Well, as far as we know, the Math works for us.
I'm reminded of a display in my Physics Text:
They talk about 2 experiments:
Both involve bombarding a golf ball with something or another to find out what it's like [mind you, we're not supposed to know its a golf ball].
1. They bombard it with balls roughly 1/10 the size of the golf ball; some of the balls hit @ an angle, causing them to change direction; thus, we know there is a curvature.
2. They bombard it with balls roughly 1/1000 the size of the golf ball; balls also hit @ an angle, but this time, we are able to detect the small indentations on the golf ball, as well as realise its' curvature.
Anyways, long story cut short:
I think that our mathematical / arithmetical / geometrical view on our Universe is like trying to travel @ the speed of light:
THat is, we can get ever & ever so close, but never the actual thing.