Evariste Galois

Brief Biography by Bernard Bychan

Text taken from The Evariste Galois Archive

His Childhood

Evariste Galois was born on the 25th of October 1811 in a small place called Bourg-la-Reine. This place is situated about 10 kilometres south of Paris. Today, it is a suburb of the French capital. In his house in the Grande Rue - nowadays called Avenue du Générale Leclerc - the Galois family accommodated a school, whose origins can be retraced to the times before the revolution. Prosperity and reputation of the family were based in this school.

His father Nicolas-Gabriel Galois his mother Adélaïde Marie Demante were very intelligent and were well trained in all the subjects considered important at that time: classical literature, religion and philosophy. There is no record of mathematical talent on either side of the family, nor did Evariste himself show any, but on the other hands there are no hints to the contrary neither.

But there is a record of Nicholas-Gabriel Galois gift for composing rhymed couplets. He used it to amuse family and friends at house parties (maybe elsewhere as well but there is no explicit mentioning of it). It's hard to imagine that his ability proved to be his undoing, years later. Evariste seemed to have inherited this talent. His cousin Mme. Bénard remembers decades later the family parties with their grandmother, when the children, i.e. Galois, his sister and their cousins recited rhymed couplets, which Evariste had composed.

At the age of ten his parents decided to send him to a college in Reims. Evariste was admitted to this school with a partial grant. But then his mother seems to have changed her mind. She regarded her son as too small and defenceless to be sent off so far from home. He was allowed to stay home, enjoy the quiet family live and she kept on being his (as well as his sister's and brother's) sole source of education. He received an excellent education in Latin, Greek and rhetoric, and it is mentioned, that she passed on her own skepticism for religious matters, but mathematics is not mentioned.

School Days

In 1823, at the age of twelve, Galois entered the lycée of Louis-le-Grand in Paris, which was his first school. Bell says in his biography "Genius and Stupidity", that the place was a dismal horror. "Barred and grilled, and dominated by a provisor who was more of a political gaoler than a teacher, the place looked like a prison, and it was." Bell - though not totally wrong - was exaggerating or even misinterpreting what he found in earlier biographies.

The turbulent political events of the time - i.e. the unbalanced power triangle between church, royalists and republicans - left their marks on the school as well. A rapid change of headmasters and there was a rebellion during his first school year and 40 pupils were expelled from the school. Galois being a freshman was not yet involved in any politcal activity. According to his school report, Evariste did very well in the first school year and he received several prizes too.

There are a lot of obscurities to be found concerning the sequence of his school years. The main reason to my mind results from the fact that the enumeration of classes used by French lyceums was confusing: The first school year was called the "sixth class" and the last year at school was the first class. Evariste had been admitted to the "fourth" class at the Louis-le-Grand as a boarder, i.e. he was remitted the first two years.

His successful start at school and the first two years show, that his mothers preparation was well founded, but during the 1825-26 school years his attitude to school changed. During the winter he was troubled by serious earache, which was caused by the bad conditions in the college buildings. Bell romanticized this year by writing, that during this time his mathematical genius was already stirring. At the end of the school year his father received a letter by the headmaster, advising him to let his son repeat the class, because he didn't seem mature for the last class (called rethorique) Due to his father's strong resistance he was put up but a few months later, in January he had to go back to the second class.

In February 1827 Galois enrolled in his first mathematics class, a course by M. Vernier. It was during this course that Galois worked with Legendre's text on geometry and he was maybe for the first time acquainted with the theory of equations by Lagrange's works. His attitude towards the other subjects didn't change. His teachers complained that he didn't participate in lesssons and hardly did any homework. But in the second school report of this class they wrote:

"Whats's dominating him is the fury of mathematics; also, I think that it would be better for him if his parents would agree to let him study solely mathematics. He is wasting his time here and he does nothing but torment his teachers and by doing so heaps punishments on himself."

His attitude doesn't change when he is finally admitted to the "first" class. Some teachers mentioned as Dupuy writes in his biography: "His fast apprehension is a legend by now, in which soon nobody will believe; there is a trace of particularness and of carelessness in his homework, if he does it at all; he is constantly busy with things, which he does not have to do, but is affecting him."

Strokes of Fate

As a simple pupil of the Mathématiques préparatoires, Galois - completely on his own - for the entrance to the École. Galois wanted to go to this school under all conditions, because it garanteed him the best possibilities in mathematics. It had been hardly ten years ago that the École had drastically modified their statutes: No longer militarilly oriented and they changed their uniformes for civilian. But the major task remained the same: to train young scientists the government service.

In June 1928 Evariste appeared there for the entrance examination, although he had not taken part in another special course in mathematics for another year. The fact that he flunked was for Galois one of the injustices, regardless if real or imagined, which poisoned his life.

