Hopefully I'm not wrong to suspect that the various formal axiomatic systems, which mathematicians develop, have varying amounts of empirical support (not that I generally know such systems, except by name, admittedly). Similarly, I suspect that some of them have no empirical support. Therefore, to begin sorting this out, I request the following.
Of the formal axiomatic systems, used in math, which have names and which you happen to know: please name any formal axiomatic system(s) which has/have: (A.) produced at least one equation or model that agrees with physical observation under some physical interpretation; or (B.) never produced at least one equation or model that agrees with physical observation under some physical interpretation.
Thank you.
If I take Peano arithmetic and interpret $1$ to mean "the sky", $2$ to mean "color", every other number to mean "blue", and $x+y$ to mean "the $y$ of $x$", then we see that our interpretation of "$1+2=3$" holds: the color of the sky is indeed blue.
Of course, most arithmetic statements would be nonsensical under this interpretation....