Hi. It’s been a while, hasn’t it? Let’s get back into it. Today we’re gonna be talking about a mathematician by the name of Évariste Galois

You might be wondering why the portrait I chose is one of Galois when he was a mere teenager. Well, that’s because he was shot and killed when he was 20. So, there’s really not that much in terms of older pictures.

Oh yeah, did I mention that he helped develop an entirely new field of mathematics through a few scribbled letters shortly before he rushed to a duel? Yeah.

The majority of this article will be pulled from “Evariste Galois 1811–1832” by Laura Rigatelli which I highly recommend.

Beginnings

Galois’s brilliance was certainly not foreign within his family. His mother Adelaide-Marie had been well educated by her father and an excellent scholar in Latin. His father Nicolas-Gabriel Galois was a playwright popular in the salons for his witty verse and cleverness. And so on the 25th of October, 1811 Evariste Galois was born. Adelaide’s previous education experience had caused her to expect only the best of her sons.

So at the age of 12 Evariste Galois bid farewell to his family as he traveled to the Lycée Louis-le-Grand. For those of you unfamiliar with the French educational system, picture the Lycée Louis-le-Grand as the Eton College or Phillips Academy of France. Founded in 1560, only educational institution to remain open during the Revolution, literally bore a King’s name yada yada.

The point being is that this place was an absolute fire hose of politics

Aside from all the politics, it operated how you might expect a stereotypical “hard” school to do so. 5:30 AM wakeup times, food that consisted of water and gruel, recreation periods which literally did not allow you to run and did I mention they could throw you in cells. Yeah, just straight up prison cells where you were kept in damp rooms without any light for doing such awful things like talking during compulsory silence or fidgeting in bed.

Anyway I would like to mention that perhaps only a few weeks after Galois arrived at the school they held a customary banquet for the teaching staff and best students. When the headmaster raised his glass for the traditional toast, as an act of protest all the pupils laughed in unison at him.

So with the expulsion of 75 of the best students in the school, Galois was able to cruise his way to winning basically every prize offered by the school in the next few years. The damp rooms, occasional punishment stints, and strict discipline wore down the young student though as did the politics of a new headmaster stubbornly against him.

Hello, math.

It was there that the 15 year old took a keen interest in mathematics, reading Elements de geometrie by the legendary mathematician Adiren-Marie Legendre. A book that was intended to cover two years of material was read in a month by Galois and from that point on he was hooked.

What happened is exactly what you expect. Constant disinterest in all other subjects, bizarre character, and generally bad conduct all led to constant punishment. But Galois didn’t care. He had higher ambitions anyway.

The Ecole Polytechnique had become the symbol of the new scientific attitude in France, with a focus on pure research, demanding entrance examination and a student body filled with men calling for “science and glory.” It still remains a prominent institute for engineering in Europe.

So as you can expect, Galois desperately wanted to attend the school. He prepared himself, studied hard and

failed the entrance exam.

He decided to try it again the next year. He returned back to the Lycee Louis-le-Grand and for once found a true mentor in Louis-Paul-Emile Richard. His class emphasized refined mathematical language, contemporary research developments, and building real connections with his students. Richard instantly saw the young Galois as being far and away above everybody else in the class and encouraged him to continue building his mathematical knowledge outside the classroom. It was Richard who helped Galois get published through his friend Joseph Gergonne. It was a decent paper, nothing revolutionary but polished and well.

That spring of 1829 was Galois’s blossoming. He had moved from simply learning mathematical concepts to beginning to advance them, all with the help of Richard. Richard once again forwarded Galois’s careers by submitting the two research papers that Galois had written to the Academy of Sciences, the highest body of science in France. Richard himself presented Galois’s work to perhaps the greatest mathematician in France Augustin-Louis Cauchy.

Cauchy was a difficult, egotistical, and mean person to work with. He had never before presented anybody else’s research in his nearly 13 years since becoming a member of the Academy. So when he himself presented Galois’s two papers to the Academy, it was an indication of the revolutionary methods that Galois at the age of 17 had already discovered.

Setbacks and Tragedy

Unfortunately, Galois received a setback, getting a fourth place at the Concours general, basically a big academic competition in France. His solution was too weird.

