I would start with energy. With obscene amounts of energy a lot of other problems get solved relatively easily. It takes a lot of energy to create fresh water from saltwater… but with excess energy why not? So, AI is tasked with creating safer nuclear or more efficient solar (or something we can’t imagine). It builds an army of robots to manage the construction. Now we have gobs electricity flowing everywhere. Maybe it makes better batteries to store and move energy around without transmission loss. Sure, why not? Now, we use all the extra electricity that isn’t being used for run cat video servers to pump tons of fresh water out of the oceans. We could turn deserts into farms.. or just massive food forests. More armies of robots could be used to tend to and gather the crops. Now we’ve got more food and fresh water then we know what to do with.. and free electricity. Things are looking good. But people are still dying of disease etc. So, we are going to need some medical nanobots that are capable of maintaining human bodies. This isn’t that far fetched. Unfortunately, people are still dying of accidents.. which are now more tragic because death is becoming less inevitable since we’ve wiped out disease and starvation. So, there are a few options here. We could grow surrogate bodies in labs and then upload our consciousness to them. Or, we could upgrade human bodies a bit.. add some metal/plastic.. some emergency nano-repairbots. If things get really rough (asteroids?) we may need to look at putting backup copies of everything in the “cloud”. I’m leaving something out here though. Every time we see people coming to the rescue something always gets in the way.. other people. If suddenly infrastructure became unnecessary.. a lot of governments would very quickly lose power. If I have all the food/water/power I need (imagine everyone “off the grid”).. why would I need a powerful central government watching out for me? Transportation? Nah, I’ve got my electric self-repairing off road vehicle for that (heck, it might even fly). That just leaves.. policing. Will people still steal when they have everything they need? Yeah, probably. Will countries still find a reason to fight? Yeah, it’s hard to believe religious extremism and territorial disputes are just going to vanish over night after going on for thousands of years. Is there a superintelligence solution to this? It’s not hard to imagine a solution.. but not a good one. The scenarios here range from a “can my superintelligence beat yours” to a police state where a strong AI controls every aspect of human life.. making sure everyone follows every single law. There may be some complex middle ground where law breakers are arrested and then a jury of “real” people show up via skype (or something) to deliberate. The point though is that when it comes to people being bad.. there is no clear technological solution. We should definitely try and get to the point where that is the only real problem we are trying to deal with though.