[mbrudd]

Pursuing this question is quite the rabbit hole, but doing research in mathematics makes me believe that math is a science: you have questions, you collect evidence by exploring examples (i.e., conducting experiments), and you formulate hypotheses as conjectures. If you're lucky, your conjectures are correct and you prove them! Proofs are even better than the accumulated evidence on which theories in other sciences depend, in that proven theorems are immune to falsifiability within the axiomatic system in use.