It's proven unsolvable for computers (i.e., Turing machines). Whether that makes it impossible for humans to solve (as a matter of course, or as a matter of Turing's proof) depends on whether you believe that we are isomorphic to computers. Which, to be fair, is exactly the belief that underwrites artificial intelligence. But then Turing's proof involves a program that inspects the halting oracle you're using, which isn't well-posed for humans evaluating halting.