From a review of A Brief Quadrivium and Teaching the Quadrivium: A Guide for Instructors originally published in Principia 3, no. 1 (2024)
Classical educators know that the canon of the liberal arts numbers seven, but very few of us make much progress beyond the trivium before we jump headfirst into philosophy. We approach advanced mathematics through the modern canon of algebra, geometry, trigonometry, and calculus, not the four arts of the quadrivium—geometry, arithmetic, music, and astronomy. Even the one common term, geometry, means different things. For most of us, it is something like applied algebra. The minority who have gone through Euclid will know that the classical art of geometry uses no numbers at all, only proportion. If we have some direct knowledge of the quadrivium this is only very rarely because we studied them as they are. We tend to learn about them, presenting them either as primitive (and therefore obsolete) forms of the STEM fields, or as a few wonder-inspiring 
diagrams of the golden ratio projected onto the masterpieces of the Old Masters sandwiched between sessions of mathematics classes hardly distinct from those offered in non-classical educational settings—two excellent starting places are Gary B. Meisner’s Golden Ratio and Mirana Lundy’s Quadrivum. In the end, if the quadrivium enters into our thinking or our teaching, it is at second or third hand, and we and our students at best come to appreciate its historical presence in the past of Western culture without acquiring the intellectual character or skills that would enable us to use the quadrivium productively in our own attempts to make the world more beautiful.
This is due to reasons both theoretical and practical. Many who would never question the enduring value of the arts of grammar, logic, or rhetoric struggle to see how the historically constructed quadrivium could be of any more than historical interest to contemporary educators. A deeper problem is that since antiquity these arts have been debased and abused, such that Latin dictionaries list “astrologer or wizard” as the second definition of the noun mathematicus. For such reasons, Plato’s Timaeus and Boethius’ De Arithmetica tend to be reserved for those undertaking advanced studies of those authors, and the immense influence exerted by these texts on Western culture is often presented as a curiosity or problem rather than as a fact whose recovery might lead to fresh insight in the present.
But what if contemporary students went beyond learning about the historical importance of the quadrivium and learned the content and skills embedded in study of the quadrivial subjects? While many of us make verum, bonum, pulchrum our motto, few of us are prepared to give any account of the final term. The classical education movement has recovered and redeployed the arts of language, showing that logic can still be used to gain certain knowledge of truth and that virtue ethics can still be a means of knowing and doing the good. Despite our recovery of the arts of language and our confidence in their ability to give us access to reality, many see beauty as being in the eye of the beholder rather than being a transcendental susceptible to objective analysis and real knowledge. Writers such as Stratford Caldecott and David Clayton have pointed to the quadrivium as the traditional means of setting the third transcendental, beauty, on an objective basis from which it can be contemplated, known, imitated, and produced.
It comes as no surprise that our inability to accommodate pre-Copernican astronomy and pre-Cartesian mathematics (with the notable exception of Euclid) to our narrative of scientific revolution and progress has not led many of us to develop classroom resources that would give our students access to these traditions and help them develop the skills the arts promise to impart. Green Lion Press, whose edition of Euclid is no doubt well known to many readers of Principia, follows a grand narrative of the “Scientific Revolution” to a great extent in their offerings, providing the text editions that make it possible for students in great books programs to re-create the discoveries of Kepler, Newton, Lavoisier, and Faraday. When I met Howard Fisher, an associate editor at Green Lion Press, I asked him why they do not offer editions of Aristoxenus, Boethius, or other “quadrivial” authors. He told me there is no editorial policy against it, and in fact, they would if they could. The problem, he said, is a lack of editors. Would I like, he added, to try my hand at doing it myself?
Fortunately for me, a humanist who has not yet mastered the arts of number, Peter Ulrickson has provided the sort of book I have long imagined but not had the skill to write. A Brief Quadrivium divides the four arts into a thirty-week curriculum, distributed approximately equally across geometry, arithmetic, music, and astronomy, ending with three brief chapters that consider the quadrivium’s relationship to modern physics, mathematics, and music theory and its propaedeutic role in “preparing us to seek the highest, unchanging things.” Upon completion of the curriculum, students will not only have been exposed to wonder, but they will also have laid the foundation of a detailed, technical knowledge of the quadrivium that they can use both to understand the nature of reality and to produce works of art, in the Aristotelian sense, imitating nature to bring order to chaos and instantiate beauty in the world.
A key component of Ulrickson’s presentation is the continuity of the quadrivium and the trivium as two parts of a whole, as opposed to the modern division of the disciplines into arts and sciences. An excellent example of this in practice is Ulrickson’s gentle but persistent and effective explanation and use of technical terminology. Relying on a philosophy of language based in Aristotelian ideas that recognizes the adaequatio of words, concepts, and things and the status of each of the components of the quadrivium as stable and articulated technai, Ulrickson provides readers with an account of terms like “definition,” “lemma,” “proposition,” and “conjecture” and encourages them to build up familiarity with them. Those who, like me, have made the transition from “literary studies” to the “trivium,” who have come to appreciate the precision that training in the arts of language can bring to conversations about the great ideas, will be pleased to ground their developing knowledge of the quadrivium in this system of language. Properly technical language is not jargon; it is rather a key constitutive element of the knowledge and practice of the art, and Ulrickson presents this in a compelling way that will resonate with classical educators.