Well, we’re still waiting on that proof of the Riemann Hypothesis.
Seriously however, how about introducing him to the Collatz Conjecture? Something to mull over when the vanilla work is finished. And given his interests, he’ll no doubt think of multiple ways of attacking the problem. I saw chess, computers and videogames listed as interests, so he perhaps he could try writing a chess engine from scratch. Design the algorithms in class and code them at home.
These suggestions might be a little advanced for eight years old, but I expect the boredom problem will get worse over time.
While he doesn’t have a proof of the Riemann Hypothesis, after reading your comment he immediately told me what the Collatz Conjecture was.
Has he read the Sequences yet?