There are SF short stories about this kind of thing (the best of which is probably
Greg Egan's "Luminous" - he's sound on the whole religion question as well and I strongly recommend him to those of you who like me are are SF
geeks readers). I think that, as there's a lot of maths we don't know, there's likely to be a lot of maths that any putative alien would know, but we don't. Like, an intelligent gas cloud or something might have an incredibly advanced understanding of, say, set theory, but arithmetic might be this arcane and little understood discipline (assuming that we developed arithmetic from counting solid objects). So they may not have a system of numbers as such.
It's also possible (I think) that a mathematics inconsistent with ours might exist - that seems to be an implication of Godel if I understand him correctly.