The thing about kirk is you almost have to go by how he's described from outside sources
Gary Mitchell recalled that Kirk at Starfleet Academy was a "stack of Books with legs...In his class you either think!...or SINK!!!" (Not the image Chris Pine instills at all so far imho)
Also the Shatner Kirk is classically read. He knows Milton (recognizes Khan's reference to Paradise Lost without any specific quotes)Pine's Kirk is no illiterate but his character does not strike one that has spent a great deal reading
Finally, Kirk Prime was a student of great commanders (not just Starfleet either)
He studied the work of Garth of Izar (His hero) General koor of the Klingon Empire, John Gill, etc...