It's an interesting question. Solving extremely difficult math problems, e.g. the Riemann hypothesis or P vs NP, would be very impressive. Or coming up with alg

It's an interesting question. Solving extremely difficult math problems, e.g. the Riemann hypothesis or P vs NP, would be very impressive. Or coming up with algorithms given many examples of desired results. There should be many benefits to having a much better short-term memory and instant access to the accumulated human knowledge. We've already seen AI do surprising things through just pattern recognition, such as predicting a patient's race from medical images when human experts cannot do it. AI might be able to understand an extremely complex system, such as the world economy, and tell us what to change to make it work better. It might not be what you asked for but in practice "any sufficiently advanced technology is indistinguishable from magic" rule will come into play even with just quantitative advances. And we might get practical quantum computers at some point...