What is the square root of two? | The Fundamental Theorem of Galois Theory

This video is an introduction to Galois Theory, which spells out a beautiful correspondence between fields and their symmetry groups. __ SOURCES and REFERENCES for Further Reading! This video is a quick-and-dirty introduction to Galois theory. But as with any quick introduction, there are details that I gloss over for the sake of brevity. To learn these details rigorously, I’ve listed a few resources down below. (a) Galois Theory Galois Theory notes by Tom Leinster: These notes are by far the best resource out there for learning the subject. They’re completely rigorous, but they’re also written in a very reader-friendly way with lots of examples and motivation. (See link here: ~tl/gt/) This playlist on Galois Theory by Professor Richard Borcherds is a gem. It explains Galois Theory from the ground up, rigorously, in almost complete generality. (