TITLE: Mathematical Advice for Interested Highschool Students
QUESTION [9 upvotes]: This may not be a research level math question, but I believe it is still relevant to Math Overflow.  

What general resources exist for students in highschool who are very interested in Mathematics?  What advice would you give to a young student to encourage them, and nurture their interest in mathematics?  If a young high school student came to you and said they were very interested in math, and wanted to know what to do to keep learning, what would you tell them?

Thank you for your help,

REPLY [6 votes]: There are two outstanding resources in English:
1. R. Courant and Robbins, What's Mathematics?, and
2. Hilbert, D. and Cohn-Vossen, S.
Geometry and the imagination.
Many of my friends (including myself) read these books in their high school years,
and decided to become mathematicians.