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Ask AI3: What is Galois?
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His work laid the foundations for Galois theory and group theory, two major branches of abstract algebra, and the subfield of Galois connections.
Galois was born on 25 October 1811 to Nicolas-Gabriel Galois and Adélaïde-Marie ( born Demante ).
At the age of 10, Galois was offered a place at the college of Reims, but his mother preferred to keep him at home.
In October 1823, he entered the Lycée Louis-le-Grand, and despite some turmoil in the school at the beginning of the term ( when about a hundred students were expelled ), Galois managed to perform well for the first two years, obtaining the first prize in Latin.
However, in spite of many claims to the contrary, it is widely held that Cauchy recognized the importance of Galois ' work, and that he merely suggested combining the two papers into one in order to enter it in the competition for the Academy's Grand Prize in Mathematics.
Cauchy, an eminent mathematician of the time, considered Galois ' work to be a likely winner.
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.
Having been denied admission to the Polytechnique, Galois took the Baccalaureate examinations in order to enter the École Normale.
Despite the lost memoir, Galois published three papers that year, one of which laid the foundations for Galois theory.
Galois lived during a time of political turmoil in France.
While their counterparts at Polytechnique were making history in the streets during les Trois Glorieuses, Galois and all the other students at the École Normale were locked in by the school's director.
Galois was incensed and wrote a blistering letter criticizing the director, which he submitted to the Gazette des Écoles, signing the letter with his full name.
Although the Gazettes editor omitted the signature for publication, Galois was expelled.
Although his expulsion would have formally taken effect on 4 January 1831, Galois quit school immediately and joined the staunchly Republican artillery unit of the National Guard.
Due to controversy surrounding the unit, soon after Galois became a member, on 31 December 1830, the artillery of the National Guard was disbanded out of fear that they might destabilize the government.
At around the same time, nineteen officers of Galois ' former unit were arrested and charged with conspiracy to overthrow the government.
The proceedings grew riotous, and Galois proposed a toast to King Louis-Philippe with a dagger above his cup, which was interpreted as a threat against the king's life.
On the following Bastille Day, 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.
The Galois memorial in the cemetery of Bourg-la-Reine.
Évariste Galois was buried in a common grave and the exact location is still unknown.

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