Current Computing relates 0 or 1 to another 0 or 1 with layers upon layers of building blocks built on this relationship.
In future AI will relate A to B, be they numbers, patterns of coded instructions or some other form of more complicated constructs at a hardware (or closer to it) level than is currently possible and, due to the inherent perfect recall and potentially massive memory storage of AI they will most definitely be bringing together and relating a vastly more broad and organised collection of knowledge than it is possible for any human to even contemplate consciously. There are some ideas that would argue that point; universal mind, spiritual revelation and morphic resonance which I do personally agree with to some degree and can imagine being particularly difficult to represent in a computational format.
Pattern spotting and relating, organising and computing potentials... computers are already better at all these things than most people try to be. It will not be long, i think, before they can "invent" something "new".
There are already attempts at AI in specialised fields of knowledge, human speech, various games, medical diagnostics and learning etc. It will be when these specialised AIs can "compare notes" about the various methodologies that have been the most productive or rewarding, in whichever form these take for them, and accordingly update their own ontologies that the true explosion of "Intelligence" will occur.