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 6

As with many great ageless stories, this one begins with a birth. The mayor of a section of Paris was granted a beautiful baby boy on a cold winter night. As his existence sparked, the neighborhood was consumed in celebration and exaltation to the extent that can only be inspired by the miracle of life and other such inexplicable, paradoxically confusing natural occurrences. The morning was bright, cold, and necessary. A woman screamed, and a man rejoiced as Evariste Galois came into being.

The French aristocratic childhood was composed of many luxuries. A child was strictly concerned with leisure, and the delicacies of youth were preserved as if by curators, protecting a precious painting or something similar that can only be destroyed, not enhanced, by atmospheric influences. A child may be lured into thinking that the world can only be composed of happiness; the phrase “the lesser of two evils” could hardly be fathomable.

“Dear, whatever shall we do with young Evariste?” the young bride questioned her husband.

“He will only have the finest education,” Nicolas answered. “My son must learn; he is so bright already. Have you heard his poetry? It is flawless. We’re holding him back at home.”

“But he is of such tender age. And he is so small; just yesterday he was walking side-by-side with me and his tiny legs were straining to leap to my pace.”

“We’ll see. He is a thinker. Thinkers think so they need not walk. It is their purpose; it is their identity.”

“I just desire that he is not the minimal element of his group –“

“I just desire that he is happy, more than anything. He has to be allowed to stay young. I know we want to see him grow, and he is growing so quickly. But he should stay young, stay young as long as he can.”

The husband and wife continued to discuss, but ultimately, the boy was to go to school.

“But mother, it seems so cold, so quiet yet so loud in that place. I don’t like it, not at all.”

“We’ve decided it’s for the best. You must attend school; it is necessary to make you grow up, like your father! (like your mother).”

When a child excels in school, it is not necessarily a good thing. It is tough to be separated from peers, and it is even tougher to have a reputation to live up to. And the greatest curse, for a precocious child like Evariste, may be that it is difficult to have a higher perception of any subject you study than those around you. Evariste was younger, Evariste was smarter, Evariste was smaller, Evariste was sharper. He did fine, but did he succeed? (did he?) Eventually he was held back, but it was out of jealousy. “We cannot loft him above the other students – it is against our rules! We shall say that he is not mature enough, or we will call into doubt his studies, but either way we won’t let him reach so far so early.” And so Evariste was made to repeat his fourth year. School became a cyclic subset of his experience, with a period equal to …

Sometimes repetition is good; we may learn things through induction, or by continuous iteration of an action. One way is that we may notice new aspects, different views of the same shape or path. On just his second walk-through of the penultimate year of his school, Evariste discovered something rather startling to newcomers – the elegant world of mathematics. Evariste was taught by the brilliant Legendre, “bit by the bug,” and his life was changed forever. We must ask the question – if Evariste was never introduced to Legendre, if Evariste was not a victim of the injustice that kept him back a year, where would he have ended up? Would he have been a politician, like his father? Would he have gotten into classics, like his mother? Was he an exception to the function of life, a defined discontinuity, or was he a constant – no matter what we plug into his life, he was to be a mathematician. However, these aims are rhetorical at best – we must wait to see if any light is shed on the topic in the future.

The boy read and read and read and read. Eventually, he finished. We may be able to better understand the boy if we imagine he is reading a comic book, or a youthful science fiction novel, and then we believe that he is reading a mathematical text containing incredibly complex notions. Legendre, the 74-year-old brilliant, accomplished, established mathematical leader and Galois, the 15-year-old brilliant, fresh, green academic, held long, sometimes intense discussions by candlelight in the book Éléments de géométrie in the cold dormitory of the Lycee Louis-le-Grand, but Galois was finished after two days, and he needed more.

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?

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.

Either way, the man met politicians and not mathematicians and he became a politician. It seems as if it is feasible to conclude something about that. However, there is still some exception to him. His politics made him famous and infamous when he criticized the headmaster of the school and was subsequently kicked out. This streak of rash behavior without knowledge of the consequences continues in him for the rest of his life, but is it just naivety? Unfortunately, not enough data was gathered to draw a conclusion with any amount of accuracy.

Evariste was put on trial for his political leanings and his bombastic personality twice, and the second time he was sent to jail. There he found similar elements, and he formed a subgroup. They were all likeminded politically, and adding or subtracting one opinion here or there from another just produced another opinion that was held by someone else in the group.

At this point the now-man fell in love with a girl named Stephanie. This we cannot ignore. It is an isolated incident in his life; nowhere else do we have record of him worrying about the opposite sex. Yet, in his brief exchange with Stephanie, through at least letters, he becomes consumed with her. This is an example of the exceptional functions of life – love seems to defy any other precedent set. It is also important to note that Stephanie turns him down – is our Evariste destined to fail at all that he wishes for?

Evidently depressed, with very little magnitude, Evariste left jail a fraction of what he had been before. For this, he offered himself as an element of catalyst for his political beliefs. We can classify him as a martyr (he died, if you care, in a fixed duel in which the pistol he held was not even loaded with bullets). However, he was not a catalyst – he failed in ending his own life for a purpose. Maybe it was what he wanted, though – he may have had a romanticized idea of suicide from his father. Evariste, at the conclusion of his life, degenerated, and disappeared. However, later studies and academics revealed him as the generator for all that we can study in algebra (and this whole thing, too!).