Often, if you are finding that a question phrased in a certain way gets incoherent answers, the issue may be the question itself, just as bad premisses lead to bad conclusions in mathematical proofs.
One problem is what you mean by mathematics. If you are think of mathematics as a set of universal truths about the relationships among non-culturally determined abstract entities, then your answer will be that it is not culturally determined.
If you think of mathematics as a set of practices, it is, in fact, practiced in different ways in different countries. Ancient Greece was interested in the proofs of Euclidean geometry, but never invented zero, which was a product of a culture of algebra developed by the Arabs. Indian logic, western medieval logic, and early modern European logics operated on very different presumptions.
Cultures, and individual philosophers within a specific culture, also disagree about the epistemological status of mathematical entities -- whether they are "real" or merely formal conventions (a position known as nominalism). The debates over such issues underlie the "philosophy of mathematics. The works of Wilfred van Orman Quine and Thomas Kuhn discuss these issues at some length.