My son (an occasional Hacker News participant) was in a similar position a few years ago. I'll list here a variety of books that should be helpful, some of which were recommended to him by summer program instructors, and others of which were recommended to me by parents of other children with similar activity backgrounds.

For access to a lot of mathematical concepts at a reasonable reading level, not at all expensive, I recommend Concepts of Modern Mathematics by Ian Stewart.

http://www.amazon.com/Concepts-Modern-Mathematics-Ian-Stewar...

Ian Stewart is a mathematician who loves to write popular writings on mathematics, and you can hardly go wrong with anything he has written.

From Zero to Infinity: What Makes Numbers Interesting by Constance Reid

http://www.amazon.com/Zero-Infinity-Makes-Numbers-Interestin...

is very accessible and covers a number of interesting topics.

The Art of Problem Solving by Richard Rusczyk and Sandor Lehoczky

http://www.artofproblemsolving.com/Store/viewitem.php?item=p...

http://www.artofproblemsolving.com/Store/viewitem.php?item=p...

is a straight-up contest preparation book, in two volumes, that your son may find interesting. Volume 2 is for high school level contests.

For an interesting (in places laugh-out-loud funny) book about the place of mathematics in modern life and how mathematicians think about mathematics, I recommend The Pleasures of Counting by T. W. Körner.

http://www.amazon.com/Pleasures-Counting-T-246-rner/dp/05215...

This one is more challenging as to reading level and as to mathematical level than the recommendations above, but well worth having around the house.