A Little Quadrivium: Classical and Modern Foundations of Arithmetic, Music, Geometry and Astronomy

A Little Quadrivium revives the medieval fourfold path of learning — arithmetic, geometry, music and astronomy — and uses it as a living framework to explore how mathematical thinking was made, used and transformed across history. Rather than a conventional survey of formulas and techniques, the course treats the quadrivium as an intellectual toolkit: texts, instruments and experiments from antiquity and the Middle Ages sit side-by-side with modern formalisms (complex numbers, Fourier ideas, non-Euclidean geometry, relativity and contemporary astronomy) so students can see continuities and ruptures in how people have measured, ordered and understood the world.

By the end of the course students will have practiced several optics for reading the world: historical texts and hands-on experiments, conceptual translation between classical and modern languages, and a habit of treating mathematics as a human, creative, and historically situated activity. These new lenses are meant to enrich not only students' technical understanding but also their ability to read mathematical ideas where they appear in art, culture and science.

Why you can never build a perfect music system; how the Pythagorean theorem connects to time dilation; how to study "diabolic" numbers without attracting the attention of the Holy Inquisition; and why chasing turtles is actually worth your time — all this (and more) is in the course!