Of course math is a formal system. If you take Zermelo-Frankel Set Theory as the foundation of math, it has a very clear, formal set of axioms.

And we do not know for certain that math is objective truth. If we did, there would be no philosophy of mathematics.

Reasoning within mathematics is objective, because math is a formal system. But to think that we know anything about anything is frankly pure arrogance. We don’t know why we are here or what our universe even is at a fundamental level. Math is a human-imposed construct that we use to try and make sense of it all.