Spotted a mathematician. ;-) > theories can be valuable in themselves Maybe they can be (in pure mathematics, or philosophy, as the sibling comment points out

Spotted a mathematician. ;-) > theories can be valuable in themselves Maybe they can be (in pure mathematics, or philosophy, as the sibling comment points out), but not if your end-goal is to apply your theory or its predictions in the real world. Then suddenly the soundest and most coherent of theories can fall apart. > There is value in approaching problems analytically rather than resorting to empirical methods. Sure, but whether your arrive at your predictions analytically or empirically it does not preclude you from testing them experimentally.