To borrow Prof. 't Hooft's imagery, I imagine that GAI would be right at the top of a skyscraper whose lower levels consist of mathematics, cognitive science, and computer science at increasing levels of sophistication.

Beginning your study of cognitive/computer science with GAI could be frustrating and fruitless, just as would be beginning your study of physics with superstring theory.

There are probably well-written and interesting GAI books/articles for laypeople, though, analogous to Brian Greene's excellent books on string theory.