[ravitation]

"Science", in the broadest sense, is only concerned with the systematic study of the physical and natural world through observation and experimentation, with the goal of explanation and predictability. To that end, science is reliant of empirical evidence, not formal proofs.

The various disciplines that generally rely on "formal proofs" are referred to as "formal sciences" (logic, mathematics, statistics, etc.), but are technically not actual "sciences" since they are fundamentally abstract (as opposed to how we defined science above) - which is why they are generally concerned with formal proofs and not empirical evidence. Of course the formal sciences frequently provide the natural sciences and social sciences with ways to describe the physical/natural world and the social world, respectively.