I think that this question is can be answered with yes and no depending on how you interpret the question. I would say yes, our number system has everything to do with what mathematics because there is no way to represent what we know about math without using our number system. For example, if we did not adopt our number system, how would we be able to understand just about anything? Would we still understand or discover things like calculus, algebra and physics? How would we quantify anything? How would we make change at a grocery store? How would we add, subtract or multiply?
On the other hand, I would say no, our number system does not have anything to do with mathematics. Our number system doesn’t determine any truth about mathematics. What we know is true about mathematics now will always be true. Our number system is just a way to represent what we know. If we didn’t have our number system, we would more than likely have another representation of what we have discovered about mathematics. To answer the above questions, the concept of calculus, algebra and physics would still remain. Whether it was discovered or represented with our number system would be a different story. We would have found another way to quantify things. Who knows, maybe we would still be using roman numerals. The use of the words “one, two, three… etc.” are essentially just words we agreed to use to represent those numbers. Our number system could go something like “popcorn, carpet, pillow dinner” if that is what we use to represent what we now call “one, two, three, four”. The number system itself does not determine anything about math. It is simply a way for people to represent what they know that is universally accepted so that information can be shared with others.