What is the quadrivium?

The liberal arts have traditionally been divided into seven disciplines. Four of these disciplines are mathematical and are called the quadrivium. These four are arithmetic, geometry, music, and astronomy.

(The other three liberal arts are verbal and are called the trivium. They are grammar, logic, and rhetoric.)

Is the quadrivium obsolete?

No. The quadrivium has enduring value. It deserves our attention today.

What is the purpose of A Brief Quadrivium?

Learning mathematics is a challenge. Ancient mathematics presents special difficulties. Our ways of speaking and writing change, and new developments can seem to displace older ones entirely.

A Brief Quadrivium is a careful synthesis of the ancient sources of the quadrivium by a professional mathematician. It offers the enduring contributions of authors like Euclid, Ptolemy, and Boethius in a usable form that makes their beautiful ideas intelligible to the ordinary student today.

One practical difficulty in attempting to study directly from ancient sources is that there are no exercises. There are simply results. For the teacher or parent this means that there is more work, more confusion. What is the student supposed to do? You are left to answer that question yourself.

In A Brief Quadrivium you find a careful sequence of exercises that teach students to reason and explain as mathematicians. The exercises are not obscure ways to test for cleverness and tricks. Instead, they build knowledge and confidence through moderate, increasing depth that is always proportioned to the learner.

What is the purpose of Teaching the Quadrivium?

The guide for instructors, Teaching the Quadrivium, has a couple of purposes.

One purpose is practical. The book lays out a daily schedule for completing the study of A Brief Quadrivium in the course of a single academic year. This schedule includes a plans for daily reading and for completing the textbook's exercises. There are also recommendations for how to assess students each week.

A second purpose is more scholarly. Teaching the Quadrivium presents a series of essays that are coordinated with student work. These essays are designed to give instructors insight into the history and philosophy of mathematics and mathematics education, and present connections between the quadrivium and modern mathematical developments.

What's next?

If you are ready dive in, you can buy the books. If you would like to learn more about the quadrivium, you can read more in the collection of essays available here. If you would like to speak with the author, please get in touch.