First Babylonian dynasty in the context of Chronology of the Ancient Near East

Babylonian mathematics (also known as Assyro-Babylonian mathematics) is the mathematics developed or practiced by the people of Mesopotamia, as attested by sources mainly surviving from the Old Babylonian period (1830–1531 BC) to the Seleucid from the last three or four centuries BC. With respect to content, there is scarcely any difference between the two groups of texts. Babylonian mathematics remained constant, in character and content, for over a millennium.

In contrast to the scarcity of sources in Ancient Egyptian mathematics, knowledge of Babylonian mathematics is derived from hundreds of clay tablets unearthed since the 1850s. Written in cuneiform, tablets were inscribed while the clay was moist, and baked hard in an oven or by the heat of the sun. The majority of recovered clay tablets date from 1800 to 1600 BC, and cover topics that include fractions, algebra, quadratic and cubic equations and the Pythagorean theorem. The Babylonian tablet YBC 7289 gives an approximation of ${\displaystyle {\sqrt {2}}}$ accurate to three significant sexagesimal digits (about six significant decimal digits).

Gilgamesh and Aga, sometimes referred to as incipit The envoys of Aga (Sumerian: lu2 kin-gi4-a aka), is an Old Babylonian poem written in Sumerian. The only one of the five poems of Gilgamesh that has no mythological aspects, it has been the subject of discussion since its publication in 1935 and later translation in 1949.

The poem records the Kishite siege of Uruk after lord Gilgamesh refused to submit to them, ending in Aga's defeat and consequently the fall of Kish's hegemony. While the historicity of the war remains an open question, attempts have been made to assign a historical date. The suggested date is around 2600 BC, since archaeological evidence traces the fall of Kish hegemony between ED II and ED III. The location of the battle is described as having occurred outside the walls of Uruk, situated east of the present bed of the Euphrates River.

The Isin-Larsa period (c. 2025–1763 BCE, Middle Chronology, or 1961–1699 BCE, Short Chronology) is a phase in the history of ancient Mesopotamia, which extends between the end of the Third Dynasty of Ur and the conquest of Mesopotamia by King Hammurabi of Babylon leading to the creation of the First Babylonian dynasty. According to the approximate conventional dating, this period begins in 2025 BCE and ended in 1763 BCE. It constitutes the first part of the Old Babylonian period (2025–1595 BCE), the second part being the period of domination of the first dynasty of Babylon, which ends with the Sack of Babylon in 1595 BCE and the rise of the Kassites.

The Third Dynasty of Ur immediately preceded the Isin-Larsa period, and its fall was due to the combined attacks of the Amorites from the west, and the Elamites from the east. As its name suggests, the Isin-Larsa period saw successively the emergence of two great powers in Lower Mesopotamia: the kingdom of Isin, which attempts to seek the succession of the kingdom of Ur after its fall and established the Dynasty of Isin, and the kingdom of Larsa, whose fall marks the end of the period. In reality, neither of these two kingdoms exercised an undeniable hegemony in Lower Mesopotamia, and they had to coexist with other less powerful kingdoms (such as Uruk, Babylon, and Mankisum), while further north their influence was non-existent and gave way to other powerful political entities (Eshnunna, Ekallatum, Mari, Yamkhad). The dynasties of this period have in common a Semitic Amorite origin, even if they quickly acculturated to Mesopotamian traditions.

Sin-Muballit was the father of Hammurabi and the fifth Amorite king of the first dynasty (the Amorite Dynasty) of Babylonia, reigning c. 1811–1793 or 1748–1729 BC (see Chronology of the Ancient Near East). He ruled over a relatively new and minor kingdom; however, he was the first ruler of Babylon to actually declare himself king of the city, and the first to expand the territory ruled by the city, and his son greatly expanded the Babylonian kingdom into the Babylonian Empire.