When I say that the axioms are unlike mathematics I mean that they are non-intuitive.

The axioms of the real numbers are rather believable and you have to be willing to accept them in order to have addition or multiplication at all, the axioms of required for the scientific method have been debated for centuries by philosophers and are still not generally accepted as fact.

For examples see:

en.wikipedia.org/wiki/Real_number
or

en.wikipedia.org/wiki/Tarski%27s_axiomatization_of_the_reals