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.
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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.

The circle

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.

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.

For all young savants, excluding the unlucky exceptions, if the savant has outgrown its surroundings in its subject of choice (in our case, Evariste and mathematics), the savant is sent on to specialize. This is the law that we have used again and again to deal with brilliance. However, as first assumed, there are exceptions (divisors of zero?). Evariste was not accepted to study with French mathematicians at the Ecole Polytechnique, and was required to stay at the school that he outgrew.

As mathematicians, we must study the exceptions. We can define a group by its torsion elements, or defy an established conjecture with a single counter-example. We look at Evariste. Dejected, he studies with an excellent math instructor, Richard, and by the end of the year, he has written multiple papers! he has excelled again in school! he has been published! Was this maybe the most efficient way of getting from point A to point B (was this a geodesic? just what surface were we on anyway?)? But we must wait. If we had waited, we would not have made such ridiculous hypotheses (how dare we?). Evariste's published paper was useless, and his useful papers were just scrapped. Maybe you need to really break in, or maybe you just need luck?

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.

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.

Around this time, Evariste's father was the victim of a framing by the Bourbon government. They did not like having a liberal mayor within Paris, and so they planted rumors that exploded into scandal that resulted in Nicolas-Gabriel's abdication of the position and effective exile in another part of France. The shame of the affair troubled Nicolas-Gabriel, and soon after moving, he committed suicide in his home. The death left Evariste without a guardian, and broke up the Galois family's close ties.

To deal with growing expenses, Evariste applied for a grant to study at the Ecole Preparatoire, and was accepted. He did not excel at the school, but instead became very politically active.

He stayed at Louis-le-Grand for another year, this time studying mathematics with an extremely competent teacher. This teacher was able to recognize the brilliance of the young man. He encouraged Evariste, and Evariste responded by producing a multitude of contemporary mathematical research. He submitted it for review to the academy of sciences in France, but his work did not get reviewed. Galois was frustrated by the turn of events.

Evariste excelled in his new school. He graduated his first year the recipient of many academic prizes. He continued to succeed in school and ran into no trouble until he reached what was to be his final year at the school at the age of 15. The headmaster dictated that Evariste was too young to be considered for graduation, and so held him back in spite of his excellent academic record. While repeating the grade, Evariste seemed to discover mathematics. He adored the textbook that the teacher used, Elements de geometrie by Adrien-Marie Legendre. He read the book in two days time and immediately became consumed with the mystique of mathematics. After that, his academic work dropped in quality and he became a nuisance in class. His teachers began to dislike him and suggested that he dedicate himself and his talents to a mathematical school instead of one with a holistic education like Louis-le-Grand. He concurred, and applied for admission at the Ecole Polytechnique. His application was rejected.

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.