Nicomachus of Gerasa was a Greek mathematician and music theorist who lived during the 1st or 2nd century CE in the Roman Empire. He came from the city of Gerasa, in modern-day Jordan. Very little is known about his personal life, but his writings identify him as a follower of Neopythagoreanism, a philosophical movement that revived the ideas of Pythagoras.

His two major surviving works are the Introduction to Arithmetic and the Manual of Harmonics. He also wrote other texts, including a Life of Pythagoras and a Theology of Arithmetic, but these are now lost and are known only from references by later authors.

Nicomachus’s historical importance stems from his role as a key transmitter of Pythagorean thought. According to modern scholars, his Introduction to Arithmetic was not a work of advanced mathematics but a systematic textbook on number theory. It classified numbers—such as even, odd, prime, and perfect numbers—and explained the mystical properties Pythagoreans attributed to them. This book became a standard text for over a thousand years, profoundly influencing later Neoplatonist philosophers and, through a Latin translation, medieval European education. Similarly, his Manual of Harmonics was a foundational text on the Pythagorean theory of music, focusing on the mathematical ratios behind musical intervals and their connection to cosmic order. His descriptive, philosophical approach helped shape the medieval understanding of the core mathematical arts.