Yep, I'm fairly certain that general learning algorithms acting upon an ANN (which is fairly general too, see the universal approximation theorem) can reach and surpass performance of the human brain. As we have approximately zero evidence that the human brain contains "magic," that is something that can't be modeled by an ANN of a practically feasible size.

But, no, it's not "any day now." The required size and structure of the ANN is to be determined.