I’ve always loved mathematics, so I was pleasantly surprised when Satyan Devadoss and Matthew Harvey’s new book, Mage Merlin’s Unsolved Mathematical Mysteries (MIT Press, 2020: Amazon US / Amazon UK), arrived in the mail recently. These mysteries consist of sixteen unsolved mathematical conundrums, each of which is “a sword in the stone waiting for someone to draw it out”, presenting a riddle “that no mathematical wizard has yet overcome”. Some of these mysteries are well-known, such as the Goldbach Conjecture, whilst others are relatively obscure, but certainly no less captivating to contemplate. The basic mathematical ideas have been elegantly reframed into captivating puzzles like Lancelot’s labyrinth, The Great Hall Window, and Round Table Tiles, and that involve solving simple physical puzzles like gift wrapping a package, perfectly slicing a cake at a festival, and designing a mirrored vault for the Holy Grail. The authors present each puzzle in a fun way that is easily understood and tested by anyone with only basic mathematical knowledge. The lavish illustrations are colorful contributions that make it easy for the reader to understand at a glance the precise nature of the problem they are being asked to solve. Even more appealing, these mysteries are presented to the reader by a fictional narrator, Mage Maryam, who weaves these puzzles into an enjoyable story that her distant ancestor, Merlin the Magician, recorded in a notebook. (Mage Maryam is inspired by real-life maths genius, Iranian-born Maryam Mirzakhani, the only woman to win the Fields Medal — nicknamed the “Nobel Prize of mathematics” — before her life was tragically cut short by cancer.) This unique book will charm and delight mathematical explorers of all ages with its beautiful illustrations, captivating story, and unsolved mathematical challenges that range from geometry to number theory and more.