AGI, in the singularity sense, will be solving problems before we even identify them as problems. Experts in a field can do this for the layman already and I think it's possible. Some don't. I do.
It'll be super interesting when it flips! When the student becomes the master and we, as a species, start learning from the computer. You can kind of get a sense of this from the Deep Mind founder's presentation on their AI learning how to play the old Atari game Breakout. He says when their engineers watched the computer play the game, it had developed techniques the engineers who wrote the program hadn't even thought of.
Even still, the engineers could teach another human how to play Breakout, so yes, I do believe they did in fact create a software to play Breakout better than they could.