The vexing problem of ancient Greek mathematics

The most important thing to know about ancient Greek mathematics is how little anyone knows about it. The scant evidence available today is tremendously indirect: reconstructions from unrepresentative survivals of fragments of translations of transcriptions of commentaries on compilations of summaries of allusions to refutations of excerpts of documents produced as part of an oral culture of learning in which the original writing may never have been expected to encapsulate what really mattered. Many centuries separate the people we want to know about and even the oldest materials we have to know them with, and most of what they did and thought is simply and definitively lost.

But that is only the start of the difficulty. Ancient thinkers lived in a very different world, mathematically and otherwise. Much of what we take for granted in mathematics today pushes that world farther away, from such rudiments as numbers and arithmetic to grand conceptions of the universe and the reasoning of mathematical demonstrations. Every generation rewrites the knowledge of its forebears, and Greek mathematics has been rewritten by more generations than it’s even possible to identify.

Reviel Netz, a professor of classics at Stanford University, California, caught the attention of more than just fellow classicists when he confronted this hard problem by making it vastly harder. His breakout book, The Shaping of Deduction in Greek Mathematics (1999), proposed that the key to getting into the heads of ancient mathematicians was to focus on the facet of their work that has survived least well across the eras: their diagrams. Marshalling an erudite array of highly indirect inferences about how diagrams must have functioned – conceptually, argumentatively, socially and so on – Netz demonstrated an exciting method to draw new conclusions from a vexingly small and problematic set of sources.

Netz’s elucidations of ancient scholarship have continued in that vein from provocation to provocation, stirring the interpretive pot with inventive ways to reimagine what old and obscure documents tell us about far older and obscurer worlds.