Is realness not an instrinsic property but just a judgement on how useful something is?
Is being real a real property of something or just a construct?
Whence the pragmatic maxim:
Consider what effects, that might conceivably have practical bearings, we conceive the object of our conception to have. Then, our conception of these effects is the whole of our conception of the object.
It misses the point of the question "is math real"?
Tbf, i am actually sympathetic to the position that "realness" is not really relavent or a well defined term when it comes to what is basically a descriptive language of patterns and relations. But "is it real" is the question we started the thread on.
The universe, as we know it, is simulatable. In other words, it can apparently be reduced to mathematics in precisely those three senses I outlined above. (If it helps, you can imagine electrons and other subatomic particles as bits of information in a coordinate space, which are constrained to operate in accordance with rules that govern logical relations between things.)
What mathematics is real? Anything that would relate to that universe or any of its constituent parts, in _any_ meaningful sense. We don't need to have found a use for it, and surely there's a great deal that is still undiscovered.
What mathematics is unreal? Whatever is, a priori, absolutely unnecessary to the existence of such a universe -- or, even worse, would break a universe described in terms of logic were it somehow made manifest.