The two heavy strokes of fate, which overtook Galois in July 1829, were surely catalysts for the tragic course of his further life. Did they have a triggering effect or did they just accelerate what had started with his experiences at the Louis-le-Grand.

The year 1829 was a time, in which the clerics resisted with king Charles X' consent the liberal decrees of Martignac. Edicts which didn't allow anymore certain religious orders (e.g. the jesuits) to teach.

These tensions prevailed also in Bourg-la-Reine, where at the beginning of the year 1829 a young priest took over the parish and soon banded together with the Ultras. Together with a member of the town council he intrigued against the liberal mayor Nicolas Nicolas-Gabriel Galois. They spread falsified vulgar poems and let him appear as the author. Due to the scandal resulting from thereof, Evaristes' father left Bourg-la-Reine and moved to Paris, where he rented an apartment in the rue Jean de Beauvais, close to Louis-le-Grand. In this flat he committed suicide on the second of July. His funeral became a triumphal procession of the liberals and in the end the priest was offended and some stones were thrown at him.

Just a few days after the unexpected death of his father, Galois took the the entrance examination to the École Polytechnique for the second time. It became a legend in the history of mathematics. He was aware that a refusal would be final this time, if he would flunk again. The examiners, though being recognized mathematicians, were not capable of detecting the mathematical genius of Evariste Galois. One of the two examiners asked the fatal question: He should describe the theory of the arithmetic logarithms. Galois criticized immediately the question, and mentioned to professor Dinet that there are no arithmetic logarithms. Why didn't he simply ask for the theory of the logarithms? Thereupon Galois refused to explain some propositions concerning logarithms. He said that it was completely obvious!

This was apparently the dot on the i: He failed the examination.

According to the biographer Bell the course of events was different and more dramatic: Galois, used to unfold his mathematical thinkung completely in his head, had a serious disadvantage before the board. The chalk and the sponge irritated him until he found a suitable application for one of the two things. One of the examiners had discussed both falsely and stubbornly a mathematical fact. In a fury and despair he hurled the sponge into the face of his tormentor. Twenty years later we find In the Nouvelles Annales Mathématiquesthis: "a candidate of superior intelligence was ruined by an examiner of minor intelligence. Barbarus hic ego sum quia non intelligor illis!

Political Life

Galois must have been interested in politics when he was still attending the Louis-le-Grand, because Dupuy says in his biography, that besides the excellent education provided at the Polytechnique, Galois hoped to participate in the various political activities of this school.

But his political activities started mainly at the Ecole Normale. He made friends Auguste Chevalier, a student from the second year. Auguste and his brother Michel, studying at the Ecole Polytechnique, had a great influence on Galois. The two brothers were ardent followers of Saint-Simonianism. Comte de Saint-Simon (1760 - 1825), alias Claude Henri de Ronvroy, linked early socialism with positivism in his philosophy. According to him society should be reorganized along industrial lines and the role of spiritual leaders should be taken by scientists.

The students of the Ecole Normale were set on fire by the events of the July revolution. M. Guigniault, the director at the time, wanted to prevent his students from taking part in the dangerous happenings. He ordered them to stay inside the building and had all gates locked to enforce his will, most of the windows were barred anyway. He reminded his students of their pledge of service to the State, which made them civil servants.

Galois wanted to take part under all circumstances and tried to escape by climbing over the outer walls. He failed, bruising his hands and knees.

Charles X had to flee from France and Louis-Philippe took over the crown. Cauchy, the famous mathematician, followed Charles into exile.

In the months after the July events, Galois must have joined the "Société des Amis du Peuple" (Society of Friends of the People). It was an organization founded that very year and its members were also the most active and aggressive ones of the republican party. They worked as a secret organization after a public start. They were regarded as very dangerous by most of the press, especially the government controlled press.

Galois seems to have been in continuous conflict with Guignault. Galois irritated him with his proposals: He wanted to introduce uniforms, like the one at the Ecole Polytechnique, which were in military style. Evariste asked for the students to be armed, so they could have military training. Apparently, most of his fellow students were avoiding Galois and his radical ideas.

Evariste Galois was expelled from school on the 9th of December - publicly announced on the 4th of January - because of an anonymous letter to the "Gazette des écoles". In this letter the director was blamed and offended for his behavior during the July revolution. Galois never admitted being the author of this letter neither to his fellow students nor to the director.

Galois immediately enlisted in the Artillery of the National Guard, almost entirely consisting of republicans.

On 15 December a trial before the Chamber of Peers began: four ex-ministers of Charles X were accused of treason. Lots of people in the street demanded the capital punishment. On the 21th of December, the day of the verdict, the situation was utterly tense. The artillerymen had planned to revolt, in case the ministers would be given life imprisonment instead of an execution. But although the verdict was not what the artillerymen and the National guard was hoping for, the expected revolt didn't occur.

