okay, to help you clarify what you're asking, you aren't asking anything about math, which is symbolic manipulation via inference rules, and you aren't asking anything about science, which is the making of mathematical models that seem to work
what you are asking about is philosophy, particularly epistemology, which asks about knowledge. whether it's arbitrary, whether there's any basis for believing the world "is" as it seems to us, etc, those all have pretty lengthy and complicated treatments. it's a very murky subject and you won't gain anything talking about it here except for idiots pretending to know about it after they skimmed wikipedia.
