I should probably just formally come out as a mathematical Platonist. It's just the most interesting way to look at reality. Maths is real, all else follows.
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@_thegeoff One question I always have is about mathematical Platonism is "which math"? Which is to say that there are multiple different ways of formalizing mathematics, e.g. you might or might not believe in the Axiom of Choice, you might be a constructivist and not follow the principle of excluded middle, or you might be a frequentist or a Baysian. If one believes that math is just a synthetic language that may describe some things in nature, it seems that one can be much more non-committal on these matters than if one takes them as matters of ontology.
@internic Why not all of them? I'm sure that depending on which axioms you chose (rather than Of Choice..) you can end up with various things that are proveable/unproveable, but I see that as just limiting which bits of the landscape you can reach from your starting point, the rest is still out there.