What would you do with a solution to 3-SAT?
Any answer other than "create a superintelligent friendly AI to optimize the universe" would be a waste of this particular genie, but there are some steps in between that and 3-SAT which I can't specify yet.
An NP oracle makes AI rather easier... but I'm not sure it currently would be as much help in FAI in particular. That is, I don't think it would help as much with the F part.
In other words, I suspect that an NP oracle is the sort of thing that if you discovered one... you should be really really quiet about it, and be very cautious about who you tell. (I may be totally wrong about this, though.)
Many experts suspect that there is no polynomial-time solution to the so-called NP-complete problems, though no-one has yet been able to rigorously prove this and there remains the possibility that a polynomial-time algorithm will one day emerge. However unlikely this is, today I would like to invite LW to play a game I played with with some colleagues called what-would-you-do-with-a-polynomial-time-solution-to-3SAT? 3SAT is, of course, one of the most famous of the NP-complete problems and a solution to 3SAT would also constitute a solution to *all* the problems in NP. This includes lots of fun planning problems (e.g. travelling salesman) as well as the problem of performing exact inference in (general) Bayesian networks. What's the most fun you could have?