I understand what you say. But my interest is actually into AI, so the same way you find pleasure in creating and understanding interesting proofs, I find pleasure in trying to think about how the human mind works and how to make artificial forms of intelligence that share the properties of human mind but not the damn limitations of the "biological hardware" and of mortality. And I also think that in fields like AI "proof by engineering" is the only way to move forward - we'll have to build them or 'evolve them' in order to prove that they can be built (I know, this is not a line of thinking that mathematicians enjoy :) )

I'd love to see AI evolving to the level at which they create art and music or analogues of these (for their own pleasure and maybe for that of humans too, if the pleasures are compatible).

I know, you'd have to share my belief that strong AI is possible (and really close too I think) and that that minds are nothing but machines themselves and that all forms of intelligence will be comparable, regardless of whether the hardware will be "biology" or "technology", "natural" or "artificial" (in a few hundreds years I think we'll even cease to make the difference between these concepts, they will appear synonyms to our non-human or not-so-human-anymore descendents, just some linguists will identify different etymologies of them) :)