The twentieth century was a time of big changes in our understanding of Greek mathematics. Many parts of what David Fowler has called "the standard story" have been challenged, and the scholarly consensus has certainly changed as a result. Three examples will have to suffice:
In Classics in the History of Greek Mathematics, Christianidis has provided a very useful collection of papers that encompass many of these changes. Here one can find Unguru's original papers (and the angry responses they elicited), discussions of the supposed "crisis of foundations", papers on the origin of Greek axiomatics, on geometry and "algebra". The papers, alas, are in their original languages (German, French, and English), but anglophone readers can be reassured that most of the articles are in English, especially the more recent ones. In any case, this is an excellent place to go to learn what the historians have been up to, and the give-and-take of debate makes it fascinating. The book is probably too expensive for non-fanatic individual readers, but it is definitely a "must buy" for libraries.
Fernando Q. Gouvêa is Professor of Mathematics at Colby College and the co-author, with William P. Berlinghoff, of Math through the Ages. He somehow finds time to also be the editor of MAA Reviews.
The Beginnings of Greek Mathematics
Studies on Greek Geometry
Studies on proportion theory and incommensurability
Studies on Greek Algebra
Did the Greeeks have the notion of common fraction? Did they use it?
Methodological Issues in the Historiography of Greek Mathematics