In no domain has the influence of ancient Mesopotamia on Western civilization been more profound and decisive than in theoretical astronomy and, principally through it, mathematics. Indeed, in the course of the last few decades it has become increasingly clear that all Western efforts in the exact sciences are descendants in direct line from the work of the Late Babylonian astronomers.
The anonymous creators of Babylonian theoretical astronomy – probably of the fourth or fifth century B.C. – drew their essential ingredients from several branches of learning and literature, chief among them mathematics and, for observations, the astronomical diaries, closely linked to the celestial omen texts.
Babylonian mathematical texts are plentiful and well edited. In respect of time they fall in two distinct groups: one Old Babylonian from the centuries about 1600 B.C., the other mainly Seleucid from the last three or four centuries B.C. In respect of content there is scarcely any difference between the two groups of texts. Thus Babylonian mathematics remained constant, in character and content, for nearly two millennia. Its nascent phase escapes us entirely.
The backbone of Babylonian mathematics is the sexagesimal number system. It is a place-value system, like our decimal system, but of base 60 rather than 10. It was used to write both whole numbers and certain fractions (the equivalents of our decimal fractions) and was without doubt the most efficient way of writing numbers in antiquity. It alone reduced the standard four operations of arithmetic to matters of mere routine, particularly with the aid of the multiplication and reciprocal tables that we find in great numbers.