Yes, Aristotle tried answering this a little while ago, but I'd like to add my own two cents, ok?

People always say things like "it's an art, not a science", but they have no idea what that really means. I've thought about it a lot and for me it comes down to this. The rules of art are continually evolving. In science, there are hard and fast rules which can never be changed. People may go back and revise theories, but that's only because the original theory was incorrect. In art, rules that used to be correct can one day become totally wrong! Let's take an example. Jokes about how bad food is on an airplane used to be hilarious. However, if you even try to talk about how bad airplane food is today, you will hear the sound of a thousand eyes rolling. You should no longer talk about how bad airplane food is in earnest. The rule no longer holds.

The second difference is that art is a commentary on what type of art came before it. Periods of art have to exist in a certain sequence. For example, cubism had to come after realism. There's no way that cubism could have come first because it was a response to realism. In science one theory may evolve from another theory, but it never provides a commentary on the previous theory.

A lot of scientists like to say things like "science is an art, because it requires creative thinking". The mistake there is that just because something requires creative thinking, doesn't make it art. Everything takes creative thinking to a degree! Even when I'm figuring out how to get to LA from SF I have to be creative. Should I take the bus? Should I drive? Should I fly? What if I take the bus one way and fly back? Can I carpool? Oh my, creative thinking!