Education changed in the central middle ages. While the arts of grammar, rhetoric, and dialectic continued to be taught as the foundation of all learning, the quadrivium, the four disciplines of number—arithmetic, music, geometry, and astronomy—received new emphasis. Some of the greatest minds of the era, among them Gerbert of Aurillac (later Pope Sylvester II; c. 940–1003) and Abbo of Fleury (c. 944–1004) gained renown for their numeracy. Teachers both, they educated many of Europe's future abbots and bishops, emperors and administrators, and authored didactic works on calculation, time-reckoning, geometry, and music.
Gerbert and Abbo drew their knowledge of number from late antique and early medieval tracts by such figures as Calcidius, Boethius, Martianus Capella, Macrobius, and Bede. Copied and recopied, the texts of these earlier authors changed little, but the pictures underwent alterations that suggest a significant shift in use and an upsurge in interest. Tenth- and eleventh-century makers of manuscripts provided pictures to elucidate textual passages that made no mention of them; where pictures were an organic part of the tract, they often added more. They experimented with placement, scale, color, and contours in ways that suggest a keen awareness of contemporary notions of materiality, sight, and the limits of representation that were themselves the product of explorations in the domains of mathematics and science.
Picturing Number in the Central Middle Ages contributed to the study of medieval image theory, drawing on visual and textual material from quadrivial manuscripts, evidence that permits investigation of period-specific notions on a range of integrated issues: the relations and tensions between word and image, the nature of cognition, and modes of representing both the sensible world, and that which was considered to be beyond the reach of the senses.