But with better science and technology, maybe. All matter exhibits mind in different aspects and degrees. Machines will never be self-conscious. But since Jones can do A, he can't be a realization of a Turing Machine. Provable limitations aren't limitations on what can be done heuristically with high reliability.
All computer programs are algorithms.
There is no feasible algorithm for checkmate in chess. Therefore checkmate by computer is impossible. There are things humans can't do too. Goedel's argument applies to lower levels of AI programs, which are simple, formal, logical systems. But higher levels are models of the mind, and can be informal just like the mind is.