History of mathematics education in Antiquity

International audienceA wide variety of documents relating to mathematics education in the Near East and the Mediterranean basin have survived to the present day. The oldest of these sources are the Southern Mesopotamian clay tablets produced in the third millennium before the Common Era. More recent sources were copied in the Byzantine Middle Ages from a long chain of texts which stem back to lost originals. Nonetheless, these late copies provide some evidence of educational activity and pedagogical orientation. As may be seen in the case studies in this chapter, these sources represent a wide chronological distribution but of diverse genres texts. Some texts, like the tablets made of nearly indestructible clay, survive in great numbers and enable a reconstruction of the mathematical instruction of ancient Mesopotamia. Excavations in Iraq, Iran, and Syria since the late nineteenth century have produced a sufficient number of tablets to permit a detailed reconstruction of the basic mathematics curriculum in the scribal schools of the Ancient Near East. Equivalent sources exist for the Greco-Roman world but in much lower numbers, and their state of preservation does not permit many conclusions. The Greco-Roman texts comprise small, disconnected fragments on papyrus, pottery, leather, and even wooden tablets covered with wax, all of which probably served in the teaching of mathematics. By contrast, relatively few texts of the copious Mesopotamian corpus report how the scribes in the Ancient Near East conceived of their work, their knowledge, and its transmission, whereas the Greco-Roman texts written on parchment generally resulted from endeavors in copying or translation and only marginally constitute direct evidence of scholastic activity. Thus, these later sources shed limited light on the practicalities of transmitting mathematical knowledge from master to disciple in different contexts and few of these texts detail elementary education. However, these sources do reveal the weighty didactic ideals of the Greco-Roman world which governed the prolific work in philosophy and rhetoric. In some cases, these ideals may be assumed to have been put into practice and corresponded to actual curricula, but this inference is speculative and probably useless. The evidence from Pharaonic Egypt represents a nadir of textual preservation and cultural reconstruction: although the series of problems found on ancient papyri probably served pedagogical purposes, the manner of instruction and the institutional setting in which these texts were used remain largely unknown.The following synthesis is therefore based on sources that are characterized by extreme heterogeneity in their nature as well as in their geographic and chronologic distribution. This fundamental fact should always be kept in mind to avoid anachronistic claims. The disparity of sources demands consideration of the varied and unevenly documented diversity of the educational settings and institutions of Antiquity. In other words, the ancient sources neither relate to the same environments nor do they refer to the same cultural and institutional codes. The available sources do not describe a complete or consistent picture of teaching mathematics in Antiquity, but spotlights may be focused on the better documented teaching contexts of Mesopotamia, Egypt, and Greco-Roman world. Even if this disparity limits our actual knowledge of ancient mathematical teaching, these difficulties highlight the fact that both the ‘positive information’ which we can claim to know as well as the kind of questions asked about ancient mathematical education depend strictly on the nature of the surviving sources