There's an interesting question in whether the game of chess is artistic or scientific. One might take a Game from the great Max Euwe and opt scientific due the mathematicians methodical and precise play. One might also look at a game from Mikhail Tal and consider it more artistic do to his extremely flashy play that looks almost magic-like. Lets really examine both perspectives.
The Science of Tactics
The goal of science is to really test a theory for approval or disproval. A large portion of chess tactics require testing a solution out (in your head). So in reality, you are using basic scientific principals to determine whether your a move will prove favorable or disadvantageous. This is especially true when testing tactical combinations that can be narrowed down to a subset of effective and often forced results.
The Art of Strategy
Chess strategy on the other hand can be far more artistic. Artistic doesn't necessarily mean completely lacking in structure and neither does strategy. Ive found strategy really favors an open mind and an open eye. With that said, there needs to be some sort of discipline when it comes to committing to an option, but not before you have accessed the situation properly.
So art or science you ask? I like to answer with a tad bit of both.