An alternate viewpoint is that mathematicians discover truths and laws about the mathematical realm, just as physicists, chemists and others discover them about the physical realm.

Mathematicians do in fact do "experiments" before proving a theorem - it's just that those experiments are often thought experiments, in terms of asking "what does (or would) this mathematical object look like, or how would it behave?", and those experiments are not mentioned in the final formal write-up.