The concept of group comes from the study of polynomial equations (in short, solving multiple equations);

In ancient Babylonian mathematics and Indian mathematics, people can use roots to solve a quadratic equation (what is a root solution, see the following supplement).

Then the ancient Greeks and ancient orientals solved some special cubic numerical equations, but did not get the general solution of cubic equations (this problem was not solved by the Italians until the heyday of the Renaissance).

During the Renaissance, Ferrari in Italy solved the general quartic equation X 4+AX 3+BX 2+CX+D = 0, and used the quartic function of the coefficient to find the root.

In the following centuries, the general solutions of quintic and above equations have not been obtained.

1770 or so, the French mathematician Lagrange proposed that the permutation and substitution theory of equation roots is the key to solving algebraic equations, which promoted the progress of algebraic equation theory. However, this method cannot give the root solution of the general quintic equation.

Subsequently, the Norwegian mathematician Abel proved that quadratic, cubic and quartic equations in one variable all have root formulas, but the general quintic equation does not have root formulas, and proved that the general algebraic equation higher than quartic has no general algebraic solution.

Abel solved the problem of constructing algebraic solvable equations of any degree. Some ideas of groups have been involved in the research, but Abel failed to realize them.

Under this background, French mathematician Galois put forward the concept of group, and thoroughly solved the problem of solving algebraic equations with roots by group theory.

Author: CSDN blogger Li Qingyan.