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.

Negatively sloped line

Evariste Galois was born on October 25th, 1811. He had a mother, a father, a sister, and he soon would have a brother. He lived in Bourg-la-Reine in Paris. Bourg-la-Reine was a very political commune that was adamantly against the monarchy. His father was one of the leaders of this opposition movement, and he became mayor soon after Evariste was born.

When Evariste was ten years old, his parents decided that he would benefit from attending school away from home. He took an admissions test for a youth college in Reims, and was accepted with a partial grant. His parents then decided to keep him home for two more years. After those two years, he was deemed fit to go to school away from home. He gained admittance into a more prestigious school, the Lycee Louis-le-Grand, and became one of the youngest attendees in his grade at age 12.

At the boarding school, children awoke at 5:30 AM. The first order of the day was to wash, and they washed in the only large water-source within school grounds - the outdoor courtyard fountain. Before eating, they were forced to study for the next two hours. They were then fed a meager breakfast of bread and water. At around 8:00 AM, the non-boarding students arrived, and real class began. It continued until around midday, at which point the boys were allowed to break for lunch. Lunch consisted of gruel mixed in with fat, some form of protein in the form of fish or meat, and vegetables. There was no concern with taste. The school administrators believed that a lack of luxuries such as tasty food would harden the boys and make them more efficient workers in whatever their eventual profession was to be. The children were then allowed a brief recess period. The only activities that were allowed were walking and talking quietly. After recess, there were more classes until 6:00 PM. At that point, the non-boarding students went home, but the boarders were subject to an hour and a half of church time.

The students did not like the school. It was always very dark. In the classrooms, there were only enough candles for two children to share one, and a heating stove made it smoky and difficult to see. The instructors would lecture down at the students, where they sat not at desks but on the steps in the room. Disciplinary actions were swift and brutal; unruly students would be placed in a cell for days at a time. On one occasion, when Evariste had just joined the school, a banquet was held to celebrate the prowess of the best 75 students at the school. They were subdued in private protest of the actions of the school, and for that they were all immediately expelled.

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.

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.

As is the case with exceptions (and also really good stories), the unusual is drawn to the unusual. Success begets tragedy; excellence breeds a Pandora 's Box full of mistakes. Evariste loses his father because of political beliefs to an exceptional death of suicide; this act sheds light on Evariste and his family life. Honor overpowers shame, and the plight of the liberals runs strong within his blood. The death of his father profoundly affects Evariste. He is transformed into a bitter, sad creature that most resembles an adult. He no longer has the characteristics of a child, unusual for a child of only seventeen - there is no role model in his family, and from this point on, he has no leisure. It is quite the contrast to his beginnings. Thus, we can conclude that suicide has a negative effect on the child of the deceased.

However, Evariste's problems may also have arisen from academic reasons. He again applied to go to an elite mathematics school, and again he was rejected. It appears as if he is simply not a member of the domain of the school - he does not seem to fit the criteria to be solved by radicals

In response, the man (no longer boy) joins another school, with less rigorous domain restrictions. It changes him drastically - he entered as a mathematician, and exited as a politician. There are many factors that could have caused that. He may have inherited his political incline from his father; it is completely evident that a child of a politician, and an oppositionist politician at that, will inherit some interest in the subject, whether out of admiration or out of deference. However, the conspicuous transformation he goes under may have been caused by his father's politically motivated suicide, a powerful gesture. The man may also have become sick of mathematics - it did not treat him well. Often, people may defect from their original line of interest if it does not reciprocate on effort, and they will find something that will. It is called trial and error.

Through mathematical analysis, we deduce that all elements of the Ecole Preparatoire are destined too be involved politically. Due to the classification of the Evariste element, it becomes intrinsic in rebellious activity.