Galois

Galois theory is a branch of mathematics that investigates the solutions of polynomial equations and how their roots relate to symmetry. It helps determine whether equations like quadratics, cubics, and quartics can be solved using basic algebra or require more complex methods. By examining the symmetries and permutations of roots, Galois developed criteria to understand the solvability of equations and the structure of their solutions. Overall, it links the concept of symmetry to the fundamental properties of equations, providing deep insights into algebraic structures and solving problems about what kinds of solutions are possible.