Yeah you could probably write software—certainly its operations on hardware—in terms of math, just like we can frame any physical system in mathematical terms.
Is the math itself fundamentally real in the same way the electrons it describes are? Or does math exist purely in our minds as we grasp the patterns of the natural world?
real does not mean the same thing as concrete
real and concrete both have effects but real is something that exists in the absence of concrete manifestation
real *should* just mean a thing that concurs with principle, but this also gets muddled up with "subjective" and attempts to cast a net over a "real" phenomena for which you don't have a model (principle) that matches it
Oooh! Another good one! Math is a language, and language is a productive process. Axiomatic systems are the products of math as a language, but math resists a complete formalization because language itself resists a complete formalization - implying that language itself is complex - entangled and embedded from within the context it was born.
From what I've been thinking about - axiomatization of an environment must be done by a system with goals to accomplish them, but by definition it is a simplification and kills complexity. The problem with this is that you can't go from simple to complex because (hyper?) complexity is the state of the natural world.
