[yequalsx]

I'm not claiming that humans can discover all true statements in mathematics. I'm saying the Incompleteness Theorem demonstrates that such a task is not computable and in the proof of the theorem a statement that can't be proven in a computable system is proved. So....can a computer ever reach the same level of reasoning? I'm skeptical.

[xlpz]

Solving a particular instance of a noncomputable problem is not the same than solving the problem itself. Eg, the busy beaver problem is noncomputable, but it's trivial to make a machine output solutions for simple cases in the same way that it's trivial for a human to do so. In fact, you cannot prove that what we are doing is essentially programming ourselves to solve ad-hoc cases of the general problem, which is computable, as opposed to somehow having in our heads a general way of solving the problem, which we know it's not computable.

Basically, what you need to prove to show that humans are intrinsically more powerful than machines is that we have the ability to generally solve noncomputable problems in a general way, ie, that we are hypercomputers.