What is the future of Mathematic and mathematicians on an automatic, computerized and digital world?

I try to explain my question and its importance. Today our society lives a moment full (in a good sense) of fast changes and convulsive advances related with technology. Other times in the History, these types of technological changes affected to our daily live and some professional jobs, like when calculators and computer softwares substituted calculists, accountants or draftsmen some years ago. In some sense the Mankind appears to be replaceable by machines in many fields, but I do not pose this question in a luddist sense, because I think that if machines can do better that job, they should do it instead of us and it will be better for all.

This question is because I thought a few weeks ago that Mathematic could be relatively safe from all these futurible changes in society and that the job of mathematicians would be one of those which could be saved, like other artistic and creative jobs like writer, poet or, maybe, philosopher. But my thoughts changed suddenly a few days ago and I become depressed because I hoped that pure Mathematic belongs to those disciplines which would constitute the last redoubt of Mankind-necessity, although helped by computers and calculators. However, my latest readings on the last advances on Information Theory, Automata Theory, Computability Theory, Computational Complexity Theory, Theoretical Computer Science, Theory of Computation and Logic have shown me the possibility of a Mathematic done only by computers working syntactically or even semantically with axioms and models in first-order or higher-order predicative, deductive or modal logics developed. I thought, like many other mathematicians, that this almost Hilbertian statement could not be achieved because of Gödel's incompleteness theorems, but this asseveration which seems to save Mathematic from a full computerization it's not true because these theorems are true in the first-order axiomatization of arithmetics (Peano) which is not complete, but some (if not all) the second-order or higher-order axiomatizations of arithmetics are complete and these theorems do not apply and, although our computers nowadays only are advanced in first-order automatic deduction, nothing impedes the existence of future computers, which could work in higher-order logics or exotic axiomatizations, solve the most important open problems in Mathematic and prove theorems which Mankind never could imagine; and, in this case, what would be the role of human mathematicians? In fact, would they have any role? Can we save Mathematic for humans? Is there any theoretical or technical impediment which avoids this terrible final? If not, How could we help the machines in do Mathematic? What is, finally, the last role of Mankind in developing Mathematic?

I'm not searching only in terms of time of computation or deduction. I do not care if a computer takes longer than human being to prove a theorem or to solve a problem, but if it can do all things that we do or even more. If we can save Mathematic for Mankind, what have us that computers have not and vice versa?

I will accept and thank all transversally or not philosophical or mathematical answers and opinions but well reasoned and founded. I repeat this is not a luddist question or manifestation.