I watched this interesting talk on game design by Jonathan "Braid" Blow and Marc "Miegakure" ten Bosch. They espouse and explore a particular design aesthetic where the designer essentially plays the role of a mathematician. "Good design" then becomes a selection of orthogonal mechanisms (axioms), and an exhaustive-yet-minimal mapping-out of what's derivable (theorems), and then demarcation of the boundary. Since it needs to be fun, the real art has to come from crafting surprise and tweaking axioms to capture exactly what you want. They both make some very interesting points, and I thought this comparison with mathematics was a particularly cool and apt way to frame the ideas.
Watch it here: