Includes index.

Alcuin of York’s ninth-century book, titled Propositiones ad acuendos juvenes ('Problems to Sharpen the Young'), is not only a major collection of ingenious and challenging puzzles, constituting one of the earliest texts in recreational mathematics, but also a treasure trove of important notions in mathematics, some of which were original at the time, leading to further mathematics in subsequent centuries. This book presents, analyzes, and discusses each one of the 53 problems in Alcuin’s text in easy-to-follow language, distilling from them the main implications they have borne for mathematics generally and for math pedagogy in particular. Each of the chapters includes 10 exploratory puzzles that are based on Alcuin’s own problems, or else on the main mathematical themes discussed in a chapter. Overall, the intent is to show how Alcuin’s book exemplifies how mathematical thinking unfolds in its core, starting with a real-world practical situation, which is then translated into a problem, from which a pattern can be extracted and a relevant insight obtained. In effect, Alcuin’s book constitutes an original and inventive exploration of what mathematics is in its essence.