This chapter comprises two parts. The first addresses the physical natural and social function of archaic and classical Greek roads. Of key importance is the fact that ancient Greek roads were not paved on the surface of the earth but were ruts inscribed into it; when a vehicle set out on such a road, it was thus locked into these ruts as a tramcar is locked onto its tracks. I gesture towards the bearing that this will have on Parmenides’ use of road imagery to develop and articulate a notion of what we would call logical necessity. The second half of this chapter examines the semantics of the word hodos. Notably, the word can signify both an object (especially the rut road just discussed) and an activity. This activity is teleological, a characteristic I explore in terms borrowed from discussions of linguistic aspect and the Kenny–Vendler typology of situations; I conclude that the activity signified by the word hodos is a kind of accomplishment in that it is both durative and telic. Exploiting the two meanings of hodos and harnessing the distinctive features of each, Parmenides imparts a distinctive shape to his ‘Route to Truth’ and endows it with specific qualities characteristic of what we would call an extended deductive argument and a demonstration

Part I addressed counting as a means of interrogating the relationship between poetic content (the ‘stuff’ that a poem contains) and the space that is needed to express it. There I demonstrated that counting had an important role to play in poetic criticism of the Hellenistic period and that later poets were aware of this, incorporating and developing counting criticism in their own programmatic poetic statements. In early mathematical education, after counting there came more complex operations: multiplication, but also calculations that in modern mathematical notation would be written as equations and solved algebraically. These mathematical procedures today form part of arithmetic. The focus of Part II is thus on how the ‘stuff’ of poetry is expressed and arranged so as to require an arithmetical interpretation and solution.

Saying things takes time; writing things takes up lines. There is always a connection between the length of a verbal utterance (in time when spoken and in space when written) and what it seeks to describe. There is a certain connection between form and content. In the terms I will be using throughout this book, it is a relationship (as yet undefined) between poetic extent and poetic content. How was this relationship perceived in Graeco-Roman antiquity?

Rather than re-counting the arguments of the individual chapters in concluding this book, I want to return to the wider perspective of number in relation to poetry. From the preceding chapters there emerge three strands which are worth crystallising explicitly.

Archimedes’ Cattle Problem is an early, extended and complex case of a poem seeking to interlace arithmetic and aesthetics, but it is not the only case. The focus of analysis in this chapter are the so-called arithmetical poems preserved in Book 14 of the Palatine Anthology (henceforth AP). They similarly challenge their readers to solve the outlined simultaneous equations, and this time, all the arithmetic is solvable. The poems constitute an odd collection: their authorship, date and purpose are all contested. AP 14.116–46 in the modern numbering are a collection of arithmetical poems, which are preceded by a collection of riddles (AP 14.14–47, 52–64, 101–11) and oracles (14.65–100, 112–15, 148–50). The arithmetical poems are attributed to one Metrodorus, whose identity is difficult to ascertain. There seems to be no consensus as to whether Metrodorus should be thought the author or the compiler of the collection. Poems 14.1–4, 6, 7, 11–13 and 48–51 are also arithmetical in nature, and there is evidence that some of them are part of the Metrodoran collection.

This book explores Graeco-Roman poetry’s engagement with and use of numbers. What I mean by this can best be explained by turning to Homer’s self-presentation in the Iliad, where the matter of enumeration intersects with the question of poetic expression.

Chapter 1 analysed Callimachus’ explicit rejection of counting as a form of poetic criticism and traced out the responses to that intervention in subsequent Greek and Latin poetry. Where Callimachus had sought to introduce a poetics that does not require numerical measurement since it focuses instead on the sophia – the sophistication – of the poem, later poets nevertheless found it necessary to address counting forms of criticism alongside an emphasis on their own slender poetry. Against the backdrop of Chapter 1’s diachronic study, this chapter examines in details the output of a single Graeco-Roman poet of the mid-first century ce and his engagement with counting as a form of poetic criticism: Leonides of Alexandria and his isopsephic epigrams.