10 - Nicomachus

Summary

Nicomachus belongs to roughly the same period as Adrastus and Theon. His exact dates are not known, but he was probably active around the beginning of the second century a.d. About his life the only clear fact we have is that he was born in Gerasa (even that is more problematic than it might seem, since there were several cities with that name). He drops a few autobiographical hints in the essay translated here, but they add up to very little. The work for which he is best known is his Introduction to Arithmetic. Though modern commentators agree that it shows him as no more than a second-rate mathematician, the book is a useful compendium of Greek studies in number theory. Through a Latin translation by Apuleius in the second century a.d., it became the Romans' principal source of knowledge about Greek achievements in this field. Among Nicomachus' other writings were an introduction to geometry and a biography of Pythagoras; both are lost. He also wrote a treatise called Theologoumena Arithmeticae (‘Theology of Number’) of which we have only a cursory summary by Photius, but an anonymous work with the same title survives, much of which is certainly derived from Nicomachus. His essay was evidently an elaborate presentation of Pythagorean theories about the symbolic and mystical significance of numbers, such as are set out much more briefly in 12 Arist. Quint. De Mus. Book III ch. 6.