Summary

Numerical notations—graphic, largely non-phonetic notations for expressing numerical values—are central aspects of most written traditions of classical antiquity, as they are with most literate societies. The Minoan and Mycenean numerals appear to derive from an Egyptian antecedent. Roman numerals, Etruscan numerals, and Greek acrophonic numerals derive from a Greco-Italic abstract system based on tallying, using a mixed base of 5 and 10. Finally, the Greek alphabetic numerals, unrelated to any of these other traditions and probably deriving from Egyptian demotic practices, use the principle of alphabetic order to create a system in which signs are not repeated. None of these numeral systems were often used directly for mathematics, and because ancient societies had a variety of non-written arithmetical techniques, their utility was principally representational and mnemonic, not computational. All of these systems have been stigmatized unfairly in modern scholarship as holding back mathematical achievement in antiquity in comparison to positional systems commonly used in the 21st century, although the Greek alphabetic and Roman numerals were both used for thousands of years across a range of media and functions.