your education is showing.. perhaps you have a different definition of mathematics
among many definitions you can define mathematics as an abstract science or as what those abstractions are studying
but holding the first definition is insufficient evidence for the inexistence of the second
i'm unclear what you think intractable equations.. whether easy or difficult to form and what the definitions of easy and hard are or why they are of consequence.. say of mathematics
a computer is a system literally built as an electrical manifestation of mathematics, albeit a subset, and in its case suffers limitations of intractability but the mathematics underlying its structure still remain
can you defend the position that the limitations of a nand gate somehow disproves quantity(o)?
also, I think Godel would be distressed to have heard the incompleteness theorems being used to deny the existence of mathematics
incompleteness is intended to show mathematics exists beyond the scope of proof
for me incompleteness does go beyond its intentions but as proof of paradox such as the existence mathematics
I mentioned the incompleteness theorems because they suggest a universe that was a consistent logical system would be arbitrarily constrained from valid portions of its state space - a testable hypothesis with no evidence. Of course, if you toss out consistency then all bets are off.
that was where this whole conversation started, 'what is reality[anything]?'
you are working from an incomplete definition of the full scale of, even recognised, mathematics which is clear in that you define it as being 'built on top of axiomatic set theory' when godel used mathematics to show axioms are limited in scope
but you, stead Godel, consider that all of mathematics, and now I'm repeating myself
In my original comment I was referring to the theory that the universe is entirely mathematics. I'm not talking about modeling with mathematics, rather that the universe is mathematics. There are no things.