Ireland's contribution to modern science is well attested, yet it is not so well known that Ireland, famed for over half a millennium for its saints and scholars, was equally renowned for the scientific endeavor carried out in its monastic schools. Nor is it generally appreciated in wider historical debate that the principles of scientific discovery - observation and analysis - flourished in early medieval Ireland. This book addresses that lacuna. For the first time, international experts introduce and explore the history of mathematics in medieval Ireland - its reception, philosophy, and the contribution made by Irish scholars to the development of science in Ireland and Western Europe. Medieval mathematics comprised the quadrivium of arithmetic, music, geometry, and astronomy, and it is no accident that the period of Ireland's great artistic achievements - such as the Book of Kells and sculptured crosses - occurs when mathematical skills merge with artistic expression. Contents include: saints, scholars, and science in early medieval Ireland * Boethius in early Ireland: five centuries of study in the sciences * seventh-century Ireland: the cradle of medieval science? * Cummian's letter: science and heresy in seventh-century Ireland * music and the stars in early Irish compositions * when art was informed by mathematics * clocks and guns: observations on medieval science and technology * the heavens, earth, and imagined lands: an introduction to the medieval medical and astronomical resources of the Royal Irish Academy (RIA) library.