Gerbert of Aurillac at Reims: the abacus and the Hindu–Arabic numerals

Gerbert, born around 946 in Aquitaine, was a young monk of Saint-Géraud at Aurillac when Count Borrell II of Barcelona visited the abbey in 967 and, at the abbot’s request, took him to Catalonia to study mathematics. For about three years he studied under Bishop Atto of Vic, and probably also at the monastery of Ripoll; the Catalan counties, on the frontier with al-Andalus, were in touch with Arabic learning. Around 970 Borrell brought him to Rome, where he met the pope and Otto I; in 972 he came to Reims, and Archbishop Adalbero soon put him at the head of the cathedral school. He held the post until 989, apart from a short spell as abbot of Bobbio in the early 980s.

His pupil Richer of Saint-Rémi describes his teaching of the quadrivium: for astronomy Gerbert used spheres, among them an armillary sphere, and instruments fitted with sighting tubes, and to introduce geometry, as Richer puts it, he had an abacus made. A shield-maker built the board, divided lengthwise into 27 columns; on it Gerbert set out nine signs that could express any number, and he had a thousand counters of horn made in their likeness. Richer marvels at how quickly large numbers could be multiplied and divided on it; as modern historians explain, a sign’s value depended on its column, and an empty column did the work of zero. Rules for the abacus are attributed to Gerbert himself, and Bernelinus of Paris, probably his pupil, wrote a treatise on the abacus that survives in eleven manuscripts of the 11th and 12th centuries.

Historians identify the nine signs as forms of the “dust” (ghubar) numerals used in the Maghreb and al-Andalus — ultimately the Indian decimal figures that had spread through the Islamic world in the 9th century. In a Latin manuscript they first appear in the Codex Vigilanus, completed in 976 at the monastery of Albelda in La Rioja; from the 980s Gerbert used his position to make them known, and in 984 he asked correspondents in Catalonia — Lupitus of Barcelona and Bishop Miró Bonfill of Girona — for books on astrology and arithmetic. Yet the figures stayed on the counters: Gerbert’s abacus had no zero, and written calculation with Hindu–Arabic numerals spread only after the Latin translations of Arabic arithmetic in the 12th century and Fibonacci’s Liber abaci (1202). Later legend, recorded by William of Malmesbury, turned the learned pope into a magician who had learnt his arts from the Saracens.