In other words, we're still taking sides. The existence of asymmetry in the universe, isomers, strongly suggests foundational elements of mathematical logic are inherently part of things, and that we can construct all the usual inductive layers up from and/or/not in some form mechanistically, purely from things as they are, reason absent. Beyond inductive, philosophical questions and completeness and p/np are perhaps innately artefacts of conciousness. Most of the maths of things as they are lies outside these problems. It's a very big universe to argue humans define all states of being... but I grant that the idea of a number which is one more than the value you count to, before entropy prevents all counting is "out there" as a value beyond existence as we understand it, and doubtless countless other numbers and values and expressions. I live in hope some shrimp like thing, or a gas giant conscious cloud is working on that problem.

Math is fundamentally a description of the physical world. Mathematicians don’t like to hear this because they have their own ideas about the platonic realm of math, but it is true. We can debate which logical rules or axioms to include, but fundamentally any math has to have some sort of rules for deductive reasoning, which carry over from observation about the physical world: effects have antecedents, with a causal link between the two.

Now we have gone from that to the present day when we have maths which aren’t yet found to align with physical reality. So I can see why people want to say that it is a mental construction. But still, even these abstract maths operate according to rules we derived from the physical universe.