Mathematics, to me, are the product of our mental systems for
processing numerosity in the brain. Numbers 1-3 (sometimes 4)
seem to be processed by the left side of the brain (at least by
right handed males, who are always the ones tested because their
brains are alike) - and rest of the numbers are handled by the
same systems as our linguistic systems.
Mathematics beyond 1-3 (sometimes 4) are handled by our systems
designed to handle analogies. We analogize real world
experiences to mental representations which are then handled
symbolically.