There is no "perfect" software for making math visualization videos. The better movies of this kind were likely made using standard 3D animation software such as Cinema4D, Maya, 3d studio, XSI and such. You'll probably have to export data from a math application such as Mathematica into these suites and do the renderings in there. It's possible to render with just POV-Ray but working with a 3D suite can get you much better results.
Some examples:
1. Not Knot, part 1 and part 2
2. Moebius Transformations
3. Sphere Eversion Part 1 and Part 2