By Jens Høyrup
Handbook on History of Mathematics Education, edited by Gert Schubring and Alexander Karp (2012)
Introduction: By lucky but adequate accident, “the Middle Ages” have become plural in English. The millennium that separates the deﬁnitive demise of the Western Roman Empire from the discovery of the New World and the Reformation can hardly be understood as one homogeneous period under any point of view – and certainly not if we look at mathematics education.
The earliest phase, lasting until c. 750 CE, is known as “the Dark Ages” – both because surviving sources for this period are rare and because this rarity reﬂects a very low intensity of literate culture. During the ensuing “Central Middle Ages” (c. 750 to c. 1050, the epoch of Charlemagne and the Ottonian emperors), attempts at statal centralization led not only to creation of the cathedral school system but also to corresponding developments of monastic learning. The High (c. 1050 to c. 1300) and Late (c. 1300 to c. 1500) Middle Ages are characterized by the rise of city culture, which led to the emergence of the university system as well as to the appearance of institutionalized lay education – connected to but not identical with the Renaissance current.
In principle we should also distinguish between partially or fully separate types of education – that of the Latin school and university tradition, and those of various kinds of practitioners. Among the latter, however, only the education of Late Medieval merchant youth is well documented in sources – for that of craftsmen we have very little evidence.