FUNDAMENTALS OF GAME DESIGN, SECOND EDITION
Mathematical Competence
Designers must have basic math skills, including trigonometry and the simpler principles of probability. Balancing games that feature complex internal economies, such as business simulations or real-time strategy games, can require you to spend a lot of time looking at numbers. You don't need a PhD in mathematics, but you should be comfortable with the subject. You may be able to handle most of the requirements with a spreadsheet program such as Microsoft Excel.
Although you need not be an artist, you should have a general aesthetic competence and some sense of style. Far too many games are visual clones of one another, depending on stereotypes and cliches rather than real imagination. It's up to you (along with your lead artist) to set the visual tone of the game and to create a consistent, harmonious look.
Expand your aesthetic horizons as much as you can. Learn a little about the fundamentals of art: the principles of composition, and which colors coordinate and which clash. Find out about famous art movements—Art Nouveau, Surrealism, Impressionism—and how they changed the way we see things. Watch movies that are famous for their visual style, such as Metropolis or Blade Runner. Then move on to the more practical arts: architecture, interior decoration, industrial design. The more aesthetic experience you have, the more likely you are to produce an artistically innovative product.