I want to make a few quick points.

First, I think that at the high school stage it is really crucial for a motivated and talented student to have a healthy balance between learning something meaningful (i.e. not get stuck in difficult toy problems leading nowhere) and actually attempting problems where he or she can make some visible progress (i.e. not just reading advanced textbooks but seeing that new things learned can be applied to prove something new and reasonably exciting).

Second, and this is based on the way I brought up as a mathematician, I tend to find a problem-based approach to learning more exciting, though of course there are people who learn in a different way. One great instance of a book which is based on this approach, and is free of two potential threats I mentioned above is "Abel's Theorem in Problems and Solutions" by Alekseev (there is both an "official" English translation, and some translation freely available online, I am not in the position to compare them at the moment). This actually, I believe, is an outstanding choice of a book for a talented high school student to work through.

Third, and this is something much more subtle, however exciting it is to do this mentoring job, it is important to remember with what level of responsibility it comes (which I am sure you know!). By the very nature of maths it is very easy to get depressed because of not having any visible outcome of what you are doing, even though on some level progress is being made. It is very important to detect such situations and do something about them.....

I want to make a few quick points.

First, I think that at the high school stage it is really crucial for a motivated and talented student to have a healthy balance between learning something meaningful (i.e. not get stuck in difficult toy problems leading nowhere) and actually attempting problems where he or she can make some visible progress (i.e. not just reading advanced textbooks but seeing that new things learned can be applied to prove something new and reasonably exciting).

Second, and this is based on the way I was brought up as a mathematician, I tend to find a problem-based approach to learning more exciting, though of course there are people who learn in a different way. One great instance of a book which is based on this approach, and is free of two potential threats I mentioned above is "Abel's Theorem in Problems and Solutions" by Alekseev (there is both an "official" English translation, and some translation freely available online, I am not in the position to compare them at the moment). This actually, I believe, is an outstanding choice of a book for a talented high school student to work through.

Third, and this is something much more subtle, however exciting it is to do this mentoring job, it is important to remember with what level of responsibility it comes (which I am sure you know!). By the very nature of maths it is very easy to get depressed because of not having any visible outcome of what you are doing, even though on some level progress is being made. It is very important to detect such situations and do something about them.....