I believe this is a topic where it is better to steer clear of philosophy and be concrete. The natural way to consider this problem is to simply compare mathematics to those areas where computers have already proved to be superior to humans, such as board games.
It is difficult not to notice that mathematics is not a game. Theoretically, the task of proving (say) a conjecture can be formalized, and made into a sort of combinatorial problem. However, this is not how we humans do mathematics, and it is not how computers would do if they are supposed to have a chance at a problem like Poincare conjecture.
The thing is, once you are above the purely formal level, the task of proving a conjecture (or, say, finding a new formula) becomes extremely complicated already as a task. You can learn the rules of chess in ten minutes, and after this you will be able to play, even against a grandmaster. (You won't be able to win, but this is a different story.) In comparison, people learn for decades just to be able to read published papers. The ``rules of the game'' are many orders of magnitude more complex.
It may be possible to teach a sufficiently advanced computer these ``rules'', but this is not a piece of cake. The first step is formalization of all mathematics. (Maybe not necessarily formalization is the usual sense, but one way or the other we have to teach a computer how to read modern mathematical literature.) This is already a formidable task, which won't be accomplished any time soon. But at least, it seems withing reach.
After this, a computer will be in a position of a beginner who has just learned the rules. (By the way, the same may be said about a human graduate student.)
The second, and still more difficult task, will be to upgrade someone who can play to someone who can win. Probably not impossible, but much more difficult then with Go (for plenty of reasons).
The point is, actual ``computer mathematicians'' is a matter of such a distant future that it does not make much sense to talk about it now. When (or if) such a time will come, everything will be different.
To answer the question itself, there are no fundamental reasons why a machine couldn't reach a level comparable to humans, when it comes to mathematics. But there are reasons why this is extremely difficult to achieve in reality. In particular, modern AI technologies, regardless of their success in many other areas, would likely be useless.