Thanks! I guess the first thing I'll do is see if I can find a good level of AoPS to start at and try it. We haven't done much lately. I think I need to ask his math teacher if he can just not do his math homework (lately, pages of dividing decimals--useful only in that he gets careless when he's bored) so he has time/bandwidth to do more appropriate stuff.
He does like programming, although he doesn't know too much yet. He has written cool programs in Javascript for mathy things like randomly selecting 20 numbers between 1 and 40 (which turned out to be much more interesting and difficult than it sounds, at least for a beginner).
Raspberry pi might be a good holiday present. (although what he really wants is an $800 synthesizer. Too bad, kid. Get a job.)
How old is your son now, Portia? What was his first proof? What does he work on with his mentor? My son's first proof was (x+y)(x-y)=x^2 - y^2. He didn't know how to multiply out (he was 6, or maybe 7). He drew some rectangles. (First he noticed that (x+1)(x-1)=x^2 - 1, but he never tried to prove that one.) My oldest son also came up with proofs when he was little (but older, maybe 7 or 8), but he always did it with words. Little guy is very diagrammy. When he was a toddler, he spent most of his time when out in public talking about floor tiles (and yet he is the most socially skilled of all my children (which isn't saying much)).
