[hvocode]

I think others addressed the "why proof not empirical data" question well, but one additional point. A logical proof is only as solid as its weakest component. In mathematics any result that has been proven may be used in a component of another proof. If you have a result that is based on empirical evidence, then every result proven based on that also inherits that empirical evidence as part of its foundation. The reason we don't do this is that if, by some weird chance, the original result that used empirical data instead of proof is shown to be false, then every result built upon it is invalidated and needs to be revisited. That would be a mess. Sticking to requiring formal proofs at least reduces that possibility - although it is still entirely possible for a proof to have a subtle mistake as well, which would have a similar cascading effect on results built upon it.