friend, arrested with him, got three months; Galois got six. He was to be incarcerated in Sainte-Pélagie till April 29, 1832. His sister said he looked about fifty years old at the prospect of the sunless days ahead of him. Why not? “Let justice prevail though the heavens fall.”

*  *  *

Discipline in the jail for political prisoners was light, and they were treated with reasonable humanity. The majority spent their waking hours promenading in the courtyard reserved for their use, or boozing in the canteen—the private graft of the governor of the prison. Soon Galois, with his somber visage, abstemious habits, and perpetual air of intense concentration, became the butt of the jovial swillers. He was concentrating on his mathematics, but he could not help hearing the taunts hurled at him.

“What! You drink only water? Quit the Republican Party and go back to your mathematics.”—“Without wine and women you'll never be a man.” Goaded beyond endurance Galois seized a bottle of brandy, not knowing or caring what it was, and drank it down. A decent fellow prisoner took care of him till he recovered. His humiliation when he realized what he had done devastated him.

At last he escaped from what one French writer of the time calls the foulest sewer in Paris. The cholera epidemic of 1832 caused the solicitous authorities to transfer Galois to a hospital on the sixteenth of March. The “important political prisoner” who had threatened the life of Louis Philippe was too precious to be exposed to the epidemic.

Galois was put on parole, so he had only too many occasions to see outsiders. Thus it happened that he experienced his one and only love affair. In this, as in everything else, he was unfortunate. Some worthless girl
(“quelque coquette de bas étage”)
initiated him. Galois took it violently and was disgusted with love, with himself, and with his girl. To his devoted friend Auguste Chevalier he wrote, “Your letter, full of apostolic unction, has brought me a little peace. But how obliterate the mark of emotions as violent as those which I have experienced? . . . On re-reading your letter, I note a phrase in which you accuse me of being inebriated by the putrefied slime of a rotten world which has
defiled my heart, my head, and my hands. . . . Inebriation! I am disillusioned of everything, even love and fame. How can a world which I detest defile me?” This is dated May 25, 1832. Four days later he was at liberty. He had planned to go into the country to rest and meditate.