The search space of all possibilities is infinite, and hence beyond the grasp of any intelligence. I firmly believe human imagination and all other forms of intelligence are restricted by mathematics and physics of our universe. And as such, the fundamental set of solvable problems remains the same.

Would be nice to hear some specific arguments against instead of Penrose-like quantum handwaving and pet analogies.

>Do you really believe the human imagination captures all of possibility? Why?

Well yes, because we are already generally intelligent. The problem is not to have the right hypothesis space built into our wetware, but to locate correct (action-guidingly veridical) hypotheses within the existing hypothesis space based upon sense-data.

Human imagination is Turing-complete.

If the AI runs on a normal computer, it is also Turing-complete and not beyond.

So they have the same limits

The difference is in the usual practical constraints of time and space.