Math is merely a different teleology, a top-down knowledge structure that begins with axioms. It is non-scientific by definition. By contrast, science is botto

Math is merely a different teleology, a top-down knowledge structure that begins with axioms. It is non-scientific by definition. By contrast, science is bottom-up--a continuing process of experimentation and analysis. Although scientists have varying beliefs, scientific literature normally makes starting assumptions only insofar as they are helpful to the process--like the (unproven but very helpful) assumption that physical processes obey consistent physical laws that don't change between experiments, or mathematical axioms and their resulting knowledge/methods. But all knowledge obtained scientifically should be held lightly and remain subject to falsification by further experimentation. There's nothing wrong with top-down knowledge structures built on a set of starting assumptions, as long as we don't "catch" worldviews like the cold without subjecting them to truth tests like correspondence to reality and internal consistency.