Although we may want to pursue the wonder of the world and open the beauty of creation with mathematics, we often find ourselves in the weeds. We teach our children to identify numbers, patterns, and symbols. We teach them to compute sums and products as though the calculator didn't exist. In short, we teach arithmetic. Why do we place such an emphasis on teaching our children to do what a calculator can do?
The answer to this my friends, can be found in the hidden meaning behind the numbers. As Nicomachus so clearly tells us, "Any attempt at philosophy must start with these mathematical subjects. They are the bridges that take us from the sense and opinions to the mind and understanding, from the concrete and familiar objects to immaterial and eternal abstractions, form matter to soul."
From matter to soul... By starting our study of the world with arithmetic, we are leading our children from the concrete to the abstract, from the matter in front of us to the soul behind it. That addition problem isn't about creating a calculator out of our own flesh and blood, but rather about leading a child towards the creator.
These mathematical subjects that launch philosophy are the study of quantity through arithmetic and harmony, and the study of size through geometry and astronomy. Of these four, arithmetic comes first, because the study of harmony, geometry, and astronomy rely on the language of numbers. In arithmetic, we are not simply teaching children to compute, but rather to think, comprehend, and communicate in a celestial language.
According to Nicomachus, arithmetic is the study of absolute quantity. The truth behind the numbers existed long before we had a language to explain it. With arithmetic, we can begin to study the world of numbers.