Chapter 13 - Concepts in Greek Mathematics

Summary

The chapter ‘Concepts in Greek Mathematics’ by Reviel Netz problematises a set of assumptions commonly encountered in the literature on Greek mathematics, which typically derive from a supposedly objective, a-historical conception of mathematical theory and practice. In sharp opposition to that tradition, Netz raises the possibility that the purpose of engaging with mathematical concepts may have been different in antiquity than what it has been taken to be. He asks central questions afresh, for instance: why do mathematical texts begin with definitions, and what is the purpose of mathematical definitions and of axioms. In connection to these issues, he highlights new aspects of the relationship between Greek mathematics and Greek philosophy, between engaging with mathematical concepts and philosophical thinking. He also advances the thesis that the relations between mathematics and philosophy changed through the various eras of antiquity, as did mathematical concepts and the role of mathematical definitions. We should seriously entertain the idea that even mathematical concepts need to be viewed within a given historical and cultural context.