That brings up a lot of hard questions. Supposing you had that AI but didn't allow it to churn in the background when not working on a problem. Human brains don't stop. They constantly process data in both conscious and unconscious ways. The AIs we've built don't do that. The meaning of the concept of "self" for a human is something a huge percentage of their thoughts interact with directly or indirectly. Will an AI ever develop a similar concept if it never has to chew on the problem for a long period?