Obviously, this question is not a research level mathematics question at all. But, I've just met an extremely mathematically talented $11$ years old student and I don't know how I can help him. For years I was working at a special school for young gifted and talented students. But, I had never met such talent at such a young age in my life. I talked to a mathematician friend of mine (who himself was an IMO gold medalist at a very young age), but he had no idea unfortunately. Basically, there is no one around with any idea. That is why I came to MO. Just in case that this question gets closed please e-mail me at asghari.amir at gmail if you have any idea.
Hmm. I was that kid. I was/am very strong in math. I was in a very strong gifted program from gradeschool to high school. I went through various Academic Olympiads. I have a trophy where I was the second best HS kid in Chicago one year...

Why second? Because I didn't try. I didn't like trying. I flunked several classes in HS and college. I have severe anxiety at times, though getting better - a very supportive wife makes me wonder what I could have done if I dealt with anxiety sooner. My parents both had anxiety and depression. There were other home issues that made me more anxious and made "success" not that important. I read everything I could find, but the things I was supposed to read. No risk of judgement there.

My point being, all the books you could give me wouldn't have helped. My issues were mental, and some of safety. If you want this kid (or any kid for that matter) to reach their full potential, issues of mental state, safety, even food and shelter may be more important than any books you could give them. I'm not saying this person has my rollup of stuff, just to be aware that there is a lot more out there than access to contests. With the Internet, access to learning materials is 1000x easier than when I was that age, so your help will be even more needed on the mental side.

One big thing I forgot to add is - struggle, and how to deal with "failure". Though learning how to push through is hard for everyone, a smart kid has a lot of expectations on them. Help them deal with not getting it right the first time. The confusion of "this is normally so easy". Help them with patience to work it through, to not get frustrated or quit because something is hard for once. That's probably the lesson I most wish I learned earlier.
