One thing is that mathematicians never become constipated. They can always work it out with a pencil
Actually, our entire knowledge of the unseen and the untouchable is based on mathematical models. How far away is the Orion Nebula? Well since we can't take our little wheel on the end of a stick and roll it out there we need another way of making that measurement. Math to the rescue. Of course there will be those who will claim we don't need to know how far the Orion Nebula is since we ain't going there anyway but that is one use for math