why don't you look and see what department math is under at your local university.
*pauses*
that's right. science. math works because it follows scientific, testable laws. what do you think physics is? math. do you believe in black holes? do you somehow think that they can be seen? no. they can only be detected mathematically. same with dark matter. same with a lot of things that simply have to exist because of how the math works. math isn't invented usually. it's discovered. fibonacci? discovered his stuff picking flowers and eating oranges. well not exactly but you get the idea.
why doesn't 1+2=5 (in a base ten system)? because if it did the universe would literally fall apart, not because some muslim decided it should be so. it really is "dangerous saracean magic".