Sara Panteri (University of Michigan)
The communis opinio posits a division of roles in the Hellenistic period between the cultural hubs of Athens and Alexandria. Athens remained the place for philosophy, whereas those in Alexandria engaged in scientific research (e.g., mathematics, geography, and anatomy) and paid scant attention to philosophy (Fraser 1972; Netz 2020). Although scholars understand Eratosthenes of Cyrene (c. 275-194 BCE) as an exception–he worked in Alexandria but had philosophical interests–they often obscure his exceptionality by separating their study of his contribution to mathematics from their study of his contribution to philosophy. For what makes this figure exceptional is precisely the fact that he was both a mathematician and a Platonic philosopher. Building on previous scholarship on Eratosthenes (Solmsen 1942; Wolfer 1954; Knorr 1986; Dörrie and Baltes 1987; Knorr 1989; Geus 2002; Vitrac 2008; Berrey 2017), I provide a new interpretation of the way Eratosthenes negotiated between these two components of his work and identity. Despite the possible tension underlying his Platonic philosophical position and his mathematical production, Eratosthenes represents a bridge between Athens and Alexandria.
Emblematic of how Eratosthenes negotiated this tension is his use of an anecdote about Plato in two distinct texts: a fragment from his Platonicus (a work extant only in a few fragments) and a letter to king Ptolemy attributed to Eratosthenes. This anecdote reports Plato’s involvement in the solution to the geometrical problem of doubling the cube. When, during a plague, the Delian oracle ordered the doubling of the volume of the cubic altar, the Delians, incapable of finding a solution, sent an embassy to Athens to ask help from Plato. Plato replied that, by making such a puzzling request, the God just wanted to blame the Greeks for neglecting the study of geometry.
The anecdote appeared at the beginning of the Platonicus and enabled Eratosthenes to place his own geometrical research under the aegis of Platonic philosophy. The other extant fragments reveal that in this text Eratosthenes elaborated on some puzzling mathematical passages in Plato’s Timaeus and Republic. The anecdote helps Eratosthenes position himself as a good student of Plato, interested in theoretical mathematics as a way to access philosophical higher truths.
In the letter to king Ptolemy, the anecdote signals that Eratosthenes intends to compete with the geometers of Plato’s Academy. At least three such geometers reportedly proposed solutions to the problem. In the letter, after pointing out the deficiencies of each of the previous solutions, Eratosthenes introduces his own as the one surpassing all the others: he invented an instrument, which potentially allows everyone to find the solution to the problem. This practical approach, emblematic of research into applied mechanics in Alexandria, distinguishes Eratosthenes’s project from that of the geometers of the Academy.
His deployment of this anecdote showcases both his theoretical and practical sides. We need to consider them simultaneously to understand the nature of Eratosthenes’s philosophical and mathematical activity.