>How can I share that feeling inside my brain algebraically closed fields give me?
That's kinda like returning home after a long day, because algebraically closed fields are about the nicest structure you can hope to find yourself working in!
That's kinda like returning home after a long day, because algebraically closed fields are about the nicest structure you can hope to find yourself working in!
Personally I'd posit finitely generated abelian groups as the nicest structures. Perhaps there is also something to be said for finite algebraically closed fields.