This statement is just wrong. I will fix it. (The correct statement is that there's a group acting on the solutions called the Galois group; it's the solutions that are being permuted.)

by Qiaochu Yuan May 25 2016 updated May 25 2016

This statement is just wrong. I will fix it. (The correct statement is that there's a group acting on the solutions called the Galois group; it's the solutions that are being permuted.)