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Évariste Galois (October 25, 1811 - May 31, 1832) was a French social activist and mathematician. In his teens, Galois discovered the necessary and sufficient conditions for determining whether a higher polynomial of degree 5 or higher, which had long been a difficult problem in mathematics, could be expressed as a solution of repeated square roots. Through this process, Galois was the first to use the term group (French: groupe), which refers to a method of grouping a sequence according to a specific mathematical condition. Galois's research became the basis for Galois theory and group theory, which are major fields of abstract algebra, and also became the theoretical basis for the subfield Galois connection. At that time, France was a monarchy with Louis Philippe I as king, and Galois was a radical republican who opposed this. Galois, who fell in love, was shot in the abdomen in a duel at the age of 21, ending his short life. #Mathematics #Equation #Algebra