The teaching of mathematics in the Dark Ages.
After the fall of the Roman Empire, Europe went through a great decline in terms of knowledge and education. Most of this was due to the relative lack of peaceful times during which books and texts could be salvaged and copied. It is partly due to its geography that England seems to have lost less than the rest of Europe. Several of the Greek and Roman ideas of Education seem to be present, for example we know that Aldhiem who was born circa 639 had knowledge of Arithmetic, fractions, Astronomy and Astrology. It can also be seen in the 6th century work by Cassidorus, De Artibus et Discioplinis Liberalium Literarum that the seven Artes Liberales were known and used in education, now split up into the Trivium (Grammar, Rhetoric and Dialectic) and the more science based Quadrivium (Arithmetic, Geometry, Music and Astronomy). This educational course was introduced into the monasteries and its four subjects were certainly not taught everywhere, but only at the highest centres of learning.
By this time the Church was established in Britain and schools were being set up to further spread knowledge of the Christian faith. By the 9th century nearly all monastic houses had schools attached where the monks and friars trained the new members of the priesthood. Since this, and extending the monasteries' libraries, were more important than a general education for the populace the instruction received at most places was limited to reading, writing and Bible studies. Further studies, including parts of Mathematics were restricted to the great Cathedral schools such as that in York.
The Bishop and head teacher of the York school in 732 was Egbert. The curriculum under him included such diverse and advanced subjects as Rhetoric, Law, Physics, Arithmetic, Geometry, as well as the Easter Calculations, which were the mathematical limit at most smaller church schools, music and singing. One of the pupils at York was Alcuin, who was later asked by Charlemagne of France to move there and help set up a school of similar standards there.
The state of education in France had degraded to such an extent that Charlemagne, educated at court by the best the country could provide, wrote of his concerns of whether even the clergy knew enough Latin to be able to interpret the Bible and Scriptures correctly! In response to this need the Palace School was set up, with Alcuin as its master, and much work was done to improve the level of education available. Indeed, one of the pupils there, Rabanus Maurus, later set up his own school with an even broader curriculum than that favoured by Alcuin.
With the return of war and strife the level of education dropped again, and remained there until Gerbert, who later became Pope Sylvester II (999 AD) found mathematical texts including the work of Boethius. Boethius was one of the few Romans of the 5th century sufficiently interested in Geometry to leave texts behind him, and others detailing work done by Roman Surveyors. When Gerbert was raised to Pope, this discovery heralded a brief resurgence in interest in Mathematics within the Church, especially after he had written his own version. After this Boethius became one of the main sources of material for the Quadrivium.
The introduction of column calculation in the 10th century also helped, principally amongst the merchant classes. Unfortunately, in Britain at least, the position of the Church meant an increasing desire to rid the country of 'pagan' ways and ideals. This included the broad education that had been encouraged up until this point, and Mathematics and the other subjects in the Quadrivium fell out of favour.
Article by: J J O'Connor and E F Robertson based on a University of St Andrews honours project by Elizabeth Watson submitted May 2000.