This question is quite unspecific....the answer to it is quite a few books long (I could name you some of those if you want to). I don't want to downvote you, though: I believe you have an interest and I should try to answer you accordingly. I still suggest that you ask a more detailed question, which would be easier to answer.

In case you would like to do that, I would also like to point out, that next to the huge topic your question covers, I see another big problem: You seem to suggest that there is "one mathematics", persumably a universal truth of which parts have been discovered by different persons over time. (Please correct me, if I get you wrong). This is highly debatable and I, personaly, think it's simply wrong. Some theories, that can be considered mathematically equivalent, were discovered independently in different times and places, e.g. the Pythagorean theorem. The fact that those theories yield the same results does not make them equal in a historical sense. It is important to study the individual context in which they arose and the methods used to do so.

In short, I would say that different kinds of mathematics have been discovered/invented by and in different cultures. Of those, some have been in contact and traded knowledge (theories, methods ect.) at certain points, either in written form or through scholars traveling and learning.