The two standard accounts of Mesopotamian mathematics (as well as the mathematics of other ancient civilizations) are Otto Neugebauer's The Exact Sciences in Antiquity [14] and B. L. Van der Waerden's Science Awakening I [16]. Although they are both still useful, they have been superseded in some of their technical accounts of the mathematics by the results of new research. Among the newer surveys of Mesopotamian mathematics are articles by Jens Høyrup [7] and Jöran Friberg [5]. Høyrup also has a book-length treatment of the technical aspects of the Mesopotamian tablets: Lengths, Widths, Surfaces: A Portrait of Old Babylonian Algebra and Its Kin [9] as well as a series of more general essays on ancient and medieval mathematics: In Measure, Number, and Weight: Studies in Mathematics and Culture [8].

The standard, and still useful, history of Greek mathematics is Thomas Heath's A History of Greek Mathematics [6]. But many aspects of Heath's analysis have been challenged in recent years. The two best reevaluations of some central parts of the story of Greek mathematics are Wilbur Knorr's The Ancient Tradition of Geometric Problems [10], which argues that geometric problem solving was the motivating factor for much of Greek mathematics, and David Fowler's The Mathematics of Plato's Academy: A New Reconstruction [4], which claims that the idea of anthyphairesis (reciprocal subtraction) provides much of the impetus for the Greek development of the ideas of ratio and proportion. A newer work, Serafina Cuomo's Ancient Mathematics [3], is an excellent survey of Greek mathematics, aimed particularly at non-specialists.