The real tragedy came in 1829. Galois’s father had been the mayor of his village since the return of Louis XVII and by all accounts was quite well-liked. However, when Charles X took the throne and emphasized the restoration of the church’s power, the very existence of a liberal mayor like Nicolas-Gabriel Galois was a threat. A plot soon arose to sink him from power. The young priest in charge of the area and a local group spread vulgar writings allegedly written by him. He was forced to flee the village and committed suicide soon after. The mayor’s death was met with grief all around and the priest responsible was pelted with stones after arriving at the funeral service.

I do want to touch on how beautiful the funeral epitaph that they gave him was.

In the same month, another event would further shake the grief-filled Galois. He had prepared for a year to try and gain acceptance into the Ecole Polytechnique once again.

He failed.

Certainly not because of his own lack of intelligence but what had always been the case throughout his life. The people testing him simply could not comprehend his brilliance. Instead of sticking to traditional ideas and textbooks when asked to describe logarithms by his examiners, Galois deviated and the administrators criticized him for it. This scolding ended in him throwing a blackboard eraser at them. Needless to say, he got a little frustrated.

So now, no more Ecole Polytechnique for him. One could only take the test twice. Faced with poor finances and the need for security Galois was forced to try and attend the Ecole Prèparatoire. Essentially a teacher’s college, though still one that had produced some notable scholars.

Once again Richard bailed out Galois by finding him a way to still submit an application to take the entrance exam through the last date had passed.

Don’t think that he was just able to breeze into getting in though. Even though he had passed the entrance exam, he still needed to get a baccalaureate in arts and sciences as well as do the oral exam. For those not familiar, a baccalaureate is kind of like a job certificate but for academic topics.

Remember when I said that Galois basically didn’t care about anything other than math? It nearly sunk his entrance to Ecole Prèparatoire as a result. He failed his art exam, but somehow still got accepted based on his pretty bad literary work to get his baccalaureate in arts. His oral examination in mathematics was so good that it excused his physics exam that he had essentially gotten nothing right on.

Oh well. He got in. His fate had now been tied to teaching for at least ten years with the pledge he signed.

Remember Cauchy and his interest in Galois’s manuscripts? The closest he got to actually discussing Galois’s works was when he told the President of the Academy to put the Galois report on the agenda for the next week. When he actually showed up the next week, he forgot all about that report and instead talked about his own work. Whoops.

Anyway back to the Ecole Prèparatoire. It was more of the same. Galois suffered from a mix of triumphant successes and horrendous failures. He continued to be a math-only person and barely studied anything else. Galois submitted a paper for a national math competition and Galois excitedly submitted one of his previous works to the Academy. Yet in typical Galois fashion one of the board members took it home, died and the paper was never found. And so Galois was excluded from the competition while of course not knowing about the whole situation.

On the bright side, he got some more articles published in a scientific journal! Alongside figures like Cauchy!

He also made some friends! One of those, Auguste Chevalier would end up being a significant influence in his future political life. Speaking of politics…..

1830

There are a lot of things that happened in France at the time, but I’ll make it simple. Charles X refused to step down and suspended freedom of the press, and everybody got mad and rioted. The ones at heads of the protests were a group of four students from the Ecole Polytechnique, literally taking rapiers from the fencing room to use.

Those four lead the charge and rallied people around the city. Galois was watching from a nearby window with a miserable eye as the students of the Ecole Prèparatoire were expressly forbidden from leaving. Oh well. It wouldn’t stop Galois from trying. He attempted to break out of the building several times desperate to get involved in the rallies. He couldn’t get out, but it was a sign of what was to come.

After all that though, the most that happened was the coronation of a new king Louis Phillipe to take over Charles X’s throne. Galois’s experience watching the revolution changed him. When he returned to his family he was noticeably bolder with powerful speeches calling for an uprising. Shortly after he found himself in a group of like-minded young republicans all soon to become some of the most influential over the next century. They all together joined the Friends of the People, a society consisting of the most ardent republicans in the party. They were unafraid of public debates, propaganda, and most importantly violent revolt. The society had initially been a public organization but was quickly forced to dive underground after a court suppression.

Galois soon found himself clashing with the new leadership of the Ecole Normale Victor Cousin. This enabled the previous administrator Guigniault to enact his policy of a “good student should not be interested in politics” which obviously clashed with Galois’s now revolutionary ideas. Galois dove into constant criticism of the schools’ regime. Despite punishments of isolation and not even being allowed to leave the building, Galois continued to bombard Guigniault with insults.

