Fermat's Last Theorem (32 page)

By the nineteenth century, mathematicians also had recipes which could be used to find solutions to the cubic and the quartic equations, but there was no known method for finding solutions to the quintic equation:

Galois became obsessed with finding a recipe for solving quintic equations, one of the great challenges of the era, and by the age of seventeen he had made sufficient progress to submit two research papers to the Academy of Sciences. The referee appointed to judge the papers was Augustin-Louis Cauchy, who many years later would argue with Lamé over an ultimately flawed proof of Fermat's Last Theorem. Cauchy was highly impressed by the young man's work and judged it worthy of being entered for the Academy's Grand Prize in Mathematics. In order to qualify for the competition the two papers would have to be re-submitted in the form of a single memoir, so Cauchy returned them to Galois and awaited his entry.

Having survived the criticisms of his teachers and rejection by the Ecole Polytechnique Galois's genius was on the verge of being recognised, but over the course of the next three years a series of personal and professional tragedies would destroy his ambitions. In July of 1829 a new Jesuit priest arrived in the village of Bourgla-Reine, where Galois's father was still mayor. The priest took exception to the mayor's republican sympathies and began a campaign to oust him from office by spreading rumours aimed at discrediting him. In particular the scheming priest exploited Nicolas-Gabriel Galois's reputation for composing clever rhymes. He wrote a series of vulgar verses ridiculing members of the community and signed them with the mayor's name. The elder Galois could not survive the shame and the embarrassment which resulted and decided that the only honourable option was to commit suicide.

Evariste Galois returned to attend his father's funeral and saw for himself the divisions that the priest had created in the village. As the coffin was being lowered into the grave, a scuffle broke out between the Jesuit priest, who was conducting the service, and
supporters of the mayor, who realised that there had been a plot to undermine him. The priest suffered a gash to the head, the scuffle turned into a riot, and the coffin was left to drop unceremoniously into its grave. Watching the French establishment humiliate and destroy his father served only to consolidate Galois's fervent support for the republican cause.

Upon returning to Paris, Galois combined his research papers well ahead of the competition deadline and submitted the memoir to the secrerary of the Academy, Joseph Fourier, who was supposed to pass it on to the judging committee. Galois's paper did not offer a solution to the quintic problem but it did offer a brilliant insight and many mathematicians, including Cauchy, considered that it was a likely winner. To the shock of Galois and his friends, not only did he fail to win the prize, but he had not even been officially entered. Fourier had died a few weeks prior to the judging and, although a stack of competition entries was passed on to the committee, Galois's memoir was not among them. The memoir was never found and the injustice was recorded by a French journalist.

Last year before March 1st, Monsieur Galois gave to the secretary of the Institute a memoir on the solution of numerical equations. This memoir should have been entered in the competition for the Grand Prize in Mathematics. It deserved the prize, for it could resolve some difficulties that Lagrange had failed to do. Monsieur Cauchy had conferred the highest praise on the author about this subject. And what happened? The memoir is lost and the prize is given without the participation of the young savant.

Le Globe, 1831

Galois felt that his memoir had been deliberately lost by a politically biased Academy, a belief that was reinforced a year later
when the Academy rejected his next manuscript, claiming that ‘his argument is neither sufficiently clear nor sufficiently developed to allow us to judge its rigour'. He decided that there was a conspiracy to exclude him from the mathematical community, and as a result he neglected his research in favour of fighting for the republican cause. By this time he was a student at the Ecole Normale Supérieure, a slightly less prestigious college than the Ecole Polytechnique. At the Ecole Normale Galois's notoriety as a trouble-maker was overtaking his reputation as a mathematician. This culminated during the July revolution of 1830 when Charles X fled France and the political factions fought for control in the streets of Paris. The Ecole's director Monsieur Guigniault, a monarchist, was aware that the majority of his students were radical republicans and so confined them to their dormitories and locked the gates of the college. Galois was being prevented from fighting alongside his brothers, and his frustration and anger were compounded when the republicans were eventually defeated. When the opportunity arose he published a scathing attack on the college director, accusing him of cowardice. Not surprisingly, Guigniault expelled the insubordinate student and Galois's formal mathematical career was at an end.

On 4 December the thwarted genius attempted to become a professional rebel by joining the Artillery of the National Guard, a republican branch of the militia otherwise known as the ‘Friends of the People'. Before the end of the month the new king Louis-Phillipe, anxious to avoid a further rebellion, abolished the Artillery of the National Guard, and Galois was left destitute and homeless. The most brilliant young talent in all of Paris was being persecuted at every turn and some of his former mathematical colleagues were becoming increasingly worried about his plight. Sophie Germain, who was by this time the shy elder stateswoman
of French mathematics, expressed her concerns to friend of the family Count Libri-Carrucci:

Decidedly there is a misfortune concerning all that touches upon mathematics. The death of Monsieur Fourier has been the final blow for this student Galois who, in spite of his impertinence, showed signs of a clever disposition. He has been expelled from the Ecole Normale, he is without money, his mother has very little also and he continues his habit of insult. They say he will go completely mad. I fear this is true.

