In math, anything above three dimensions is called hyperspace. It's pretty difficult if not downright impossible to picture any more than 4 dimensions (space and time) in your mind, but scientists are discovering new dimensions trapped within particles. So yes, there are more than three dimensions in mathematics. You can actually find distances between points (w,x,y,z) and (w',x',y',z') by taking the square root of (w-w')^2 + (x-x')^2 + (y-y')^2 + (z-z')^2. This works for any number of dimensions.
Hopefully that answered the question alright