Arithmetic is the first of the mathematical arts and the first road of the quadrivium. All of the mathematical arts are extensions of logic. The powers of all the mathematical arts to form logical habits of the mind oriented towards reality cannot be overstated. Have you ever heard the question “when am I going to use algebra?” Well, that is the neat thing, algebra, geometry, arithmetic, etc. are all transcendently powerful and cause the one who studies them classically to become reasonable, logical, and on the way to wisdom. It is a faculty of freedom and gives the mind a lens to view the world. Arithmetic more specifically is concerned with the nature of numbers and their eternal relationships. It studies the kinds, forms, and representations of numbers. Arithmetic studies the relationships of these numbers through the various operations. So arithmetic in essence is the study of numbers and operations and displays the harmony of discrete quantities. The classical study of arithmetic should be a playful and wonder inspiring study.
Geometry is concerned with numbers in space and displays the harmony of continuous quantities. Historically, Euclid’s Geometry was the standard for the study of geometry for over 1000 years. Geometry in the classical tradition –aka Euclid’s Geometry –cultivates wisdom and virtue in the student by giving the student a geometric way of the seeing the world. This happens through a focus on proofs, first principles, and the ability to illustrate a mathematical concept artistically. In many ways geometry is the foundation for philosophy and theology.
Harmonics has to do with harmony in its purest sense. It is, in its simplest form, the study of numbers in time and displays the harmony of ratios and proportions. Harmonics can be closely related to the modern study of music theory. However, there are differences. The student who studies harmonics classically learns to see how all reality sings, in a sense. The interconnectedness of the physical and the unseen parts of creation are erringly apparent in the study of harmonics. The study of harmonics along with the study of the rest of the mathematical arts literally educates a student in the structures of reality.
Astronomy is the study of numbers in time and space. It is concerned with the harmony of shapes in motion. Jain and Clark tell us “The ancient Greeks attempted to understand the actual mathematical relationships among the heavenly bodies in terms of size, distance, and geometry.” Through the classical study of astronomy, every major scientific came to pass. This is not surprising since God made the skies rule over the earth. Untold and marvelous mysteries can be made known by looking at and studying the sky. Both in Romans 1 and Psalm 19, the scripture, tells us about how creation tells us mysterious about our God. The classical study of astronomy opens this up for a student who studies it and give the student an astronomical view of the world.
An Example of how this looks in the Homeschool:
I really believe it is the way you look at it and teach it. I am still learning so much about this. Therefore, ideally, we would teach math mimetically, engage the student socratically when needed, and keep the perspective that mathematics is about a lens for viewing the world. I know there is so much more than that, so let us turn our attention to some resources that can bring us all to the next level of understanding in this area.
Articles & Resources Related to the Mathematical Arts
Understanding Mathematics: From Counting to Calculus by Keith I. Kressin
Toward the Quadrivium: An Introduction by Classical Conversations (free video clips)
A Discussion on Arithmetic & Geometry by Classical Conversations
A Discussion on Astronomy by Classical Conversations
A Discussion on Harmonics by Classical Conversations
Beauty for Truth’s Sake: On the Re-enchantment of Education by Stratford CaldecottMathematics: Is God Silent by James Nickel