We have splinters of super intelligent AI now. This manifests as high speed computations tens of thousands of times faster than humans. Humans have content addressable memory. Think of a military parade of 10,000 men - you want corporal Smith. You say:- Corporal Smith - sound off. He says here Sir. A search has to inspect each person, and interrogate them or read their tag.
Humans have cross associative memory, where other cues are used - Corporal Smith is 8 feet tall = there he is!
We are getting to know how the minds works, how it recalls, cross associates, and understands. I find it is reasonable to extend growth in that area to a future AGI with all aspects of it's 'mind' have all the aspects of a human mind, but with a 'clock speed' of 10-100 Gigahertz. Will this be faster - assuredly, will it be smarter - not so easy to predict, fast as hell, dumb as a rabbit??. The specter of an AGI with and IQ of 20 billion is unassessable. Will it become an appliance or a King - what if we have 500 of them - will they associate or will they seek war? They might not care about us at all, and be content with their own affairs - setting a few oracular subroutines to answer our questions. The pace at which this tech is advancing support what Flankk suggests - it does indeed loom!!