The Greeks lumped the Quadrivium (arithmetic, geometry, astronomy and music) together under one titled subject called “mathematics.” Christians study mathematics because it develops virtue of the mind (not sure what that means). Perhaps it means what Plato was after, the mind leading toward pure reason and a love of wisdom. It is the belief that pure reason and love of wisdom leads to objective truth known. All of this is in opposition to a practical approach to mathematics (“when are we going to use this?”) The Incarnation grants the Christian freedom to pursue mathematics because of a greater appreciation for the created order. The authors believe that education should incorporate both the formative and the practical. The goal for the Christian using mathematics is wonder, work, wisdom and worship.
Arithmetic- What is missing in modern texts is a recognition that numbers are transcendent and can lead to wonder. The fact that unity and plurality can exist at the same times leads us to truths of the Godhead.
Geometry- Tools such as propositions and proofs in Euclid’s geometry give students the ability of how to think not just what to think. A base of Euclid’s geometry is deductive proofs. Geometry should be seen as a next step after arithmetic as it naturally flows and is the starting point of algebra.
Astronomy- Time keeping and navigation were essential parts of living in ancient days. The stars were thought to reveal patterns to deep mysteries of the universe. A grasp of geometry was essential to the discipline of astronomy. “The method of astronomy is mathematical empiricism.” Astronomy helped birth modern science.
Music- It is the chief are of the Quadrivium. Music of the world and music of humans. Rather then explain what music is in the quadirivium the authors get very excited about how it can be found in the other three disciplines. They also see music as helping the mind comprehend infinitestimals but fail to explain why that is important.
Brining back these disciplines is believed to foster greater wonder, work and wisdom and worship.