> Laws of mathematics are a definition. Nothing. More. If I wanted to make new laws of mathematics, I would just have to get enough people to believe me.

Not even that. "Laws of mathematics" are just the laws of logic applied to an arbitary set of axioms. If you choose appropriate axioms, you end up with "everyday maths". However, you are free to choose any other set. No set of axioms is any more or less valid than any other - they are completely arbitary (with the caveat that they should not be contradictory, of course).