EL 118 Final Project: The Tragic History of Evariste Galois

A study of the fabled life of a brilliant mathematician using discrete models of mathematical logic

Dylan Cashman

DISCLAIMER: The author of this work did not intend for this to be a factual biography. It is in no way to be used as factual evidence in the study of Galois' life. It also is not a formal treatise, in any way, of modern mathematics. It is simply an exploratory project.The author of this work did not intend for this to be a factual biography. It is in no way to be used as factual evidence in the study of Galois' life. It also is not a formal treatise, in any way, of modern mathematics. It is simply an exploratory project.

The biography is divided up into seven different versions of the same story. They range from the most abstract, Biography 7, to the most literal, Biography 1.

Biography 4

Evariste Galois was born the 25th of October of 1811 to afluent parents Nicolas-Gabriel and Adelaide-Marie Galois in the small commune of Paris called Bourg-la-Reine. His father, a staunch supporter of Napoleon, was a particularly politically active Republican, and when Evariste was 3 years old, Nicolas-Gabriel was elected mayor of Bourg-la-Reine. Unusual for the period despite her affluence, Evariste’s mother was extremely learned. She was an expert at Latin, versed by her father, a scholar. He also had an older sister, Nathalie-Theodore, and a younger brother, Alfred.

Evariste lived a happy family life for the first twelve years of his life. He was home-educated by his mother in several topics, including the classics, philosophy, and religion. He inherited the political leanings of his father, and was similarly influenced by the republican nature of the population of Bourg-la-Reine.

Bourge-la-Reine was historically a very liberal commune. In 1792, during the French Revolution, it was temporarily renamed Bourg-l'Égalité (meaning "Equality borough"). Later, after Napoleon abdicated in 1814 and Louis XVIII took the throne, restoring power to the Bourbons, Bourg-la-Reine felt the tides of discontent wash through; indeed, Evariste’s father became mayor as an opposition leader. Once Napoleon finally lost power after his military loss at Waterloo, the Bourbons’ power was unconditional. Bourg-la-Reine, as well as large parts of Paris, still remained firmly Bonapartist, prompting the Bourbons to murder hundreds of remaining supporters of Napoleon. In an attempt to stifle the rising agitation of the liberal Independents party, Louis XVIII passed a law that added weight to the votes of wealthier French citizens, and the political war was cemented. It was in this hostile political environment that Evariste Galois was raised and attended school.

While Evariste’s sister was sufficiently educated by her mother, the Galois family decided that it would be best for the clever boy to attend a school in Paris. It was originally planned that Evariste attend a college in Reims, and Evariste passed the entrance exam at the age of ten. However, his parents changed their minds – they elected instead to keep him home longer, and allow him to appreciate a pleasant and quiet family life. After another two years, at the age of twelve, Evariste gained acceptance into the highly-esteemed Lycee Louis-le-Grand in Paris, and his parents allowed him to attend. Evariste found himself attending an incredibly strict institution, and he was separated from his happy home life and fully entrenched in the academic life that would consume him for the next nine years.

At Louis-le-Grand, school life must have come as quite an uncomfortable transition from the cushioned lifestyles of the Parisian upper crust. The students were chaperoned without the slightest comforts – absolute silence was required during most of the day at the boarding school. Meals consisted of fat-enriched gruel, meat, and vegetables, or in some cases, scant portions of dry bread and water. The only available source of water for bathing was the ornamental fountain in the courtyard of the Hotel de Langres, the site of the school. The typical day consisted of over ten hours of classes beginning at 5:30 AM and ending around 6:00 PM, including breaks for meals. Even the classrooms, where most waking hours were spent, were uncomfortable; the students were required to sit on steps in the rooms listening to lectures with their exercise booklets in their laps, and the building suffered from a swarming rat infestation. The only heating came from a stove in each classroom that projected smoke throughout the study areas. Outside of the classroom, rules were strict as well. During the short recreation period at midday, pupils were only allowed to walk around the courtyards of the building and converse with each other. Running was prohibited – it was thought that the civilized sort that the school sought to produce would be too dignified to run. If any rules were broken, a student could be punished with a stay in an isolation cell for a minimum of four days, an archaic practice that elicits comparisons with the harshest prisons. Even the model student was known to get in trouble at some point; it becomes easy to forget that it was mere children that were subject to these harsh regulations.

