Évariste Galois
Thomas Cayne, Storyteller. Anthropologist. Naturalist. Madman.
Updated Dec 16, 2018 · Upvoted by Philip Whan, Major History Buff and Hugh Weller-Lewis, MA Literature & Social Sciences, The Open University (1991)
In 1832, a young man aged 20 died after an obscure duel. In the few writings that he left and in his final letter which he composed in the night before the duel, he laid the foundations of a number of theories which totally changed Mathematics.
His name was Évariste Galois.
The genius emerges
Already at a very young age, Galois showed his exceptional talent at various occasions.
He found a copy of Adrien-Marie Legendre's Éléments de Géométrie, which, it is said, he read "like a novel" and mastered at the first reading. At 15, he was reading the original papers of Joseph-Louis Lagrange, such as the Réflexions sur la résolution algébrique des équations which likely motivated his later work on equation theory, and Leçons sur le calcul des fonctions, work intended for professional mathematicians, yet his classwork remained uninspired, and his teachers accused him of affecting ambition and originality in a negative way.[1]
Later Galois tried to enter the prestigious École Polytechnique at several occasions, but it never worked out:
On 28 July 1829, Galois' father committed suicide after a bitter political dispute with the village priest. A couple of days later, Galois made his second and last attempt to enter the Polytechnique, and failed yet again. It is undisputed that Galois was more than qualified; however, accounts differ on why he failed. More plausible accounts state that Galois made too many logical leaps and baffled the incompetent examiner, which enraged Galois. The recent death of his father may have also influenced his behavior.[2][3]
His novel take on Mathematics indeed further obstructed his tries to be a part of professional mathematical life at many points in his short life.
For example, one of the best and famous scientists of the day, Siméon Denis Poisson, found Galois’s manuscript on equations unreadable, and this was a common feeling mathematicians had when they browsed through a text of Galois.
The Mathematics appeared to come from another planet, displaying techniques so novel that the world in the 1800s simply was not ready to capture.
Even today, if one reads proofs and ideas by Galois, one is stunned by the level and originality of his writings. In this modern era of Mathematics which has so much evolved in comparison to Mathematics before 1900, the proofs are ingenious, and breath taking.
(And then thinking the guy was in his late teens when he composed the ideas, while being actively involved in the revolution, in the 1830s!)
This is not the place to summarize Galois’s ideas, even in a nutshell, but let me say that he almost single-handedly founded Group Theory and Galois theory — two of the most important topics in modern day Mathematics.
While still in his late teens, he solved one of the holy grails in Mathematics, by obtaining necessary and sufficient conditions for a polynomial to be solvable by radicals.
This problem stood for 350 years before Galois (and, independently Niels Henrik Abel) came along !
Revolution
Galois’s life was characterized by revolution. Besides his uncanny futuristic Mathematics, he was involved in protests, and sometimes incarcerated. (He also wanted to participate in the July revolution of 1830, but was prevented by the director of his school.)
On the following Bastille Day (14 July 1831), Galois was at the head of a protest, wearing the uniform of the disbanded artillery, and came heavily armed with several pistols, a rifle, and a dagger. He was again arrested. On 23 October, he was sentenced to six months in prison for illegally wearing a uniform. He was released on 29 April 1832. During his imprisonment, he continued developing his mathematical ideas.[4][5][6]
About a girl
His fatal duel took place on May 30, 1832. It is not sure what the motives were, but it has often been speculated that a love affair lay at its origins. (Some days before his death, he wrote a letter to his friend Chevalier about a broken love affair.) I also read that the duel was the outcome of a fight over a prostitute. We will perhaps never know for sure.
In any case, his opponent was a better shooter, and Galois was fatally wounded. He was found by a passing farmer. (His "second" seems to have just walked away, leaving him to die.)
The next morning he died.
Galois knew that this was going to happen, so he decided to spend the night before the duel writing down his (final) mathematical ideas in a letter which he sent to his friend Chevalier, together with three attached manuscripts.
The great mathematician, physicist and philosopher Hermann Weyl said of this testament:[7]
"This letter, if judged by the novelty and profundity of ideas it contains, is perhaps the most substantial piece of writing in the whole literature of mankind."
Clearly, this is a bold statement of Weyl, but nevertheless, I think it is also clear that Évariste Galois deserves to be officially nominated for the title of smartest mind ever.
It is almost scary to imagine what could have happened to Mathematics (and Science) if he would have lived for another 40 years.
Footnotes
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