The most awe inducing results during undergrad was Galois theory, but you need quite a bit of mechanics to be able to understand the proof. But what was the es

The most awe inducing results during undergrad was Galois theory, but you need quite a bit of mechanics to be able to understand the proof. But what was the essence of that awe? For me, when I had that special feeling, it came from the flash of insight of seeing that this thing is like that thing. It was seeing mappings and patterns, and I think this can be conveyed to the novice without having to show something as complex as Galois theory.