Galois Theory

Galois Theory is a branch of mathematics that connects field theory and group theory, helping to understand the solutions of polynomial equations. Named after mathematician Évariste Galois, it reveals how the symmetries of the roots of an equation relate to the structure of the field of numbers they belong to. Essentially, it shows that some polynomial equations can be solved using radicals (like square roots), while others cannot, based on the properties of their roots. This theory is fundamental in understanding why certain equations, like quintics, cannot be solved with simple formulas.