In spite of the hardships students were subject to, Louis-le-Grand was thought to be one of the finest schools in Paris, and Napoleon himself had a hand in some of the administrative aspects of the school. Evariste was quick to make a reputation for himself as a brilliant student; in his first year, in spite of being one of the youngest children in his year, he won many prizes for his academic prowess. He continued to impress his teachers, easing through the progression of the school until the start of his fourth year. Laurent Laborie, an elderly theologian was appointed headmaster at the school. A stickler for rules and regulations, Laborie prevented Evariste from progressing to the final grade at Louis-le-Grand, arguing that he was far too young to fully appreciate the complexities of the course. In direct opposition to Evariste, his parents, and his high level of work, Laborie placed Evariste in the penultimate year of classes for a second consecutive year.

Instead of merely repeating his same studies, Evariste took the placement as an opportunity to learn new subjects. He took his first advanced mathematics class, and found that he had discovered himself anew in this singular school of thought. Bored with the normal texts allotted to youths, Evariste first met his match when his teacher, Jean-Hippolyte Veron, offered to his class the celebrated text Elements de geometrie by the prominent French mathematician Adrien-Marie Legendre. The text contained complexities that many students struggled to understand, as well as rigorous analysis and brilliant connections that could only be created by the most learned of men. It is rumored that Galois read the book like a novel, finishing it in two days. He soon became complacent in other subjects, dedicating the entirety of his mental capacity to the study of mathematics. His teachers became frustrated, and eventually they suggested to his parents that he be removed from the school. They felt that he would be much better-suited to study at a mathematical academy, where he would be free to focus on only that which interested him. Galois was happy with the suggestion, and with the consent of his parents, he set his sights on the premier mathematical institution in France, the Ecole Polytechnique.

The first hurdle that Evariste faced in his mathematical career was the entrance exam at Polytechnique. The exam was intended for adults well-versed in the contemporary mathematical language of the time. Administered orally, it required prospective students to thoroughly describe their problem-solving processes, elaborating on the accepted methods to showcase their understanding. Evariste had had little formal mathematical training, and subsequently failed the entrance exam. The following year, Louis-le-Grand offered an intense mathematics course taught by the competent and intelligent Louis-Paul-Emile Richard, and Evariste elected to enroll again in the school that he recently rejected.

Richard was an incredible teacher, but his best attribute was perhaps his ability to recognize brilliance. He instantly noticed Galois as being far ahead of other students, and encouraged Galois to explore any intuitions he had in the material. Possessing rare humility, Richard based some of his lessons on solutions crafted by Galois. In this benevolent atmosphere, Galois had his first mathematical paper published. While this paper was not more than a trifle compared to the ground-breaking theory that was being introduced at the period, it was not representative of the work of Galois. Richard recognized that the boy’s theories were revolutionary, and with his encouragement, Galois wrote two memoires, or extensive mathematical treatises, and submitted them to the French Academie des Sciences to be reviewed by the most prominent mathematicians in France, including Augustin Louis Cauchy and Joseph Fourier. These memoires contained absolutely incredible work – groundbreaking theory on Algebra that was to completely transform the study of the subject. Beyond solving certain problems put out by the mathematical community, the works introduced the idea of treating algebra in completely axiomatic, abstract manner, depending strictly on logic. It was perhaps the most significant movement in mathematics of a period that included discoveries that allowed us to accurately model forces such as heat and fluid movement. It is mind-numbing to imagine such work was written by a seventeen-year-old.

Tragically, the works effectively disappeared. They were submitted by the instructor, Richard, in the care of Cauchy, with the idea that his prominence would allow their quick recognition throughout the field. However, Cauchy was a very self-centered man; the research of others was of little concern of his. The two memoires were taken home and subsequently lost by Cauchy. He forgot about the work of Galois, and gave no response to the eager young mathematician. Galois waited for more than a year for any word, but soon deduced that his work had been for naught.