The final straw came soon. An anonymous letter in a school newspaper tore apart both Cousins and Guigniault outlining all of their sins. When confronted with the letter Galois simply shrugged and gave no indication as to whether he had written it or not. And so at last after a supposed confession by Galois to Guignault, he was expelled. Nobody defended him, not even his fellow students. The most they did was not completely align with Guigniault.

Galois didn’t care though. He had never really enjoyed the Ecole Normale anyway and nobody in the school at that point had been particularly fond of him. However that didn’t mean he didn’t want to get the last word in. In a final published appeal, he called on the students at the Ecole to “speak out for your own honor and according to conscience”

A Political Firebrand.

Now that Galois was out of school, he could be as inflammatory as he wanted. With the National Guard, unfortunately, being forced to disband by Louis Phillipe shortly after he joined Galois turned to letter writing and publications. He started with a letter published in the Gazette des Ecoles slamming the teaching of mathematics in schools, book publishers, and of course entrance exams.

Galois needed money of course, so what better than giving math lessons? These certainly weren’t normal math lessons though, this was more like a presentation of new mathematical concepts and theoretical research that he had done.

For the first session of his course, over 40 people showed up to listen.

The course ended up completely failing. It turns out that when all your friends are political activists supercharged advanced mathematics may be slightly alienating. Oh well. Galois resigned himself to boring tutoring lessons and occasionally attended Academy lectures to become more in tune with the latest developments of the time. There he continued his habit of being brilliant but rude.

The trouble continued when Galois got arrested. After a great legal victory the Friends of the People held a nice celebration banquet. At that banquet Galois toasted Louis-Phillipe with a cup of wine in one hand and a knife in the other hand, a gesture repeated by many of the other guests. Needless to say he was arrested the next day for making a threat against the King. Whoops!

Under lock and key! I am responsible for that gesture but don’t chide me, because the wine made me lose my head

Letter from Galois to his friend Auguste Chevalier while in jail.

The Trial of Evariste Galois

Galois, not exactly known for his delicate words bluntly said at his trial that he had done it. However, he claimed that he had added the word “if he betrays us” to soften the blow. He used the stand as a soapbox against Louis-Phillipe to “doubt his good faith.” The trial as a whole was a mess. Witnesses were unable to fully assert what they had heard, the journalists barred from courtroom access made constant noise outside and contradictions lay all around.

After a wave of defiant and confused witnesses, Galois had the chance to speak. Shockingly enough, Galois was temperamental and rebellious calling the men of the restoration “children” and outright daring them to execute him. The judge thankfully cut him off.

The trial from a legal perspective is actually somewhat interesting so I will go into it slightly. Witnesses such as M. Petit and M. Delair all heard ruckus and noise but neither were able to fully ascertain both the brandishing of the knife and the speaking of the words at the same time. The waiters all claimed to have heard only mild political chatter. On the other hand the butcher Guèret claimed to have not only heard the “Long Live the Republic!” phrase but also to have heard somebody shout for the guillotine for Louis-Phillipe. Unsurprising to anyone who has made it this far, Galois called him an idiot loudly in court.

Lecomite, Souillard, Billard and several other witnesses all concurred with each other that Galois’s remarks had provoked heavy applause from the audience. Hubert and Raspail all advocated for Galois and claimed they were not intended to provoke a reaction. Gustave Drouineau straight up refused to testify as he felt it out of line to discuss what happened at a private banquet and was fined as a result.

Despite the banquet being private, the public prosecutor claimed it to be in theory public because several witnesses were able to hear the meeting from the outside thus making the meeting public. After all previous precedent established that places like restaurants and hotels were public.

Interestingly enough the Chevalier brothers ended up writing an article in a newspaper about Galois condemning his violent acts but defending him as a scientific and mathematical genius. Galois had continued complaining of the lack of recognition which he was receiving for his mathematical talents. So with his newfound notoriety why not also advocate for his scientific skills?

On the bright side, Lacroix and Poisson finally got around to examining Galois’s work! On the negative side, they straight-up did not understand it in the slightest and so gave it an awful review. Their report was genuinely factually wrong and unable to understand the revolutionary methods that were brought forth by Galois.

Despite all his antics, the jury emerged with the verdict of not guilty. Galois was silent for a while when he heard it, then picked up the knife and walked off.

So, what was the future to come for Galois now that he was free? Guess we’ll find out in Part 2! See you then!