Classical belief is that the universe has four dimensions, three spatial dimensions and one time dimension. It isn't a matter of proving them or not, they are merely foundations that all our approximations in physics are built upon. Don't get any idea that physics is a true or exact science in any way. I, however, would say that it is the most accurate approximation of Truth mankind has ever created. This all starts to get into philosophy though.
I myself don't really understand the other geometries, but there are all sorts of other views about the geometry of the universe, such as Riemannian geometry or hyperbolic geometry. I hope I gave you a satisfactory answer. I can't understand how you think the three spatial dimensions are proved any more than time.