Let me get ti straight. It sounds a lot like P=NP means, there are no computer algorithms with O(n^k)? Trying to simplify the explanation might be just as impos

Let me get ti straight. It sounds a lot like P=NP means, there are no computer algorithms with O(n^k)? Trying to simplify the explanation might be just as impossible. Obviously I have no clue. Are there other complexity classes that were shown to be non existent in deterministic machines?