## Mathematics in Ancient Iraq

The mathematics of ancient Iraq, attested from the last three millennia BCE, was written on clay tablets in the Sumerian and Akkadian languages using the cuneiform script, often with numbers in the sexagesimal place value system (§1.2). There have been many styles of interpretation since the discovery and decipherment of that mathematics in the late nineteenth and early twentieth centuries CE (§1.1), but this book advocates a combination of close attention to textual and linguistic detail, as well as material and archaeological evidence, to situate ancient mathematics within the socio-intellectual worlds of the individuals and communities who produced and consumed it (§1.3)

Iraq—Sumer—Babylonia—Mesopotamia: under any or all of these names almost every general textbook on the history of mathematics assigns the origins of ‘pure’ mathematics to the distant past of the land between the Tigris and Euphrates rivers. Here, over five thousand years ago, the fi rst systematic accounting techniques were developed, using clay counters to represent fixed quantities of traded and stored goods in the world’s earliest cities (§2.2). Here too, in the early second millennium bce, the world’s first positional system of numerical notation—the famous sexagesimal place value system—was widely used (§4.2). The earliest widespread evidence for ‘pure’ mathematics comes from the same place and time, including a very accurate approximation to the square root of 2, an early form of abstract algebra, and the knowledge, if not proof, of ‘Pythagoras’ theorem’ defining the relationship between the sides of a right-angled triangle (§4.3). The best-known mathematical artefact from this time, the cuneiform tablet

Plimpton 322, has been widely discussed and admired, and claims have been made for its function that range from number theory to trigonometry to astronomy. Most of the evidence for mathematical astronomy, however, comes from the later fi rst millennium bce (§8.2), from which it is clear that Babylonian astronomical observations, calculational models, and the sexagesimal place value system all had a deep impact on the later development of Old World astronomy, in particular through the person and works of Ptolemy. It is hardly surprising, then, that ever since its discovery a century ago the mathematics of ancient Iraq has claimed an important role in

the history of early mathematics.