On the 31st of December 1830, Louis-Philippe dismissed General Lafyette and disbanded the National Guard. So it was, that in January 1831 Galois, no longer a student, and not a member of he National Guard anymore he tried to found a private algebra class to earn money for his living. His mother was not capable to support him financially.

His course started as planned ont the 13th of January with about 40 students attending it, most probably mainly friends and not mathematicians. So it's no wonder that they couldn't follow his abstract lectures.

Poisson asked Galois for a new copy of his memoire, so he wrote a new introduction and submitted his work on the 16th of January to the Academy.

Because they refused to hand over their arms, nineteen officers had been arrested and charged with conspiracy to overthrow the government. As the so called "trial of the nineteen" caused a lot of attention in Paris, the government surely was afraid of an unpopular sentence, so the trial ended with an acquittal for the whole group. The members of the Société des Amis du Peuple organised a banquet in honour of the artillerymen, which was held on the 9th of May at the restaurant "Aux Vendanges de Bourgogne". As Alexandre Dumas, who was one of the guests - says in his memoirs: "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." Naturally, Galois was one of them.

Even though they had planned not to provoce the police with the toasts, many guests couldn't restrain from flamboyant republican speeches. But Galois "toast" immediately led to chaos and an untimely end of the event. He had raised a knife and said: "To Louis-Philippe!" When others followed his example, most people afraid of the police left the room in a hurry - some even through the open windows into the garden.

The next day, the police arrested Galois at the apartment in Paris, where he lived with his mother. He was charged with incitement to an attempt on the life and person of the King of the French. Galois was imprisoned at Sainte-Pélagie. He wrote to his friend Auguste Chevalier: " ... I am under lock and key ! ! ! ... I was the one who made the gesture ... But don't blame me, because the fume of the wine had me lose my head ..." On the 15th of June 15 he was tried for threatening the King's life.

His strategy of defence, worked out by his lawyer Dupont, was, that people didn't hear all of his words due to the din in the room. "To Louis-Philippe, if he betrays us!", was what he said, while accidentally brandishing the knife with which he was cutting his meat during the meal. After a long trial the verdict was not guilty.

A short while after the trial, Galois's memoir on the resolution of equations was rejected by the Academy. Poisson was a referee.

Just a month after his acquittal, Galois ran into trouble again. The republicans organised a patriotic demonstration for the celebrations of the 14th of July at the place de la Bastille. They wanted to plant a symbolic tree of liberty. A poster was prepared to incite people to attend the demonstration, but the police confiscated all the posters and wanted to arrest those republicans, which were considered responsible. They broke into Galois house - as they did with the other suspects as well - during the night preceding the 14th. Galois had been warned and was not home, but the following day he was preventatively arrested together with his friend Duchalet, roaming the streets of Paris. He was dressed in Artillery Guard uniforms - which was strictly forbidden - and armed to the teeth, carrying besides his usual knife, several pistols and his regulation carbine.

This time after three months of preventive detention, Galois was harshly punished to nine month in prison until April 1832.

Fallen In Love

In the spring of 1832 Galois prison term came to an untimely and unexpected end. One of the worst world-wide raging cholera epidemics had arrived in France and was taking the lives of many people all over France. Especially poor people, due to the bad hygenic conditions they lived in, fell prey to the terrible disease. The prisoners in Sainte-Pélagie were also in jeopardy, so the officials decided to transfer the youngest and those in bad health to a clinic.

In this clinic, called after the owner Faultrier, he met Stéphanie, the daughter of Jean-Louis Poterin-Dumotel, one of the doctors. It's hard to recover the kind of relationship the two have been in. But from what is left of two letters, which he had received of her, we can be sure, that he was desparately in love with her. We don't know, if there has been a love affair or if she had turned him down immediately, but it looks as if her refusal was one of the main reason for his tragic death.

The Duel

The duel and the events leading to it are blurred by time and the phantasies of novelists and what's worse biographers. We can rule out or at least it is highly improbable that the duel was a plot of the royalists to murder him. Though this version is a favorite legend lingering in many biographies. Most probably it was Galois himself who incited this interpretation. He wanted himself to appear as a victim of the government, whichshould enrage the masses to revolt. He dropped remarks pointing in this direction: At a meeting of the Friends of the People and in his last letters. The most likely reason is: He was weary of life, because of his unhappy love affair, his fruitless efforts for gaining recognition for his mathematical work, his financial and work situation and he felt finished up a blind alley in politics as well. So his duel was like a staged suicide. It is still not clear who the other dueller a supposed political friend was.

One thing is clear, though it kills a favorite legend: He didn't lay down his mathematical theory in the night befor the duel. He pointed out the cornerstones of his scientific life in a long letter to his friend Chevalier, so that everything might be properly evaluated and not be lost.