Does everything need to have an application in order to be useful?
What problems does music solve? Do poems facilitate solving some problems more quickly or easily? And if not, are they useless?
What problems does music solve? Do poems facilitate solving some problems more quickly or easily? And if not, are they useless?
I definitely appreciate things more that provide valuable utility or some other derivative value. You're right that some works are appreciated beyond their utility, for how they are experienced.
I do think there may be utility in these things even when the pattern is more apparent than the application. A good poem makes us feel something. I just wouldn't get the same feeling from a math problem unless it solved something for me. Not to diminish your appreciation for this, just that I find a poem more accessible.
But poetry is a fantastic analogy, and I think you may have selected that subconsciously. A great moment of seeing something mathematical with total clarity is exactly like the moment you suddenly understand a poem and have access to what the poet meant. Math doesn't actually have problems and doesn't need to be solved. It exists whether you figure it out or not.
What's sort of neat about this is that it physically demonstrates that fact.
As for music, I do think it fits the human nature (not necessarily a "problem") of longing for company. Or put it other way, we can't have our mind "empty" for long. The practice of "mindful emptiness" is meditation imo.
By definition yes. Other things can be enjoyable, of cultural or historical interest, or just interesting pieces of knowledge, but to claim that something is useful is to claim it has applications.
Music is entertaining and enjoyable to listen to. Poems can communicate mental states and feelings succinctly.