Lucy Keer

Start with a field F, create an extension field E by adjoining some elements r_i. Now look at the automorphism group G(E/F).

(If everything is "nice") the subgroups of G(E/F) correspond to intermediate fields between E and F, depending on which r_i they stabilize.

Starting from G(C/R) gives an intuition I didn’t remember and may or may not have gotten at the time…

That doesn’t give an intermediate field; https://en.wikipedia.org/wiki/Fundamental_theorem_of_Galois_theory … uses Q(√2,√3) which is quite intuitive

That's the one I remember, but course was contextless 'bla bla splitting field bla solvable group bla'. Understanding something this time!

Also I followed my usual method earlier and looked up what John Baez had to say: http://math.ucr.edu/home/baez/week201.html …

he says that about everything though