This speech by Director Steven Soderbergh has been making the rounds. It's a long, but I would argue, necessary read over the state of cinema.
What really interested me was his take on art as problem solving:
Art is also about problem solving, and it’s obvious from the news, we have a little bit of a problem with problem solving. In my experience, the main obstacle to problem solving is an entrenched ideology. The great thing about making a movie or a piece of art is that that never comes into play. All the ideas are on the table. All the ideas and everything is open for discussion, and it turns out everybody succeeds by submitting to what the thing needs to be. Art, in my view, is a very elegant problem-solving model.
I don't quite agree with what he's saying here, but our sentiments are very similar: art is important because it explains things that may be unexplainable with plain language.
Our minds are constantly looking for connections between things and sometimes the best way to make those connections is by relating it to something that's conceptually the same, but practically different. In the Bible, Christ did this with parables. With movies, it's done by putting a similar story in a different setting. Science Fiction arose from this concept: it commented on modern problems by placing the story in a futuristic setting or an alternate reality. Doing so helped us get a fresh look on modern problems by eliminating biases that may have resulted come from personal feelings rather than the facts of the problem.
It may sound obvious, but art solves problems by helping us think creatively. Creative thinking isn't a skill that most people just have; it's something that needs to be developed, cultivated and maintained. This is why it's so scary that we consistently see the arts cut out of schooling due to budget issues. Science, rational thinking, mathematics: they all require various levels of creativity. Not because they're "soft" or because they're inexact, but because they require a mind that's willing to bend in order to fully comprehend.
We may be able to teach our kids the concepts of chemistry, but how are they supposed to expand the discipline if we're not teaching them to think creatively?