On Wed, 22 Aug 2018 04:31:31 -0700 (PDT), Gary Harnagel
wrote:
And one can choose axioms that allow us to prove anything
mathematically- including things that are contrary to nature.

Sure, but the REAL test is does nature approve of them.

What you call "REAL test" belongs to physics, not mathematics.

Mathematics is strictly logical philosophy which in principle has
nothing to do with Nature, i.e. physics. So you can choose your
axioms so your mathematics becomes very useful for physics. Or you
can choose your axioms so your mathematics has no use at all for
physics. If done property, both will be equally valid as mathematics.
Don't confuse the utility of math with its validity, they are very
different things.