The problems of exceptionality: The case of Archimedes and the Greeks

ABSTRACT The points at which Greek mathematics in general and Archimedes' contributions in particular are exceptional are here assessed by way of a comparison with the extensive evidence from ancient China. While underlining the need for caution concerning the extent to which concrete conclusions are possible, the outcome is broadly to confirm Netz's argument that a key factor in Archimedes' success and influence was the way in which in a social and intellectual environment that favoured debate, he was able to contest an assumption found in both the Platonic and Aristotelian traditions. Where they had imagined a sharp division (albeit differently defined) between what they assigned to ‘physics’ and to ‘mathematics’ respectively, Archimedes showed how those two inquiries could be treated as complementary to one another, thereby opening up the possibility of new styles of physical demonstration.