In Mesopotamia the scribes of Babylon and the other big cities were impressing on clay tablets economic and administrative records, literary, religious and scientific works, word-lists, and mathematical problems and tables. Nearly all of the texts that give us our fullest understanding of Babylonian mathematics date from the Old Babylonian Period about 1800-1600 BCE. There is also a second corpus of later evidence, from around 650 BCE to perhaps as late as the first century AD, but until recently this has been largely ignored by historians and is only now undergoing serious study.

As a result of the extensive excavations of the nineteenth century there are many more tablets available in museums and universities throughout the world than have yet been translated or even catalogued. However, of those that have been translated, only a relatively small proportion have been shown to have mathematical content, perhaps five hundred or so, compared with upwards of 500,000 extant tablets. Nevertheless, this is a significant number when compared with the paucity of Egyptian mathematical texts.

Most of the tablets are rectangular but there are some that are round in shape. They usually fit comfortably into the palm of a hand and are about an inch thick, although some are as small a postage stamp and others the size of a large book. The writing is in cuneiform (‘wedge-shaped’) script and it is usually found on the front and the back of the tablets, and sometimes on the side as well. All of the Babylonian tablets are written in Akkadian, a Semitic language, although some mathematical tablets do use a few Sumerian words.

For their numeral system, the Babylonians used the sexagesimal (base 60) place-value system. Why they chose a sexagesimal system is not known but it may have been related to their astronomy, with its 360 day year. They wrote their numerals from left to right using just two symbols:

for the unit and

for ten.

If there was no value in a place (which is what our zero symbol signifies) a space was sometimes left but otherwise meant 1, 60, or 3600 (or indeed 1/60, 1/3600 etc) according to context. In much later sources, mainly astronomical texts dating from 300 BCE onwards, a special symbol is introduced to mark empty places within numerals; but not at the end of a numeral, so the absolute value of the whole is still left floating.

For example (assuming we know from the context where the integer part ends and the fractional part begins):

denotes 2 x 60 + 31 + 4/60 + 13/3600.