Babylonia was an ancient cultural region in central-southern Mesopotamia (present-day Iraq), withBabylon as its capital. Babylonia emerged when Hammurabi (fl. ca. 1696 – 1654 BC, short chronology) created an empire out of the territories of the former Akkadian Empire. Babylonia adopted the written Semitic Akkadian language for official use, and retained the Sumerian languagefor religious use, which by that time was no longer a spoken language. The Akkadian and Sumerian traditions played a major role in later Babylonian culture, and the region would remain an important cultural center, even under outside rule, throughout the Bronze Age and the Early Iron Age.
The earliest mention of the city of Babylon can be found in a tablet from the reign of Sargon of Akkad, dating back to the 23rd century BCE. Following the collapse of the last Sumerian "Ur-III" dynasty at the hands of the Elamites (2002 BCE traditional, 1940 BCE short), the Amorites gained control over most of Mesopotamia, where they formed a series of small kingdoms. During the first centuries of what is called the "Amorite period", the most powerful city states were Isin and Larsa, althoughShamshi-Adad I came close to uniting the more northern regions around Assur and Mari. One of these Amorite dynasties was established in the city-state of Babylon, which would ultimately take over the others and form the first Babylonian empire, during what is also called the Old BabylonianPeriod.
Babylonian mathematics (also known as Assyro-Babylonian mathematics) refers to any mathematics of the people of Mesopotamia, from the days of the early Sumerians to the fall ofBabylon in 539 BC. Babylonian mathematical texts are plentiful and well edited. In respect of time they fall in two distinct groups: one from the Old Babylonian period (1830-1531 BC), the other mainlySeleucid from the last three or four centuries B.C. In respect of content there is scarcely any