Others (mathematicians) can peer through the notation to the thing beneath. That's extremely difficult for me to do, and once I've done it I can see something interesting, but beautiful? No, that tree is intriguing but beautiful to me it ain't.

I’ve stumbled across bits of program code I’d call beautiful: simple, understandable, clearly correct, and… elegant. Win I find them, I experience the same feelings as when seeing a beautiful painting. My wife’s like “why are you smiling and laughing at words on the screen”, but it’s not the words, it’s what they’re saying and how they’re saying it.

That must be what a mathematician feels when they see a beautiful proof, or formula, or relation.