This book is a textbook on mathematics from around the year 100. It was not renowned for its originality - rather, the book was famous in antiquity and in the middle ages for being a useful primer covering the mathematical knowledge of its time.I am no mathlete, and Ill admit some of the esoteric concepts and convoluted proofs that Nicomachus throws out there made my eyes glaze over. For me, the more interesting aspects of this book concerned Nicomachus philosophy. Nicomachus was a Neo-Pythagorean who embraced a mystical, symbolism-heavy view of numbers and mathematics. Most of his thoughts about philosophy are outside the scope of this book, but the Introduction will occasionally allude to them. Nicomachus subscribed to the Platonic idea of eternal forms, with the wrinkle that numbers are a superior kind of form out of which the other forms are made and under which they are classified. Numbers are the highest forms and the properties seen primarily in them are also the essential properties of things in the world, conferred upon them by number. The “scientific” numbers (the numbers we deal with everyday on earth) are related to, but not identical to, the ideal “platonic” numbers. This philosophy led its practitioners to search for all kinds of meaning in numbers. They believed that through mathematical proofs, they could uncover universal truths - the number seven was associated with the leader of the universe, odd numbers were considered male and even numbers female, etc. This attitude towards mathematics persisted for centuries, at least among certain factions, but frankly it is hard for me to really grasp the rationale behind it. To modern minds, all of the time and energy spent on proving these mystical numerological proofs seems pointless. This book gave me a little bit of insight into how Nicomachus and the thinkers who followed in his footsteps thought about numbers, which was interesting at times. But I have no idea who I would recommend this to, other than specialists interested in the history of mathematics (and even then, this probably takes a distant backseat to Euclid). I dont know how to even begin to rate this one, so Im just going to give it a pass. A strange little book that opens a window onto an even stranger way of viewing the universe.