What is the Quadrivium and
Why is it Important?
The quadrivium includes the four mathematical arts of arithmetic, geometry, music, and astronomy. These were original proposed by Plato in the Republic dialogue. Both the mathematical content and the mode of study were important. He argued that mathematical study aided in the first steps of a philosopher-ruler's education, lifting our eyes from the world of bodily objects perceived by senses to another world of reality engaged with by reason. The final step, after mathematics, is the study of dialectic, or metaphysics; mathematics also lends aid to this higher study. These four mathematical topics engage with the topics of essence, measure, relation, and motion - although other framings have been proposed throughout history.
This page serves to give a brief synopsis of the topics of the quadrivium. We aim to update it periodically with more information regarding each of the topics below.
Arithmetic
Arithmetic is the study of number, or multitude, and is closer to number theory than elementary computation. It studies topics such as unity and multiplicity, odd and even, prime and composite. A foundational text is Nicomachus' Introduction to Arithmetic. The game Rithmomachia was designed to teach this art.
_Ex_Libris_rare_-_Mario_Taddei_jfif.jpg)
Astronomy
The quadrivial study of astronomy goes beyond the observation of celestial objects (though that is an important part) to analyze and reflect on their motions. For this reason it was also called 'Spherics' and makes use of spherical trigonometry as well as mathematical models of motion.
Geometry
Geometry is the study of magnitude, or alternatively the art of all thing measured. It comprises lines and figures, both curvilinear and rectilinear. The study of stereometry, that of (3D) geometric bodies is also sometimes included in this discipline. The standard text for study is Euclid's Elements of Geometry
A Brief(est) History
The quadrivium as an educational course begins with Plato's exhortation to study 'higher things'. It was formalized in late antiquity by various philosophers and received into the educational curriculum of the Christian church, both east and west. It's decline was complete in modernity.
Music
The quadrivial study of music classically includes harmonics, rhythmics, and metrics, in addition to reflections on the music of the spheres. Rather than the practice of music or music appreciation, this study asks fundamentally how things properly relate to one another and places an emphasis on the study of ratio and proportion.
Modern Mathematics?
The modern disciplines of algebra and calculus merit attention for their importance to contemporary mathematical education. Their engagement with the ordering and infinity of mathematical objects indicates a need for research regarding their importance for the quadrivium.