To me, > any conceivable mathematical calculation can be done by a single device shuffling 1’s and 0’s back and forth seems right. It does not say that Turin

To me, > any conceivable mathematical calculation can be done by a single device shuffling 1’s and 0’s back and forth seems right. It does not say that Turing's machine solves every problem. It says it does every conceivable calculation. That was Turing's contribution (anyway, one of them). The controversy at the time (1930's) was that there were a number of proposed definitions for what are conceivable mathematical computations (Kleene, Post, Herbrand ..). All of them gave schemes that the authors claimed were exhaustive. Turing's paper convinces a reader, as it convinced Godel, that his definition does indeed do everything mechanically possible (and everyone else's definitions, since they all prove to be equi-powerfull). Of course Godel knew there were unsolvable problems. The question was whether there was a single maximally-powerful device.