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While Amadeus gives a great answer about what intelligence is, let me try to answer your question from a literature standpoint. There are two authors with, in my opinion, absolutely outstanding AI...
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Source: https://writers.stackexchange.com/a/34820 License name: CC BY-SA 3.0 License URL: https://creativecommons.org/licenses/by-sa/3.0/
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While Amadeus gives a great answer about what intelligence _is_, let me try to answer your question from a literature standpoint. There are two authors with, in my opinion, absolutely outstanding AI representations, for AIs of varying weirdness. First, the Culture series of Ian M. Banks; but also A Fire Upon the Deep from Vernor Vinge. Banks plays with different personalities of AIs that are in principle not too far advanced from us, just scaled up a lot, while Vinge gives us a _very_ weird and hostile "transcended" AI with literally unfathomable possibilities. Long story short; unless you wish to read those books (which I wholeheartedly suggest to do for anyone vaguely interested in SciFi), especially the Banks books play with the idea that the AIs are personalities (though they are clearly not human and don't pretend in any form or fashion to be such - they are huge spaceships...) with individual traits and such. They are advanced enough that they are far, far beyond individual humans (including being able to have interactions with thousands of humans at once), but are still very much represented as a singular individual with likes, dislikes, opinions, strategies, short-term needs and so on. He plays on this dichotomy of them being like "persons" in some aspects, but then quite obviously _not_. The Vinge AI is just plain different; the book may give you an idea how to present an incredibly advanced, totally incomprehendable AI, and how to experience it only through the outwardly visible effects (its actions), and comparison to the protagonists of the book, who are fighting against it (without spoiling anything here - the AI is a not-too-large subplot in that book, with a main story about something also somehow related to intelligence, but not in an AI sense).