[RightWhale]

What he said was more indirect. If we ever are able to prove all of math it can't be by logic, so if we do it, it would be something that logical machines can't do.

[js1138]

Machines don't have to be logical, even if their operation is deterministic. We tend to program computers to be logical in the strict sense because we don't want them wandering off while crediting our mortgage payments.

But computers can be designed and programmed to solve problems stochastically, in which case they can arrive at solutions without the designer/programmer being able to explain how.

The information for constructing the solution comes from input data rather than from the programmer. This is, in a simple way, equivalent to being able to know that something is true without being able to prove it.