DD, what's this thing you have for "demonstrability"? I can demonstrate objectively that 1 mL of hydrochloric acid will neutralize 1 mL of sodium hydroxide, but that fact is not nearly as important to me as the unquantifiable sense of pleasure I get from listening to John Mississippi Hurt.
Your request for a list of problems art has solved is rather childish. Most people feel that art is an end in itself, not a means to an end (an end which you've as yet to explain intelligibly). Science is also a noble pursuit in and of itself, even if occasionally we get useful items like x-ray machines and solar panels.

