 
Summary: CHAPTER 2.1
e two cultures of mathematics in
ancient Greece
Markus Asper
The notion of `Greek mathematics' is a key concept among those who teach or
learn about the Western tradition and, especially, the history of science.1
It
seems to be the eld where that which used to be referred to as `the Greek miracle'
is at its most miraculous. e works of, for example, Euclid or Archimedes
appear to be of timeless brilliance, their assumptions, methods, and proofs, even
a er Hilbert, of almost eternal elegance. erefore, for a long time, a historical
approach that investigated the environment of these astonishing practices was
not deemed necessary. Recently, however, a consensus has emerged that Greek
mathematics was heterogeneous and that the famous mathematicians are only
the tip of an iceberg that must have consisted of several coexisting and partly
overlapping elds of mathematical practices (among others, Lloyd 1992, 569). It
is my aim here to describe as much of this `iceberg' as possible, and the relation
ships between its more prominent parts, mainly during the most crucial time for
the formation of the most important Greek mathematical traditions, the h to
the third centuries bc.
