Showing papers by "Reviel Netz published in 2010"

What Did Greek Mathematicians Find Beautiful

Abstract: he question posed in the title is not one we can readily answer. It overgeneralizes—asking us, in its unrefined state, to lump together Classical, Hellenistic, Roman, and Late Ancient authors, astronomers, and catapult builders, pagans, Christians, philosophers, and pure scientists. My own response concentrates, therefore, on authors of elite, sophisticated mathematical works in the Hellenistic era: Archimedes and his satellites. Nor do the ancients provide us with any help: the proofs were public, and their form became shared, but whatever feelings of aesthetic joy mathematicians experienced concerning them, they kept to themselves, and we need not assume that any two mathematicians had quite the same experience of beauty in reading the same text. The role of such an inquiry, then, is to suggest the kind of questions we may ask. Negative results are to be expected, and I shall offer mostly those; a very tentative positive thread is pursued throughout the paper. The argument deals primarily not with the kind of explicit views ancients held concerning mathematical beauty,1 but rather with the kind of mathematical entities that authors, more or less tacitly, found attractive. Whether or not this attraction should even be conceptualized in terms of the “aesthetic” is a difficult question in its own right, belonging more to the abstract theory of the aesthetic than to the concrete history of aesthetic practices. There are two main reasons why I find the category of the aesthetic useful: first, because the discussion will often involve the way in which the mathematical act was felt, an embodied experience of words and images, and second, because the practices to be discussed are related to practices of art: literary, visual, and musical.