Around this time, the King, Louis XVIII, died from chronic health problems. His brother, Charles X, assumed the throne and a new regime begin in Paris that was even more critical of the former supporters of Napoleon. Tragedy befell the Galois family when Charles X supporters targeted the extremely liberal mayor of Bourg-la-Reine, Nicolas-Gabriel. Conspirators conjured up forged documents that suggested vulgar behavior, and a scandal ensued that resulted in the expulsion of the Galois family from Bourg-la-Reine to Paris. Consumed with shame, Nicolas-Gabriel committed suicide.

The death of Evariste’s father had a profound impact on him in both ideological and practical ways. Ideologically, this marked the first involvement of Evariste into the volatile politics in Paris. He recognized that his father’s death was a direct result of the corrupt methods of the Bourbon monarchy, and would soon develop a disgust at the presence of such malignant rulers. In addition, the task came to Evariste to continue the family legacy of political activity – he could still be a credit to his father if he continued his liberal mission.

Practically, Evariste faced the daunting task of pursuing his education without his father as a benefactor. Evariste had no source of income, and could no longer drift academically. He had to establish himself, find a way to pay his own way through the schooling that he thirsted for. He attempted again to gain entry into the Ecole Polytechnique, where he would be given a grant and be able to study with the best mathematicians in France. However, he faced similar problems as with his previous attempt; the examiners did not acknowledge his brilliance. Instead, they only noted that he had a deficiency in ability to accurately reproduce the theory already published in textbooks. He failed the entrance exam, a crushing defeat made worse by the fact that the institution allowed a maximum of two attempts to enter the school. His dream, mathematical study at the Polytechnique, was closed to him forever.

Instead, Evariste took up study at the less-prestigious Ecole Prepatoire. While the school was meant to train teachers, it distributed grants and would allow Evariste to study mathematics further in an academic setting. He passed the entrance exam, although without brilliant marks, perhaps owing to his newfound distraction of politics, and at the age of 18 was admitted to the school. The school managed to cultivate both his mathematical interests as well as his political interests. He became friends with activists, and found himself in the middle of a hostile intellectual movement against the crown.

In July of 1830, the political atmosphere was quickly growing with hostility and volatility. When democratic vote suggested an opposition majority in the French Parliament, King Charles X feared a coup d’etat. He used his powers to suspend the powers of parliament and, in addition, banish the freedom of the press. Predictably, the Parisian liberals were unable to accept these fringes on their freedom. Calls to arms from the now illegally-printing liberal presses were answered heartily by the city population, especially from the intellectual elite. Riots ensued, and Charles X was soon forced to flee Paris for his safety. In the mix of revelry and confusion that followed, the need for a replacement government was acknowledged. One of the revolutionary, liberal newspapers endorsed a prince who was sympathetic towards the rioters, and the Parisian public soon approved the instatement of a new king, Louis-Philippe.

Galois was prevented by the headmaster of his school to participate in the riots, but he clearly intended too; it was only the stone walls of the institution that prevented him. He found it disgusting that the headmaster prevented students from participating, but as soon as the revolutionaries were decided victorious, befriended them as a loyal supporter. Galois later sought to expose this hypocrisy in a letter to a newspaper. The headmaster denied all allegations, and was so enraged with the perceived libel that he began a battle with Galois that resulted in his expulsion from the school. Thus, Galois fought his political battles at the expense of his education. At this point, he became a prominent figure amongst liberal thinkers.

The most scandalous political action of Galois came at a banquet for the members of the Societe des Amis du Peuple, a liberal, revolutionary political group. A series of political toasts were made, praying for success in the battle of art over savagery in the form of political self-determination. Galois, full with wine, stood up with a jackknife in hand, and threateningly shouted, “To Louis-Philippe!” The murderous gesture was treated with mixed enthusiasm, and the party was soon disbanded for fear of political consequences of a perceived threat on the life of the king. A highly-publicized trial followed in which the government attempted to pin Galois with accusations of inciting revolt in a public place and threatening to attack royalty. A long and arduous court battle followed in which many witnesses chose solely to argue their ideologies, until the case served as a political forum. Galois was eventually acquitted, but the incident emblemized him as a counter-monarchical figure.

