I suppose one could say that mathematics is an of interpretation of reality, especially if one subscribes to the idea that the "fundamental reality" is ultimately unknowable due to our human limitations, but again, the intent is to represent something in such a way that it is independently verifiable by other agents.

As for beauty, I don't think that beauty is necessary for art. I certainly think that a lot of art deals with beauty, but just as much has been created that revels in the ugliness of things, or in some other aspect, which I understand that people often characterize as "beauty". Personally though, I think that particular word works against art of all stripes because by and large, the casual consumers of art tend not to understand the difference between "beautiful" and "pretty." Similarly, most approach the arts with an expectation, not of enjoyment, but entertainment. For example, I might enjoy feeling a particular sadness or feeling a well-crafted loathing for something-- that is, I don't always look for artistic experiences that will leave me feeling good about what I've just experienced, if that makes sense.