# Galois.

Another short title whose name I really admire the mathematical aspects.

On the previous post, we have talked about a sad tragedy on Math, Abel' story. Unfortunately, we have other tragedies on Math. If you think Abel was too young to die, don't cry now — it's time to talk about Évariste Galois (1811–1832). Yes, a brilliant mind who passed away by the age of 20.

[DISCLAIMER: Galois is one of the mathematical figures who I most appreciate works and life story. So I'll add some personal points on this post, the same way I did on Euler's and Kepler's). Once I was reading something about Group theory while studying the Rubik's cube and I ended up considering it brilliant. 'Hey, who was the genius who made this? Ah, this guy… Galois. Who's this person?' And I read his life story. WHY DID HE DIE SO YOUNG? :'( ].

Galois came from a well structured and wealth family. His father was the city major and his mother was a cult woman. Besides their life stability, Galois was frequently pointed as a 'bad student', 'rebel' and similar adjectives. He used to study in a conservative school, hardly opposing to conservative ideas from professors and friends. By that time, he started focusing on politcs. His first contact with math was by the age of 16, and the the subject started to make part of his life.

Galois started to live among his two passions: politics and math. He met the works of Cauchy, Gauss and Abel. His first article was written by the age of 17, about continued and periodic fractions. He submitted it to Paris, but again Cauchy totally ignored the works from the young Galois (by the way, Cauchy made it a lot of times, meaning that, if you had a short life, like Galois had, your submission had a chance to be forgotten forever on Cauchy's table).

Galois' father committed suicide in 1829. The fame of 'bad student' prevented him of getting a place into École Polytechnique and he saw himself forced to attend École Normale Supériore. Early on his first months at the institution, Galois wrote three articles, most about number theory. But they were lost and the young boy was totally ignored by academic community. Frustrated, he started to dedicate more to politics, since math seemed to have closed its eyes for his brilliant efforts.

We are talking about 1830, a year of many revolutions and rebellions in France. Due to his rebel fame, Galois was expelled of the institution. He then enlists to National Guard, who was declared illegal by France absolutist king, Louis Philippe. Interesting fact — Galois tries to share his mathematical knowledge with his political friends, but unfortunately the subject was too difficult and advanced for them (it was difficult even for the Academia). So Galois gave up on the idea of doing math with war colleagues.

It did not take too long to Galois be arrested as an order violator. However, the political euphoria did not stop the young mathematician to move forward on his group theory studies. He was arrested, tied, took a shot from a guard, etc, and KEPT DOING MATH. If a stomachache is enough to make you take a break of math, remind Galois' story.

In 1832, he leaves the prison and has a disagreement with friend because of a woman, Stéphanie-Fellice, which Galois was in love with. So they decided to solve the problem with a physical duel. Galois opponent was famous for succeeding at duels.

In the last night before the duel, Galois knew he should expect the worst. He spent his last hours writing about math and politics, finishing details about his group theory and running against the time that was left. The bad predictions consolidated — Galois lost the duel and passed away. There are some speculations about his death — some believe that the duel was a trap due to political reasons (the old story of government chases…). But there are no confirmations about that.

Galois' works are recognized only in 1895, with Sophus Lie publications, several years after his death. Galois group theory were the basis for modern abstract algebra of XX century. They have direct applications on geometry, crystallography and nuclear physics.

While Abel reached the edge of classic algebra, Galois came to give a kickstart on modern algebra. Two brilliant minds, two big tragedies for math. :(

But in very simple words, what's group theory? Well, in very simple simple example, try to imagine the roots of a equation as a set, not individually. These roots, inside a set, are what Galois called 'group'. (again, this is oversimplified explanation).

If you are willing to know more about Galois theory, I strongly recommend this book, by Dover publications:

Hope you have enjoyed this post!

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