Writing Practical Mathematics in Greek and Roman Antiquity

Abstract

Recent years have seen increasing interest in the historiography of mathematics outside the canonical texts. In the case of ancient mathematics preserved from classical antiquity, this has included a focus on reading texts as evidence for mathematical practice, and attempts to place them in their socio-historical context. This thesis aims to explore how mathematical knowledge was presented, organised, and adapted to its function in applied contexts in Greek and Roman antiquity, through four interlocking case studies: architecture, land surveying, ‘practical geometry’ in Greco-Roman Egypt, and mathematical geography. All of these are linked by their use of mathematics at some level to record and to control space. • Chapter 1 introduces the topic, and considers ancient definitions of mathematics, as well as modern historiographical notions of ‘traditions’, ‘cultures’ and ‘modes’ of mathematical writing. It also provides an outline of the textual evidence for ancient mathematics in practical contexts. • In chapter 2, Vitruvius’ discursive account of architecture prompts an examination of the social context and perceived mathematical competence of Roman architects. • In Chapter 3, the existence of several sets of geometrical problems as part of the Corpus Agrimensorum Romanorum allows for a survey of the possibilities they present for studying mathematics in a Roman context. I also suggest that the role of the agrimensor is paralleled by that of an ‘architectural surveyor’, with whose activities a tranche of procedural problem texts are associated. • Chapter 4 considers the surviving corpus of mathematical papyri, which contain a number of geometrical ‘problem-texts’, frequently characterised as ‘algorithmic’. While they are far from homogeneous, the general style of these texts is functionally similar to those found in the ps-Heronian corpora of problems. But the papyri provide unrivalled direct evidence for the kind of mathematical writing produced in Egypt between the 1st-6th centuries CE. The problem texts prompt two complementary approaches: on the one hand, I follow the lead of Imhausen’s work on Egyptian mathematical papyri in trying to abstract away from the literal problem text to uncover the structures which enable the creation and understanding of this kind of material; I also borrow the notion of a mathematical ‘toolbox’ to suggest the existence of a small number of widely-adopted ‘algorithmic’ subroutines. • Chapter 5 examines the use of mathematical diagrams in the ‘direct’ evidence for ancient Greek mathematical problem texts, i.e. the Greek mathematical papyri: diagram studies have been important in recent years and this section compares and contrasts the (physical) diagrams of the papyri (with the use of an appendix containing commentary and images), laying the foundation for future comparative work with similar diagrams preserved in the medieval manuscript tradition. • Chapter 6 considers ancient geography, and in particular the hybridisation of the apparatus of deductive mathematics in Ptolemy’s Geographical Guide (where the apparatus developed for proportions and abstract points and lines interacts with the hard data and the hard board of a map). The final chapter summarises the findings and highlights areas for future research.