We can solve protein folding, we're doing that on a daily basis. We just can't do it fast enough (yet) because we're using (somewhat constrained) brute force for a search space with a very large number of dimensions. As a consequence of that the computations with the current algorithms are for practical reasons limited to relatively small proteins.

But the methods are as far as I understand well understood and it is more of an optimization problem than something unsolved.

Edit: or did you mean 'solved' in an analytical way?