I see no requirement that pi would be the same in an alternate universe, much less Schwarzchild, Riemannian or Euclidean Geometry and so forth.
I say this because space/time itself is a quality of the extension of field - physical laws - and may not be the same, or may be dimensionally skewed or not exist at all - in an alternate universe or domain.
Likewise, any logic conditioned on the arrow of time could be invalid in an alternate universe - even the concept of numbers (e.g. "three") requires a material existence, i.e. physical law.
For lurkers: What is Mathematics?
Mathematics can work in an arbitrary number of dimensions imagined or not, and does so regularly. The fact that an alternate universe may not have any dimensions that we recognize certainly doesn't invalidate the fact that the mathematics is perfectly capable of operating in the dimensions that it does have. Space and time are arbitrary labels that we give dimensions in our universe, but mathematics only makes the distinction when applied to our universe and universes like it, mostly for our own convenience. Note that theoretical physicists regularly work on models of the universe with vastly more dimensions than four even though that is the only dimensions we can perceive, and often work in spaces that are entirely constructs of the imagination. Everything is still correctly derivable in those spaces if you take those spaces as axioms for deriving applied mathematics.
Logic in mathematics has no concept of time or any other property of our universe, hence why it is easily applied to all. You have confused applied logic, which takes our universe as an axiomatic environment and derives the consequences of mathematical logic in that environment, with pure logic from which the applied logic you are referring to was actually derived. If you look up first-order logic, it is essentially set theory type mathematics and spaceless. Rhetorical or applied logic is first-order logic applied to our universe (and sometimes not even that). You could just as easily re-derive "applied logic" for any other universe as well. If you stick with strict mathematical logic in arguments and avoid derivative applied logic, your logic is portable to other universes.
Numbers definitely do exist in mathematics independent of a physical existence. We take them to mean something slightly different in practice (i.e. there are some subtle differences based on the axiomatic existence of our universe), but a material existence is immaterial (no pun intended). You can count things that don't physically exist.