This first week in school, the high school students and I began our journey into another old math text. Last year, we worked through part of Elements by the Greek mathematician Euclid. This year, we’re studying a book called Introduction to Arithmetic by another Greek man named Nicomachus. Elements was important to the Western world because it was the most influential geometry book in history. Nicomachus’ Introduction to Arithmetic, while it wasn’t as influential over nearly as long of a time as Elements, still did for numbers what Elements did for geometry: it laid invaluable groundwork for the future of mathematics. That is to say, it laid invaluable groundwork for us!
The history of math teaches us that mathematics is not just a collection of arbitrary methods of calculation wrapped up in a textbook; in fact, it’s really not that at all. Mathematics is, first and foremost, the art of knowing the beauty and order of creation through number. As Nicomachus states, number is “in the mind of god.” Unlike Nicomachus, who was influenced by a pagan math cult, we know exactly who this God is through Christ. Number is inherent in the way Christ holds the universe together, so to know what numbers are (not just how to use them or why to use them) is imperative for a Christian mathematics education. Math textbooks are great for a structured understanding of the current body of mathematics, and they provide number skills important for everyday life and for mathematical occupations. But math textbooks also necessarily obscure the “what” of mathematics to accomplish those ends. Historical math writings like Euclid’s Elements, on the other hand, exist within math history—a history which is, unlike textbooks, messy and unfinished. But historical math writings are also where the “what” of mathematics is tackled head-on. And when we see the giants of mathematical history deal with the big “what” questions in math, we learn how to better understand the answers ourselves.
Introduction to Arithmetic is one such writing: a treatise on what numbers are, how they interact with each other, and how they are an integral part of creation. It delves into mindblowing patterns in numbers and leaves you looking for more. It brings some familiar math concepts to the table, but it often turns them at a strange angle, forcing you to see them in new ways.
This writing is also a gold nugget for students in particular, because it lays out mathematical concepts plainly without assuming much about the reader. Many other primary math writings get extremely complex and contain intricate proofs that require mathematical understanding higher than a high school education. Not so with Introduction to Arithmetic! Even in unabridged form, Nicomachus’ work is quite accessible, especially with the guidance of a teacher. That makes it the perfect window into the minds that formed the math we know and use today. I’m looking forward to reading through it with the high schoolers this year!
In Christ,
Mr. Hahn
