MATHEMATICS

   Many of the practices and concepts of mathematics were first developed in Mesopotamia, where professional numeracy predated literacy. In the Chalcolithic period, counters and tokens facilitated the administration before the use of archaic cuneiform writing in the Uruk period. Various numerical systems and measurements corresponded to different commodities (e.g., grains, liquids, fields), using decimal as well as sexagesimal metrologies. This was simplified in the third millennium when sexagesimal metrology began to be adopted generally.

   Archaic tablets show that scribeshad to calculate quantities of raw materials or ingredients that were produced, exchanged, and consumed. Mathematics was an integral part of scribal training, and practice tablets from as early as the Early Dynastic period demonstrate that geometry was essential for the task of dividing up plots of land for farming and irrigation purposes. This was done by measuring the sides of areas rather than angles, and fields with an irregular outline, for instance, were divided up into simple rectilinear parts, which were then added up. Trigonometry never developed in Mesopotamia, although the so-called Pythagorean theorem had been practically applied since the Old Babylonian period. At this stage various tools essential for operating sexagesimal arithmetic had been invented, such as tables for reciprocals, place value systems, and standardized constants for calculations and conversions. Many school tablets, especially from Nippur, give evidence for the standards of Babylonian mathematics, both in algebra and geometry, as do the professional accounts in the economic sector, private as well as institutional, using sophisticated forms of tabulation. Apart from serving the purpose of the economy and its administration, mathematics was essential for the high achievements of Mesopotamian astronomy.

   See also ASTROLOGY/ASTRONOMY.