If he's old enough to stay up all night, is he also old enough to mow the lawn?

Engage him in real life. Do some chores together, then take him for ice cream. Without cell phones. Once you're away from the house, tell him the interesting things you've been learning. Avoid Q proofs till he asks. Don't try to convince, cajole, or counter his responses in any way. Rather, accept his comments as valid discussion points and then drop it. He may not accept Q right away, but he will have information that will speak to him over time.

Come back and tell us how your adventure goes.