synonymGalois (Galois) Generally refers to Ewalist Galois
Evariste Galois (October 25, 1811 May 31, 1832) was a French mathematician.Founder of group theory.The group theory is used to completely solve the problemRadicalsolvealgebraic equationAnd thus developed a whole set of theories on groups and fields, which people callGalois theoryAnd call the "group" created by itGalois group（Galois Group）。
The significance of Galois's research achievements in mathematics was not recognized by people. He once submitted three academic papers to the Academy of Sciences, which were returned or lost.He turned to politics and supported the Republican Party. He was arrested twice.He died in a duel in 1832.
One of the founders of modern group theory It is systematically expounded by group theory that equations of quintic and above cannot be solved by formulas Using group theory to solve two of the three major drawing problems in ancient times (trisection angle and multiple cube)
E variste Galois (October 25, 1811 May 31, 1832, French pronunciation eva ʀ ist galwa), a French mathematician, andNiels Henrik Abel And called the founder of modern group theory.He died young in a duel that was almost suicidal, which caused all kinds of speculation.[1]
Galois' parents are both intellectuals. Galois' mother is responsible for his education. His father was elected mayor of Bourg La Reine when Galois was 4 years old.
At the age of 12, Galois entered LouisRoyal High SchoolHe did well in school, but he didn't begin to learn mathematics with H.J. Vernier until he was 16 years old. His enthusiasm for mathematics exploded, and he could no longer raise any interest in other subjects.The school described Galois as "strange, strangeOriginalityAnd closed ".
Portrait of Galois in his youth.
In 1827, Galois confidently entered his ideal (academic and political) university: comprehensive engineering school, but was defeated because of the inept examiner.
In 1829, Galois put him in thealgebraic equationSubmit the result of the solution toFrench Academy of Sciences, byAugustin Louis Cauchy (Augustin Louis Cauchy) was responsible for reviewing, but Cauchy lost both the article and the abstract (two short-lived mathematical geniuses in the 19th centuryAbelBoth of them were "planted" in the hands of Cauchy).
What's worse, when Galois applied for the comprehensive examination for the second timeEngineering UniversityHis father committed suicide when he was maligned in the election.Just father's unjust death affects himFailed the exam, which also led to hisPolitical outlookAndoutlook on lifeMore extreme.
Galois entryNormal University(Ecole Normal Sup é rieure). The next year, he wrote three papers on the results of equation theory to win the mathematics award of the Academy of Sciences, but the papers were sent toJean Baptiste Joseph FourierAfter the death of Fourier, Galois had to watch the award fall to Abel andCarl Jacobi (Carl Jacobi).
1830July revolution It happened that the royalist forces died, and the president of the Normal University locked the students in the high wall, which caused Galois strong dissatisfaction.In December, Galois denounced the principal's practice in the school newspaper and was expelled from the school.Due to strong supportRepublicanismAfter May 1831, Galois was imprisoned twice for political reasons, and he also tried to commit suicide.In prison, Galois is still tenaciousMathematical research, while modifying hisEquation theoryHe wrote a preface to the book to be published.
It is said that in March 1832, he met a doctor's daughter in prison and fell in love. Because of this relationship, he fell into a duel,[1]Galois, who knew he would die, wrote down all his mathematical achievements in a crazy book on the night before the duel, and wrote "I have no time" from time to time. The next day he died in the duel, on May 31, 1832.This legend is richromanticismColor was questioned by later historians.
On the night before his death, Galois was still working hard to sum up his academic thoughts, sort out and summarize his mathematical work.He hopes that one day his research results will be known to the world.
A portrait painted by Galois's brother in memory of Galois.[2]
His friend August Chevalier followed Galois's will and sent his mathematical paper toJohann Carl Friedrich Gauss Compared with Karl Jacobi, they were lost until 1843Liouville He affirmed the correctness, originality and profundity of Galois's result, and published it in 1846.
Personal achievements
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Galois used the idea of group theory to discussequationOfSolvabilityThe whole set of ideas is now called Galois theory, which is one of the basic pillars of contemporary algebra and number theory.Its direct inference results are very rich:
He systematically explained why there is no formula solution for equations of more than five degrees, and there is a formula solution for equations of less than four degrees.
