Geometry and mechanics are beautiful to me, but even many mechanics problems are more elegantly using the methods taught in physics over those taught in maths (

Geometry and mechanics are beautiful to me, but even many mechanics problems are more elegantly using the methods taught in physics over those taught in maths (mechanics), simply because you if you use the right derivatives or logarithms to start with (e.g. energy instead of speed, decibels instead of absolute power) then you often avoid having to touch calculus, logarithms etc entirely. The beauty in maths for me has always been in finding ways to use it only to the extent that it makes unintuitive problems more intuitive. Math for maths sake isn't intrinsically beautiful, because for most of us it's more like having all the cheat codes to a game when the levels are too hard than figuring out how to play.