It seems to me there are two quite different questions here...
#1, the fundamentals of nature are what they are regardless of who's doing the describing, yes.
But #2, what different species, or alternative human cultural histories, will care about while investigating those relationships may be subject to wild variation, as may their approach to various topics.
For instance the discrete/continuous issue Torco brought up is much more realistic than you guys gave him credit for  if a species starts out with a mainly continuous view of quantity, and here I'm talking about their roots, not what they are "capable of conceiving of" which is different and stupid to assume a limit on, then whatever mathematical structures they work out may be very different in flavor from ours.
An even deeper point of potential variation is what the purpose of math is conceived to be by the society/species. For instance I could easily imagine aliens that are not highly tolerant of purely theoretical musings, with only practical concerns considered legitimate. They'll get the same value for pi that we do, but they may not give a shit that e = 1 and might, for example, not bother to work out something like complex numbers until such time as working with electricity forces it. Or they might not care about proving things absolutely, the way we do. Proof is what our mathematicians are usually after when they investigate a behavior, as this is part of our conception of what understanding consists of: the immense value (as we see it of) of demonstrations that something must be true. Another culture may find it sufficient that something only seems to hold... and perhaps get some wrong answers that way, too.
Another point of variation: what the operations are. The hierarchy of operations we use goes like this: first there's counting, i.e. incrementing by one; then there's addition, which is a way to count incrementings; then there's multiplication, which is a way to count additions; then there's exponents, which are a way to count multiplications; and though we have little use for it there is also "tetratation", a way of counting exponentiation. So there's room for variation: a species/culture could just stop at multiplication, say, the way we usually stop at exponentiation, while another may go several levels further. It's not necessarily even arbitrary, there are reasons one might stop at multiplication  for example the fact that while addition and multiplication are commutative, exponents aren't. It might be held as a value that that makes them untenable, say. Perhaps another species might work out a different extension of multiplication that is commutative. (That may be impossible, but if anybody wants to argue that it is, I demand proof!). Also, for alien species, there's no reason an operations system even has to be based on the notion of counting (but I think anything human would have to be). What else might it be based on? Maybe operations could be based on the properties of things rather than their quantities, for example shape deformations, or cycles of change. Exactly how to make that work I couldn't say, but it seems plausible that ten thousand years of a species' smartest minds might be able to make something of it. Whether a conworlder could make something of it is less likely.
