I mostly agree with you. > all our science is based on math I disagree with this. A great deal of our science is based on math. Physics is certainly extremely

I mostly agree with you. > all our science is based on math I disagree with this. A great deal of our science is based on math. Physics is certainly extremely mathematical. Building theories in physics is very axiom-based. But mechanics is not the only kind of science. Much of science is highly empirical. We don't reason out our experiments from first principles. We have some assumptions and we try to address them. An example of what I mean is the study of microbiology. Of course there are examples of fundamental ideas, like selection pressure, but "axiom" is a term of art that I just wouldn't apply here.