Overview

The earliest number systems for which we have written records include the Babylonian, Egyptian, Greek, Roman, Chinese, Hindu, and Mayan. Some systems employed the repetition of symbols to express larger quantities, while others involved either explicit multiplication of quantities by powers of a basic unit or the specification of powers by position in a string of symbols. Full development of the positional system, the basis of modern arithmetic calculation, could not occur before a symbol for zero and the computational rules for its use were established, a situation that did not fully materialize in Europe until after the Renaissance.

Background

What we know about the number systems of earlier civilizations is largely the result of the archaeological research of the past 200 years and is necessarily incomplete. Far more effort has gone into understanding the societies of the ancient Near East and the Mediterranean world than...