Galois group

A Galois group is a mathematical concept that describes the symmetries or transformations of solutions to a polynomial equation, like those with roots in algebra. Imagine it as a set of ways you can shuffle or rearrange the solutions without changing the equation’s fundamental structure. These symmetries help mathematicians understand whether certain equations can be solved using simple formulas and reveal deep connections between algebra, geometry, and number theory. In essence, the Galois group captures the inherent structure and relationships among the roots of an equation.