The Roman educational system was very similar to the Greek's, but the emphasis on what should be learnt and why was very different. Roman children were taught at home until about the age of twelve, and probably learnt similar things to the Greeks, letters, music and, at this stage, a greater proportion of elementary Arithmetic and counting, using both the abacus and their fingers. At the age of twelve the boys would then progress to a school of Literature where they would learn Grammar and elements of Logic, Rhetoric and Dialectics. As with the Greeks, many Romans would learn little more of Mathematics than what they acquired from their lessons at home unless required by their occupation. This was not always the case, however, and boys would often also attend lessons given by a special Mathematics master. This, for purely practical reasons, would be taught through several examples and was heavily calculation based. The Roman who sought to learn more than this small measure was indeed the exception rather than the rule.
The Roman attitude of utility and practicality is seen in Quintilian's work where he recommends that Geometry is to be studied for two reasons. The first is that the mental training developed by the subject through the logical progression of axioms and proofs is vital, and the second is that its usage in political discussions, questions on land-measurement and similar problems is very important. Sophists employed here would be more likely to teach their students the art of speaking, Oratorio, and of current affairs than advances in science and Geometry.
During this time many other texts were written recommending various educational courses for those in the middle and artisan classes, as well as the ruling class. For example Vitruvius, writing for architects, suggests that his students should include in their general education knowledge of Geometry, Optics, Arithmetic, Astronomy, and others (Law, Medicine, Music, Philosophy and History). Galen recommends to prospective doctors in the 2nd century that they should have studied such varied subjects as Medicine, Rhetoric, Music, Geometry, Arithmetic and Dialectics, Astronomy, Literature and Law. And there are others, Varro and Seneca are just two who also recommend Geometry and Arithmetic as being necessary. Boethius used his literary talents in writing and translating Greek texts into Latin. His understanding of mathematics was rather limited, however, and the text he wrote on arithmetic was of poor quality. His geometry text has not survived but there is little reason to believe that is was any better. Despite this his mathematics texts were among the best available to the Romans and widely used.
From the above comments it can be seen that, although Mathematics in education was often frowned upon, it must have been taught where it was necessary. The low opinion of Mathematics is probably due in part to the professions which required mathematical or scientific learning. These professions were generally considered 'illiberal' and were looked down on. Those requiring an advanced level of Logic, Rhetoric and Oratorio were far preferred. This attitude is reflected in those found in Britain throughout the Mediaeval and Renaissance years, and it is only recently that this has been changed.
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.