THE most common criticism against mathematics not being a natural science is that it does not describe the physical universe. If this were true, then it would admit that there is no property of number, space, change and time in the universe that existed independently of the mind, which is an absurd position.
THE second criticism is that mathematics is not experimentally falsifiable, however the existence of different geometries proves that under certain circumstances it is possible to show that certain postulates do not apply, as in the case of Euclid's fourth postulate which was shown to be false. Furthermore while mathematics might not be entirely experimental, the results of the natural sciences show that it is indispensible in explaining phenomena, suggesting it does actually exist.