As long as Galois's passion for politics continued it was inevitable that his fortunes would deteriorate further, a fact documented by the great French writer Alexandre Dumas. Dumas was at the restaurant
Vendanges de Bourgogne
when he happened upon a celebration banquet in honour of nineteen republicans aquitted of conspiracy charges:

Suddenly, in the midst of a private conversation which I was carrying on with the person on my left, the name Louis-Phillipe, followed by five or six whistles, caught my ear. I turned around. One of the most animated scenes was taking place fifteen or twenty seats from me. It would be difficult to find in all Paris two hundred persons more hostile to the government than those to be found reunited at five o'clock in the afternoon in the long hall on the ground floor above the garden.

A young man who had raised his glass and held an open dagger in the same hand was trying to make himself heard – Evariste Galois was one of the most ardent republicans. The noise was such that the very reason for this noise had become incomprehensible. All that I could perceive was that there was a threat and that the name of Louis-Phillipe had been mentioned: the intention was made clear by the open knife.

This went way beyond my own republican opinions. I yielded to the pressure from my neighbour on the left who, as one of the King's
comedians, didn't care to be compromised, and we jumped from the window sill into the garden. I went home somewhat worried. It was clear this episode would have its consequences. Indeed, two or three days later, Evariste Galois was arrested.

After being detained at Sainte-Pélagie prison for a month Galois was charged with threatening the King's life and brought to trial. Although there was little doubt from his actions that Galois was guilty, the raucous nature of the banquet meant that nobody could actually confirm that they had heard him make any direct threats. A sympathetic jury and the rebel's tender age – he was still only twenty – led to his acquittal. The following month he was arrested again.

On Bastille Day, 14 July 1831, Galois marched through Paris dressed in the uniform of the outlawed Artillery Guard. Although this was merely a gesture of defiance, he was sentenced to six months in prison and returned to Sainte-Pélagie. During the following months the teetotal youth was driven to drink by the rogues who surrounded him. The botanist and ardent republican François Raspail, who was imprisoned for refusing to accept the Cross of the Legion of Honour from Louis-Phillipe, wrote an account of Galois's first drinking bout:

He grasps the little glass like Socrates courageously taking the hemlock; he swallows it as one gulp, not without blinking and making a wry face. A second glass is not harder to empty than the first, and then the third. The beginner loses his equilibrium. Triumph! Homage to the Bacchus of the jail! You have intoxicated an ingenuous soul, who holds wine in horror.

A week later a sniper in a garret opposite the prison fired a shot into a cell wounding the man next to Galois. Galois was convinced that the bullet was intended for himself and that there was a
government plot to assassinate him. The fear of political persecution terrorised him, and the isolation from his friends and family and rejection of his mathematical ideas plunged him into a state of depression. In a bout of drunken delirium he tried to stab himself to death, but Raspail and others managed to restrain and disarm him. Raspail recalls Galois's words immediately prior to the suicide attempt:

Do you know what I lack my friend? I confide it only to you: it is someone I can love and love only in spirit. I have lost my father and no one has ever replaced him, do you hear me …?

In March 1832, a month before Galois's sentence was due to finish, a cholera epidemic broke out in Paris and the prisoners of Sainte-Pélagie were released. What happened to Galois over the next few weeks has been the subject of intense speculation, but what is certain is that the events of this period were largely the consequence of a romance with a mysterious woman by the name of Stéphanie-Félicie Poterine du Motel, the daughter of a respected Parisian physician. Although there are no clues as to how the affair started, the details of its tragic end are well documented.

Stéphanie was already engaged to a gentleman by the name of Pescheux d'Herbinville, who uncovered his fiancée's infidelity. D'Herbinville was furious and, being one the finest shots in France, he had no hesitation in immediately challenging Galois to a duel at dawn. Galois was well aware of his challenger's reputation. During the evening prior to the confrontation, which he believed would be his last opportunity to commit his thoughts to paper, he wrote letters to his friends explaining his circumstances:

I beg my patriots, my friends, not to reproach me for dying otherwise than for my country. I died the victim of an infamous coquette and her two dupes. It is in a miserable piece of slander that I end my life. Oh! Why die for something so little, so contemptible? I call on heaven to witness that only under compulsion and force have I yielded to a provocation which I have tried to avert by every means.

Despite his devotion to the republican cause and his romantic involvement, Galois had always maintained his passion for mathematics and one of his greatest fears was that his research, which had already been rejected by the Academy, would be lost forever. In a desperate attempt to gain recognition he worked through the night writing out the theorems which he believed fully explained the riddle of quintic equations. The pages were largely a transcription of the ideas he had already submitted to Cauchy and Fourier, but hidden within the complex algebra were occasional references to ‘Stéphanie' or ‘une femme' and exclamations of despair – ‘I have not time, I have not time!' At the end of the night, when his calculations were complete, he wrote a covering letter to his friend Auguste Chevalier, requesting that, should he die, the papers be distributed to the greatest mathematicians in Europe: