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 5

On the 25th of October in 1811, the world of Mathematics was bestowed a gift. Evariste Galois was born in a quaint, free-thinking section of Paris called Bourg-la-Reine. He was born into a relatively blessed family; the parents were both of an educated background, and there was wealth in the family. Preceded by a sister and followed by a brother, Evariste seemed to be a part of a quintessential privileged middle-class family in Paris. Even though he would possess an intelligence that was unrivaled in his time, he found his beginnings to be humble compared the greatness he would eventually achieve.

The Galois family was a happy one. Evariste was free to roam the beautiful Parisian countryside, and we can imagine his curious and considerable intellect taking walks and making observations similar to Marcel Proust. Such a relaxed atmosphere was perfect for developing a great mind. He indubitably witnessed countless political arguments his father, the mayor of the commune, engaging in debate with local political figures. He was astounded as they stayed talking late into the night, waxing political theory and feeding off of each other. It was this love of argument that may have inspired his mind to master logic; his mind was cultivated in the healthy soil of a culturally relevant household.

Bourg-la-Reine was somewhat of a thorn in the side of the prevailing Bourbon monarchy government in France. In the glorious reign of Napoleon, there were no stronger supporters than those in the small section of Paris. However, after the fall of the Emperor, the commune changed hands, and it suddenly found itself in the opposition. Bourg-la-Reine remained the black sheep; its continual refusal to follow in the footsteps of its country marked it for conflict like a bullseye. This political atmosphere would have a profound effect on Evariste, planting the seed of rebellion in him that would flower in his young adulthood.

The brilliance of Evariste was quickly recognized by his mother, and she saw the importance of sending him to study at a boarding school. At twelve, he was torn from the floating, fluff-filled life of aristocratic Paris and thrown into the prison-like Lycee Louis-le-Grand to study with other children. At this point, his life diverged completely from the track it had been on. Prior to school, he had been encouraged to create and think freely; his father was an intensely free-thinking politician and his mother had been something of a classics scholar. Evariste had been known amongst his family for composing poetry and performing readings for friends and relatives. The French school system was in contrast solid, cemented, harsh, dim, and dry. Evariste was forced to study in cold classrooms heated by a smoky fire, infested with hostile, disease-ridden mangy rats, listening to stern lecturers who stood above the class in a pulpit, acting as both pedagogues and policemen. The seats were cold stone steps, the desks were non-existent. The system was designed to inspire discipline and acceptance, and there was no time allotted during the day for free expression. The only time when the children’s time was not strictly scheduled was the short recess period, in which children were allowed to walk within the grounds of the school building and talk to one another. When a child disobeyed any of the vast number of illegitimate and arbitrary rules, he was thrown in an isolation tank for at least 4 days straight, where he was fed old, stale dry bread with only plain water to choke it down with. The punishments were not just reserved for the worst of crimes – it could be for simply speaking during class, or disrespecting the word of a teacher, or acting like any child of such tender age would and attempting to have fun.

A new stage in Evariste’s life began. As he marched into his classes for the first time, he must have been intimidated. The other children, mostly older than him, were firmly entrenched in the military-styled institution. He was cold, lonely, and treading in the unfamiliar territory of maturity and responsibility. He found the work new, unusual, but not unwelcome. His studies proved to be impressive, and he was the recipient of many awards in his first year. In his youth, Galois found that success was easy – he only needed to utilize his formidable intellect to prove his ability to act the precocious youth. However, it also marked the first introduction of a contrarian authority in to Evariste’s young, naïve mind. Even the best students were disciplined sometimes, and basic, genuine childish urges were interpreted as lazy and common tendencies. Evariste could see the injustices of the situation; the youths were being forced into a transformation, from innocent to battle-worn, and yet they had no form of expression. Their proverbial fire was squelched, and they were expected to come out of school as mechanical, efficient academics.

The young boy excelled, however, and exalted himself with his academic prowess. He was marked by his unusually small stature and young age, and, when a conservative head master was put into place at the school, Evariste was told that he could not proceed to the final year of school – he was simply too young to appreciate the complexities that arose in the mature class. Instead, Evariste was required to stay in the grade he had recently completed. He and his family were frustrated; there was no viable reason that Evariste could not complete the final course. He performed better than most of his classmates that were allowed to proceed. The Galois family conceded, however, and Evariste used the repeated year to take more subjects that he had not yet studied. He decided to take Mathematics, a subject that he had not delved into on more than a remedial, automatic level.

Evariste found his calling that year. His instructor, Jean-Hippolyte Veron, decided to instruct the class using a text by the famous and accomplished mathematician, Adrien-Marie Legendre. Evariste found in the book a wealth of information and questions like he had never seen or experienced before in his life. He devoured the work, page by page, digesting it rapidly and always hungering for more. It is rumored that he completed the entire text in two days time. At the tender age of 15, he became a scientist, studying Legendre like it was a new discovery whose veracity was the hinge of some unified understanding of the mysteries of the world. His incredible intellect used the work like firewood, and he immediately dedicated himself to the study of mathematics. His teachers noted that he no longer gave effort in academics, and he was found to be a much more unruly student. He had changed to such an extent that it was recommended that he leave the school and study in an institution dedicated to mathematics. Evariste was enamored with the notion.

A lot hinged on Evariste’s acceptance into the Ecole Polytechnique, the best mathematical institution in the entire country, if not the world. There, Galois would get to study with many geniuses, and would receive financial aid directly from the government to pursue his studies. However, in order to be admitted to the school, a student needed to pass rigorous examinations. Without the knowledge of his parents, swelled with pride and confidence, Evariste scheduled an examination in mathematics. However, with little mathematical education or indeed life experience at 15 years of age, he failed the entry exam. He decided to remain at Louis-le-Grand. It was not without protest, though – he knew the classes at his old school would not challenge him, and could not sate his growing hunger. He was again frustrated at the inability of the academic world to identify his ability, and a certain brand of cynicism was born within him that would soon metastasize into a major part of his personal philosophy, whether for good or for bad.

In some ways, failing the entrance exam was a boon for Evariste’s mathematical future. During his next year at Louis-le-Grand, his math course was put together by a very excellent teacher, Louis-Paul-Emile Richard, who was known for recognizing and cultivating brilliance. Galois and Richard discussed math for hours together on a level that nobody else in the school could understand, and Richard soon saw that he was in the presence of greatness. He was often shocked at the complexity and elegance of Galois’ analysis of the problems he presented, and found that the role of instructor and instructed were often switched. Richard could not understand why Galois was not admitted into the Polytechnique, and suggested that he be allowed to bypass the entrance exams.

After a surprisingly short tenure as a student of mathematics, Galois found himself with original ideas. At such a young age, there were very few venues for him to demonstrate his theories, and for a long time they simmered beneath the surface of his brain. It is thought that while he ignored other subjects, he worked intensely at his own discoveries. We can only imagine the wealth of insight that he was in possession of; yet, Galois was turned back again and again when he tried to share it with the rest of the mathematical community. Richard noticed the singularity of Galois’ methodology and encouraged him to submit his ideas to be studied by other mathematicians of the day, and Galois did so.

The French scientific institution failed the community of progress that day, as it would fail Galois repeatedly throughout his tragic life. Richard forwarded the memoires written by Galois directly to the famous and respected mathematician Augustin Louis Cauchy, who briefly skimmed them and asserted their potential by promising to present them to the Academie des Sciences for review. Galois was awash with hope, appreciating the chance to finally become distanced from his peers and be granted the credit he deserved. However, Cauchy was an opportunistic, cold-hearted, self-concerned creature, and promptly lost Evariste’s papers within his house. When he finally found them and read through them, he promised the Academy that he would present them at the next meeting; he apparently forgot his claim, because the next lecture he gave was on his own research. Galois waited with bated breath for his ticket to mathematical recognition, financial freedom, and entrance to whatever learning institution he wished, but it did not come. He grew more cynical with each week that went by, bringing no news. An intelligent young adult, he eventually concluded that the Academy would never give him a chance.

At this time in his life, Evariste faced two great tragedies. When a new political regime came into power, finally ending any remnant of a Napoleonic government, Bourg-la-Reine, Evariste’s hometown, was targeted as a problem area. The new king, Charles X, was extremely intolerant of dissenters, and found a problem with the liberal, vehemently Bonapartist mayor of Bourg-la-Reine, Nicolas-Gabriel Galois. Evariste’s father was framed by government officials, who unearthed a planted scandal to defame the well-liked political official. Nicolas-Gabriel was horrified; he had always stood for the high morals of reason, and he could not live with the idea of being a hypocrite the people whom he had served and lived with for so long. He left the commune to live elsewhere in Paris, where he believed he might escape the shame. As each day went by, he expected it to be easier to deal with. However, much like the Poe-created telltale heart, the elder Galois could never cope with the intense regret he felt. One day, when his family had left their Parisian home, Nicolas-Gabriel Galois committed suicide.

Evariste was crushed. He had always had fond memories of his father, and he found, at a young age, that he would never be able to experience the care-free life that he had known so well in his childhood. From that point on, his family life was a shambles. There was no home for Galois – he was forced to either continue his academic life and become a mathematician or end up on the streets of Paris, homeless and unloved. His future existence was dependent on the success of his career, and he was not confident that it would pick up anytime soon.

Like a good fiction, the timing of tragedies in the young man’s life was almost comically precise. The time for the entrance exam for the Polytechnique had arrived, this time with a stipulation in the rules that dictated it was the final chance for Galois to be accepted into the school; any person could only apply for acceptance a maximum of two times. Galois entered the oral exam and was met with two extremely dry, insignificant yet pompous old mathematicians administering the test. They are now only remembered with the disrespect they showed Galois – their evaluation was nothing short of insulting, and Galois responded in kind. Disgusted at their lack of understanding and the basic questions they asked, and frustrated with having to argue over mathematical properties that in his brain were casually apparent, he famously threw a chalkboard eraser at one of the mathematicians and stormed out of the room. They did not admit him into the school.

Galois was extremely disappointed in mathematics; he had dedicated himself to it so completely that he had neglected all other parts of his life, and it had failed to provide for him. He enrolled in the Ecole Preparatoire as a means of keeping up with his education, and also as a means of keeping himself afloat, since it provided him with a grant. Established by the government to train academic instructors, the school did not hold half the prestige of the Ecole Polytechnique. However, it introduced Galois to his other love in life, the politics of the revolutionary party in France.

Galois recognized that his father had fallen from glory and committed suicide for purely political reasons. Upon his father’s death, he dedicated himself to the same cause, internally. At every turn in his life after that, any observer would note that Galois’ distrust of authority, especially the monarchy presently in dictatorial power of Paris, was cemented in place. At the Ecole Preparatoire, Galois found a number of sympathetic adults to his political inquiries. He became active in a political newspaper that circulated amongst schools and the intellectual community. When the new king stifled democratic progress with a decree blocking the freedom of the press, massive riots broke out throughout Paris. Galois and his political allies at the school sought to join the protest, but yet again, Galois found that his authority prevented him from doing what he wanted; treating them as if they were mere school boys, the headmaster of the Ecole Preparatoire mandated that no members of the school would leave, and ordered that the doors of the complex be sealed. Galois faced opposition from every angle; his academic life was stifling, disappointing, and not even worth his time – he was not learning anything from inferior professors, and he repeatedly found the academic system full of obstacles – and the political atmosphere around him was exploding in a battle between new, enlightened ideals and old, established precedents. He found himself more and more interested in political activism, and eventually he bound politics to be his new muse.

He first became known amongst the liberal party when he wrote a letter to a local newspaper exposing the political hypocrisy of the headmaster of his school. For this, he was expelled, and free to participate in the revolution full time. He joined the national guard, which, in its dedication to Bonapartist ideals, at the time was simply a gathering point for revolutionaries, and became well-known in political circles.

At a banquet for an opposition party group entitled the Societe des Amis du Peuple, political scandal found Galois just years after it had so tortured his father. The atmosphere of the party was infused with gunpowder – it was a gathering of fiery, radically liberal thinkers, behind closed doors. There were a number of raucous toasts throughout the evening, but one trumped them all in its boldness – that of Evariste Galois. After imbibing enough wine to considerable alter his faculties of reason, Evariste took out a jack knife that he had procured for reasons still unknown, and thrust it into the air. He accompanied this gesture with an ironic statement: To Louis-Philippe! The other banqueters were shocked; did he just threaten the new king of France while brandishing a weapon? Many cheered loudly; Galois had voiced the same thing they all wished to, and they felt that it was a reasonable suggestion. However, many others feared to be associated with treason of such a drastic level, and many panicked attendees trampled out the door.

Galois was arrested the following day by officers of the king, in front of his mother at her new house. He was subsequently put on trial in a spectacle of publicity for the opposition party. Dozens of witnesses were called, and Galois became somewhat of a spearhead for the movement. Eventually, the court ruled that Galois was not guilty of any crime. His innocence did not last long, however. Soon after, in a celebration of the anniversary of the original riots against the crown that Galois did not get to participate in, the opposition party planned another set of protests. They soon became riots, and Galois was one of the most vehement members of the rioting. He wore his National Guard uniform even though he was no longer a member, and carried also with him the pistols and weaponry he had been given from that position. Galois was incredibly invested in the politics of his party; he served his duty with the same dedication that, only a year earlier, he had applied himself to the study of mathematics. In spite of the obvious danger, Galois tried to appear as repugnant as possible, military gear in full tow. When the riots were broken up, he was charged with unlawful possession of weapons, amongst other small crimes, and was sentenced to nine months in jail. Galois had finally become a political prisoner; his profession had finally officially changed!

While in prison, Galois found himself surrounded by free thought. The prison he was taken to was solely used to the great number of political prisoners taken by the Bourbon regime, and Galois and the others often spoke late into the night, arguing over the beautiful ideals that they would have loved to live in a free France. It was a romantic atmosphere, and in a strange turn of events, it seemed to inspire Galois to fall in love with a girl who sometimes came by the prison. When a cholera epidemic broke out in Paris, Galois and many other prisoners were moved to a private clinic to protect them from the high-risk small quarters of the prison. There, he met the daughter of the doctor of the clinic, Stephanie Poterin-Dumotel, and subsequently began courting her with letters. It is clear that he fell in love. Galois had not found salvation in any area of his life over the last 8 years, since he had left home. After hours of discussing with other prisoners what their utopias would be, Galois must have been ecstatic to find his own in a human being who treated him with respect and care. The two shared a letter correspondence, and Galois seemed to be happy. However, Stephanie seemed to have different ideas of the entire affair. She wrote a final letter to Evariste, telling him that she had never had any intention of having a non-platonic relationship with him. His love was completely unanswered. As with almost every facet of his life, his subscription did not matter. He was unable to get what he wanted with all of his heart, and the repetition hung heavy on him. The disappointment surrounding Stephanie seemed to be the proverbial straw that broke the camel’s back, and when Evariste was finally released from prison, he was a broken man. He lacked the fiery spirit that had interested him in politics, and no longer had faith in the scientific world to provide some greater truth. When he was back on the streets of Paris, he was little more than a shell.

Evariste found only one more use for his life – a sacrifice. He foresaw himself receiving acclaim for martyrdom. Filling out the stranger-than-fiction narrative of his life, at the time of his release from jail, his political group, the Societe des Amis du Peuple, had decided that it needed a funeral to stage a final, violent riot at. Since the first days of his political activism, Galois had been fascinated by the idea of self-sacrifice. He may have seen it as a way of re-uniting with his father, both in the afterlife and in their methods of dieing. The members of his party protested at first, but eventually they gave in. Evariste’s fame and notoriety would make him the perfect martyr for the cause – he was well known both because of his place in academics, and the publicity surrounding both of his court cases and his expulsion from school.

An intricate plot was crafted, which included Galois and others writing false documents such as letters and journal entries that suggested that Galois had no idea of his imminent death. Many of the writings actually suggested that his death might be the result of the tyranny of the Bourbons. His actual death was also planned out. He was to engage in a duel with another member of the Society, except he was to be holding a blank pistol. They would both march ten paces paces, turn, and fire. His opponent’s pistol, however, was actually loaded.

Galois feared death in that it was an ending to any of his earthly accomplishments. Because of this, he wrote a letter to his friend and confidant, Augustin Chevalier, within which he tried to summarize many of the thoughts that swam in his head regarding mathematics. The point of the letter was clear; Augustin was not a mathematician, and Galois mentioned nothing of the plot for his life. It was solely to preserve the ideas that Galois knew were important. What Galois did not know is that the very ideas he put down in that letter would be deciphered, studied, and lauded upon for well over 150 years. And so, like Jesus leaving the Garden of Gethsemane to be betrayed, Galois proceeded to the duel the next day and was killed. The attendees of his funeral numbered in the thousands, and the political atmosphere was saturated with tension. However, during his funeral, news of an important Napoleonic general’s death was passed around, and the Society agreed that the General’s funeral would be a better-publicized situation to rally around, and the party abandoned Galois’ funeral. His death had accomplished nothing – he was no martyr, he was an accident.