I judge the beauty of math and code by the how concisely and simply they can model the object in question - if the math exists abstractly and isn't trying to model any actual thing or concept it isn't particularly beautiful to me because it isn't an accomplishment of expressiveness - it's instead just a coincidence that if you put some symbols together you only need those symbols.

There are, of course, times that concise expressions aren't possible and multiple strange and arbitrary values come into play (coefficients of friction or earth's gravity at sea level aren't particular nice numbers or expressions) and that just tends to highlight how beautiful things are when those icky real-world numbers can be canceled out and you're left with a clean expression.

To be beautiful it must first exist.

It’s far more difficult to come up with novel mathematics without some external inspiration.

  Are you as theoretical physicist interested in string theory? 

aint much of a Venn diagram on that one, only thing more circular is a non-rotating black hole, or a couple singular rotating points

This is really interesting to me. It could imply that an ugly theorem is less valuable. What if a theorem is ugly but useful vs a beautiful but esoteric one?

It doesn't matter. Constraints enable art, not the other way around.