The first three liberal arts focus on language and literature. We spend the vast majority of our years learning to read, write, and speak. Then come with the quadrivium. The mathematical arts as it were, arithmetic, geometry, harmony, and astronomy. Nicomachus tells us that the last three arts, geometry, harmony, and astronomy flow out of the first. Arithmetic gives us the tools to understand and explore the mathematical arts, as grammar gives us the tools to explore language.
In primary and secondary school we practice scholé and leisure in the three R's, reading, writing, and arithmetic. The primary reason for this should appear obvious now that we know Nicomachus. However, we still struggle to connect the importance of language with the importance of mathematics. The importance of learning to read, write, and speak is obvious to most everyone, but the importance of arithmetic is less so. Is there a great divide between the first three liberal arts and the last four? Do our minds struggle to jump the chasm? In a modern world full of computers and technology many students challenge the tedious tasks of learning to manipulate quantities. They are right to do so, for while the mathematics begin with arithmetic, they don't end there. Arithmetic is the beginning of the study of the natural world. This general revelation was given to us in the created order and our ability to understand it is rooted in the mathematical arts. When our students challenge the mundane mathematical assignment of computation we need to be prepared to show them the beauty that this truth is leading toward. Just like a parent will teach grammar to an elementary student, but not neglect to read the great books to the student, we need to spend time practicing the art of arithmetic while also thinking about and admiring the beauty.
Let's explore how to do this over the next few weeks as we focus on a few key questions:
- What are the mathematics?
- Why do we study them?
- What makes a mathematician?