Here's my list; Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics - John Derbyshire ( some of it may be beyond a 15 year old, but then again ...) Fermat's Last Theorem - Simon Singh The Code Book - Simon Singh The Equation that Couldnt be Solved - Mario Livio The Golden Ratio: The Story of Phi, the World's Most Astonishing Number - Mario Livio Poincares Prize - George G Szpiro Four Colors Suffice - Robin Wilson Tracking the Automatic Ant - David Gale Finding Moonshine, A Mathematician's Journey Through Symmetry - Marcus Du Sautoy, Five Golden Rules - John Casti Labyrinths - Luis Borges -(not strictly mathematics - but there is 'The Unimaginable Mathematics of Borges Library of Babel' - William Bloch) The Tinkertoy Computer - A.K. Dewdney Cogwheels of the Mind, The Story of Venn Diagrams - AWF Edwards Flatterland - Ian Stewart, or any of his other recreational math books The Man Who Loved Only Numbers , The Story of Paul Erdös and the Search for Mathematical Truth - Paul Huffman Any/some of Clifford Pickovers books - If he or she likes art as well as maths; Tilings and Patterns - Grunbaum and Shephard MC Escher - Sandra Forty