Nicomachus

Nicomachus of Gerasa was a Neopythagorean philosopher and mathematician who lived in the Greco-Roman world of the first and second centuries AD. He came from Gerasa, today Jerash in Jordan, and is considered one of the key transmitters of Pythagorean thought in the imperial period. His reputation rests mainly on his treatises on arithmetic and music, which served for centuries as basic textbooks.

Little is known about his life with certainty. His Manual of Harmonics was written at the request of a noblewoman, which suggests he enjoyed some standing as a scholar, and in it he mentions frequent journeys that left him short of time. His approximate date is inferred from the authors he cites, such as Thrasyllus, and from later writers who refer to him. His main surviving works are the Introduction to Arithmetic and the Manual of Harmonics; of others, such as a Theology of Arithmetic or a Life of Pythagoras, only fragments and later summaries remain.

His thought places number at the centre of reality. He distinguishes between the purely intelligible number, which he regards as divine, and the number that measures material things. He argues that arithmetic comes before the other mathematical sciences (music, geometry and astronomy) and grounds them. The Introduction examines odd and even numbers, primes, composites, perfect and amicable numbers, but without abstract proofs: he states results and illustrates them with numerical examples, which sometimes leads to false claims. In the Manual he links music to the order of the universe through the harmony of the spheres and considers the role of ear and voice in understanding music.

His influence was considerable. The Introduction was used as a textbook in Neoplatonic schools, and Boethius translated and paraphrased it into Latin, keeping it present in medieval education within the quadrivium.