{Prescient Chimera} is on my side of the field. I play {Accumulated Knowledge} but it is countered. Do I still scry? What does "Whenever you cast a..." actually mean? If you pay the mana and it leaves your hand is it considered cast?
Yes you still get to scry. It says cast and you cast the spell, it just didn't resolve
601.2. (http://imtgapp.com/forum/index.php?action=imtg;area=rule;number=601.2.): To cast a spell is to take it from where it is (usually the hand), put it on the stack, and pay its costs, so that it will eventually resolve and have its effect. Casting a spell follows the steps listed below, in order. If, at any point during the casting of a spell, a player is unable to comply with any of the steps listed below, the casting of the spell is illegal; the game returns to the moment before that spell started to be cast (see rule 717, "Handling Illegal Actions"). Announcements and payments can't be altered after they've been made.
Resolved.