Has your son tried other activities that might be appealing to high-IQ, math-minded children? What about chess, Lego robotics clubs, or even card trading games that meet at comic book stores, etc? It seems to be that with two math PhD parents and the level of achievement and instruction you describe, you might be disappointed in these camps pedagogically, and the price is so high. I'd look for other ways to connect with similar children socially first, if that is a main goal. You might be able to find peers for free. I don't know where you live or how likely it is that there are other children near you in somewhere near the same ballpark, though.
