Math is a social construct in the sense that if no-one is computing, math doesn't happen. You can say "2 and 2 is 4", but if you are not there, then there is no 'and', 'two' is meaningless or redundant, and the mathematical constants never appear except in their fuzziest form. Numbers are words and ideas, not physical laws.
Math is used to describe the physical universe, so it is shaped into a form that matches the universe as well as possible, giving it a framework. All things we would call math use this same framework.
But describing a Law and being a Law are different things. Math can describe a perfect circle, but that doesn't mean there is one. There is no circle that is as exact as the circle which is described by pi to 5 million digits. It is questionable if there is anything in the universe that really looks like 'two' -- especially if you were to describe '2' to 5 million digits.
Math measures things that exist, and it does this very well. But it can also do things that the universe that it is describing cannot. It is not confined by the same natural laws as the universe.
The truth in numbers is not fundamental. It is built by humans.
Magenta: The things we describe are truths and laws. There will be, anywhere and anytime, magnitude of change in a field as you move away from its source. Whatever describes this will be a mathematical idea, and we should be able to see a relationship between the described and the language describing it. But the phrase "gravity fields" is nonsense... there is only one, a dimpled one spreading across the universe. Breaking this thing down into tiny pieces is useful for us, but not something the universe does.
Likewise, digital math counts on being able to specify a certain amount; 1, or 2.1567, or Pi. But you could just as easily have about 1ish, maybe 2ish, a little over 3 -- it would often describe the real world better. But it doesn't move into the abstract well, and doesn't do human tasks well (e.g. money management). We start with an exact (impossibly exact) ideal and work from it. We have good reasons for doing this, but the fact is that mathematics is an over-engineered and idealized tool, not a map of a real territory... until we shave off some of the extra bits to make it look more map-like.
You have a mathematical truth as being an exact thing like 1+1=2, and you also have it as a real thing. They mix together, but I say they aren't necessarily bound to each other.
Ariels: They are True within the mathematic system. What does that mean? If physics describes reality, what could math be describing that is even more real? It sounds as though you are making The Truth a thing outside of reality -- e.g., a social construct.
Ariels 2:
"Show a bit of mathematical knowledge that is valid in one social setting and not valid in another social setting"
There is a Calvin & Hobbes cartoon in which Calvin is asked to answer 5+6. So he imagines a planet 5 big hitting a planet 6 big. Does he get 11? Nope. Nor I think, would an astrophysicist; but he is not in an 'astrophysicist' social setting, and his teacher is not pleased. But an even more clear example: dividing by zero is either something easy to do that we do all the time (there are 20 acorns on the ground; no one wants any of them; how many does each person pick up?), or absolutely forbidden.
The universe is a non-mathematical system. You cannot find a 'one' or a + or a factorial. Math doesn't exist in this universe. The words we use for math don't seem to refer to anything objectively real.
Try an analogy. A triangle is anything such that the sum of the angles in the plane is 2 right angles. A symbol is anything that can convey meaning to a sentient being. I draw a triangle. The sum of the angles in the plane is 2 right angles. I make a symbol. It conveys meaning to sentient beings. Therefore... Both math and symbols are true. But of course, neither math nor symbols are particularly true; they just sometimes correspond to truth, or close enough to build us a spaceship.