Galois theory (second lecture)

We continue our historical introduction to the ideas of Galois and others on the fundamental problem of how to solve polynomial equations. In this video we focus on Galois’ insights into how extending our field of coefficients, typically by introducing some radicals, the symmetries of the roots diminishes. We get a correspondence between a descending chain of groups of symmetries, and an increasing chain of fields of coefficients. This was the key that allowed Galois to see why some equations were solvable