Mathematicians and scientists use math to model the world by constructing mathematical objects that capture important properties of physical things (while ignoring those properties that are not relevant for the investigation). Hence, from the basic useful mathematical objects, a whole complicated structure follows which contains many new ideas relating to or emanating from the original ones. Long after most of the basic objects of math were created, attempts were made to axiomatize the subject (i.e. provide a small set of basic axioms from which the rest of math can be derived), but math was not developed from these axioms. When the basic axioms are fundamentally altered, this is not necessarily the case.

When you want to outsmart the world, you turn to the facts. And the facts are in the science.