"Mathematics describes truths." This does not mean that mathematics is the truth. That's what physics and logic and chemistry and all the other sciences are about. Mathematics is merely the language used to explore these sciences, and language is most definitely a social construct.

Some time ago, as I began reading a history of mathematics, I was surprised and amused to find that there are African cultures alive and well today, in the modern age, that simply have no concept of mathematics. I don't mean that they don't recognize the formula for the area of a circle. I mean that they have no concepts for numbers greater than two. After two they literally begin using "two-and-one", "two-and-two", "two-and-two-and-one", and so forth. If you bought one sheep for two bags of rice, the shepherd would smile and be happy, but if you tried to buy two sheep for four bags of rice, he'd look confused and wonder if he was being cheated. The concepts just aren't there.

Even when you get into mathematics as we study it today, you discover that concepts can be relative. Remember geometry? Circles, rectangles, parallel lines and so forth? Many centuries ago a fellow named Euclid tried to prove the parallel postulate, and found that he couldn't. It was one of those things that simply had to be assumed to be true in order for Euclidean geometry to be consistent. But as the centuries went on, non-Euclidean geometries were unveiled. Here, if you defined a plane as the surface of a sphere or a hyperboloid, redefined lines appropriately, and changed the parallel postulate, then you would still have a consistent geometry.

Eventually it was proved that if one geometry was consistent, then all the other ones must be as well. And while no culture in history ever began exploring geometry from a non-Euclidean point of view, it's intriguing to think of what would happen if one did. (The Pythagorean Theorem would look vastly different, for a start.)

Mathematics is not "real". It's not something that was ever discovered, it was invented and reinvented throughout history as a way of explaining the physical world using abstract symbols. Logic, you could argue, is immutable and culturally objective. Same goes for physics. But these are not mathematics, and should never be confused with it.