Is it possible to enter custom math/scripting formulas for keyframe animation inside Premiere Pro?
Not from within premiere. You would need to do that in AfterEffects.
AfterEffects is better suited to do animation regardless. Once you've set up your compositions, you can then import them directly into premiere and lay them into a sequence using Bridge.
This way you can easily jump back and forth between AE and PPro and any changes made to your AE Comp will immediately update in PPro provided you have Bridge and the Dynamic Link Option enabled.
Depending on what exactly you are trying to accomplish you actually could do this by making images of the portions you want to animate and using the Motion effect on the various layers, however it will be pretty tedious to do.
As Martin Andrews mentioned, After Effects is much better equipped for handling this kind of thing, but depending on your specific goals for the animation, it is likely possible in Premiere.