His luck against authority ran out eventually, however. The liberal revolutionaries found that they needed some sort of official place in French politics, and they found that the easiest way to accomplish this was to commandeer a French institution. They encouraged their members to join the French National Guard, and eventually the Guard became largely composed of opposition forces. This served two purposes – to unite the cause under an easily recognizable force and uniform, and also to arm the member incase the need for weaponry arose. The party members would often attend riots and meetings in full National Guard garb. When the government became wise to this tactic, it began expelling members of the National Guard.

On July 14, 1831, on the anniversary of the riots in Paris just a year before, the Societe des Amis du Peuple planned a public gathering in the same mindset of the revolution that took place the previous July. The gathering quickly turned riotous, and Galois, a vehement supporter, finally found himself marching through the streets of Paris with revolution in his heart. He wore a National Guard uniform, and was armed with several pistols. Police dispersed the crowd and chose to arrest the important players; Galois was taken in and found guilty of possession of illegal arms. He was sent to prison for nine months.

During his political activity, Galois still kept up with his math studies. He summarized all his findings in another memoire and submitted it in late 1829 as an application for the Grand Prix de Mathematiques, a prestigious award given out by the Academie des Sciences. However, bad luck struck again. The French mathematician Fourier took home Evariste’s submission to study, and two weeks later he mysteriously died. The memoire appeared to slip through the cracks like its two predecessors, but this time Evariste was dogged in his pursuit for a response. He wrote letters and eventually resorted to utilizing a newspaper to create negative press for the Academy. The Academy did review his memoire; however, they did not understand it. It was dismissed as unfinished. Galois was ultimately frustrated with the math system in France. His work, now several years old, had still not been recognized. When it had finally been given a chance, it was dismissed as lacking attention to detail and proper notation, aspects of the work that Galois himself knew were not important. While in prison for his political actions, Galois often pondered deeply on what had happened with his life. He had lost faith in the world of mathematics; his genius had been smothered.

While Galois was in prison, a cholera epidemic broke out in Paris. Since the close quarters of the prison were believed to serve as a breeding ground for sickness, many of the prisoners, including Galois, were moved to a more spacious clinic under the care of Doctor Jean-Louis Poterin-Dumotel. While staying there, Galois met and fell in love with the doctor’s daughter, Stephanie. The two exchanged letters, but evidently Evariste’s love was unrequited; Stephanie turned him down, insisting that the two stay platonic. Evariste was crushed; he had failed in yet another aspect of human life. Upon finally leaving the prison, he was dejected and dispirited.

At the time of Galois’ release, the Societe des Amis du Peuple had concluded that action needed to be taken to overthrow the Bourbons. A dispute over royal succession had arisen, and the Society felt that it was necessary to attack the enemy at its weakest point. A dramatic protest needed to take place, with the hope that sufficient riots would form to overthrow the government. In order for such a spirited, violent group of people to gather, the Society felt that it needed to resort to a drastic measure. It needed a funeral of a prominent member as a rallying point. No one had died recently – someone needed to offer their life.

Galois had often been quoted by friends and family as claiming “If I were only sure that a body would be enough to incite the people to revolt, I would offer mine.” Dissatisfied with his personal life, disillusioned of the academic world, and effectively estranged from the family that shaped him following the death of his father, Galois finally had the chance to offer himself. After much protest, the Society conceded. Galois and other members helped create a number of alibis and false documents to incite unrest in the publicizing of his death, and a plan was hatched to have Galois die the next day.

Galois was not eager to die. He knew that there was so much that he could have contributed to the scientific world, even if it were not immediately recognized. Half out of nobility and half out of desperation, he frantically wrote down the mostly-formed theories he had not yet published in a letter to his friend Augustin Chevalier, pleading with him to submit them to the Academy for review. The contents of that letter form the basis of Modern Algebra and are still researched today.

Galois died the next day of a gunshot wound. He was set up to duel a member of the Society. Given an unloaded gun, he simply had to wait to receive the life-ending bullet. At his funeral, many people showed up with minds centered on revolution. However, near its beginning, news began to circulate of the death of a prominent general who had been appointed by Napoleon. Liberal leaders decided that the general’s funeral would produce more publicity and public sympathy, and decided to postpone the riots for his funeral. Nothing took place at the funeral of Galois. He had died in vain.