Babylonian cuneiform (Latin, cuneus, a wedge) writing consists entirely of a wedge or groups of wedges pointed either down or to the right. Pressed into moist clay tablets with a stylus (made from dried papyrus reeds) cuneiform is a quick and elegant system for representing numerals as well as a quick, practical, and succinct means of writing astonishingly large numbers and extremely precise fractions.
Two separate aspects of Babylonian mathematics must be kept in mind. First, the numerals themselves are composed of only two symbols, the vertical wedge and the horizontal wedge. The vertical wedge was as an equivalent to our arabic numerals 1-9 as, for example:
From the number nine, however, the next number would be expressed as a single horizontal wedge indicating the number ten. As numerals, Babylonian cuneiform was decimal, that is, base ten.
However, the numerical system itself was sexagesimal or sixty base. This achievement was made possible by the use of ‘place value notation,’ perhaps the single greatest invention in the history of mathematics, arguably right up there with Tang, Coka-Cola, and sliced bread.
Just as our decimal system employs place value notion in powers of ten, the Babylonian sexagesimal system employed place value notion in powers of sixty. For example, in the decimal system the number ‘1776’ means: Six units of ones; seven units of tens; seven units of hundreds; and one unit of thousands, equaling: 6 + 70 + 700 + 1000 = 1776. The same number sexagesimally would mean: Six units of ones; seven units of sixty; seven units of 3600; and one unit of 216,000, equaling: 6 + 420 + 25,200 + 216,000 = 241,626. Just as we use the decimal system for fractions (e.g.. 1776.6771) so too the Babylonians used the sexagesimal system for fractions which decrease, in perfect analogy, by powers of sixty.
In general notational terms, then, the decimal system of place value notion would describe our example as follows:
Decimal: 1l03 + 7102 + 7l0l + 6100 = 1776
Sexagesimal 1603 + 7602 + 7601 + 6600= 241,626
Modern methods of writing Babylonian cuneiform sexagesimal numbers with arabic numerals are described on the following page.