Galileo improved upon Aristotle and used mathematics to do it. To suggest that these disciplines must remain separate or non-interchangable is to introduce constraints that are unnecessary, just like suggesting theology must be compartmentalized into the realm of faith, as if faith by definition has no basis in fact; as if science can operate without shaping principles attendant to each observer.
Your opinion. Try to use any to prove the other. Laws are used as evidence in scientific theory however those laws are determined by mathematics, not science. Faith has no basis in fact. Name a fact observed by faith. Faith has long been defined by philosophy. Ones opinion will not change the definition.
Actually the conjectures of Copernicus and Galileo regarding heliocentrism were not based on mathematics, and provided little mathematical advantage over the Ptolemaic system.
They stuck because they were good inferences and led to good research. But they were the result of imaginative thinking, not logical necessity.
This is pretty common in science.
"as if science can operate without shaping principles attendant to each observer."
Did you just argue for complete relativism? That doesnt sound very conservative.