# Quadrivium: the noble fourfold way to an understanding of the universe

## That’s Maths: Plato saw the value of arithmetic, geometry, music and astronomy

According to Plato, a core of mathematical knowledge, later known as the quadrivium, was essential for an understanding of the universe. He outlined the curriculum in his Republic. Quadrivium means four ways, but this term was not used until the time of the Roman philosopher Boethius, in the sixth century. It is said that an inscription over the entrance to Plato's Academy, in Athens, read "Let None But Geometers Enter Here". This indicated that the quadrivium was a prerequisite for the study of philosophy in ancient Greece.

The quadrivium originated with Pythagoras around 500 BC. The Pythagoreans sought the unchanging fundamentals underlying nature and society. Their quest was to find the eternal laws of the universe; the quadrivium became the name of the scheme they organised their studies into.

It arises from number, the subject revered by the Pythagoreans, and comprises four disciplines. The first is arithmetic, concerned with the infinite linear array of numbers. Moving beyond the line to higher-dimensional spaces, we have geometry. The third discipline is music or harmony, which is, fundamentally, an application of the pure science of numbers evolving in time. Fourth comes astronomy, the application of geometry to the world of space.

Arithmetic studies numbers, music the relationship between numbers and time, geometry magnitudes, and astronomy those magnitudes' distribution in space

Pythagoras distinguished between quantity and magnitude. Objects that can be counted yield quantities or numbers. Substances that are measured provide magnitudes. So cattle are counted whereas milk is measured. Arithmetic studies quantities or numbers; music involves the relationship between numbers and their evolution in time; geometry deals with magnitudes; astronomy deals with those magnitudes’ distribution in space.