Do you mean the halting problem in Turing machines? Okay, we have a proof that a machine can't solve the halting problem for every arbitrary Turing machine, bu

Do you mean the halting problem in Turing machines? Okay, we have a proof that a machine can't solve the halting problem for every arbitrary Turing machine, but we can build algorithms that solve it for some cases. Now, can a human solve the halting problem for every arbitrary Turing machine? We obviously can't, either. Make the machine complex enough and we can't wrap our minds around it.