Greek numerals: the Milesian (alphabetic) numeral system

Basic characteristics and notation

The alphabetic system assigns the first nine letters to units (1–9), the next nine to tens (10–90) and the final nine to hundreds (100–900). To provide the required 27 symbols, three archaic or otherwise unused letters are taken into service. These are traditionally known as digamma or wau (written ϝ or ϛ) for 6, koppa (ϟ) for 90, and sampi (ϡ) for 900. A small mark called the keraia (a character resembling an acute) is placed after a sequence of letters to indicate that the sequence is being read as a number. For background on letter assignment see Greek alphabet and numerals.

How values are formed and examples

The system operates primarily by addition: the numeric values of the letters in a group are summed to form the whole. For example, the number 241 is written by combining the signs for 200, 40 and 1 (commonly printed as ΣΜΑ followed by a keraia: ΣΜΑʹ). The sign for six may appear as the archaic digamma ϝ or the ligature-like ϛ, and texts may show either form; both represent the same numeric value. For convenience and clarity in modern typography, see a concise guide at modern usage.

Thousands and higher orders

To represent thousands and larger numbers the system reuses the same letter signs but distinguishes them by an additional mark. A left-side keraia or lower numeral sign placed before a letter indicates that the letter value should be multiplied by 1,000 (so ͵α = 1,000). By applying the same device to each reused letter, the notation can express values up to 999,999 without introducing new letters. For a technical note on these century-old conventions and their typographic rendering consult numeral marks and Roman comparanda for context.

Origins and historical development

Before the alphabetic system became widespread, Greek speakers used other methods to indicate numbers. An earlier acrophonic or "Attic" system assigned values to a smaller set of signs and combined them in a way comparable to Roman numerals; that system was gradually replaced in many areas by the Ionic alphabetic scheme during the classical and Hellenistic periods (commonly dated to the later 1st millennium BCE and standardized by the 4th century BCE in some sources). Even earlier civilizational scripts such as Linear A and Linear B used separate numeric signs rather than alphabetic letters. For historical surveys and comparative tables, see Linear numerals and Attic numerals.

Practical uses and surviving applications

In modern Greece the alphabetic numerals survive chiefly for ordinal and enumerative uses similar to how Roman numerals are used in the West: numbering chapters, monarchs' regnal numbers, list items in outlines, or dates in manuscript colophons. Cardinal arithmetic in everyday life uses Arabic numerals, but one still encounters alphabetic numerals on clocks, bookfronts, and inscriptions. Digital typography and character-encoding standards also include specific marks for keraia and the lower numeral sign; resources on encoding illustrate best practices at encoding notes and type handling.

Notable features, conventions and distinctions

• Additive principle: letters simply add, with no place-value multiplication other than the thousand-mark convention.
• Obsolete letters used as numerals: digamma (ϝ/ϛ), koppa (ϟ) and sampi (ϡ) are retained for their numeric roles even though they dropped out of the standard alphabetic sequence for spelling purposes.
• Variations and ligatures: historical inscriptions and manuscripts show regional handwriting variants, ligatures and alternative glyphs; both ϝ and ϛ have been used for 6, for example. For a visual comparison consult glyph forms and Unicode references.
• Comparison with Roman numerals: both systems are non-positional and rely on letter symbols, but Roman numerals use subtraction in certain conventions while the Greek alphabetic system is strictly additive in usual practice.
• Encoding and digital use: modern standards assign separate code points for keraia and related historic letters; guidelines for fonts and input are summarized at digital typography resources.

Because of its long history and continuous—if partial—use, the Greek alphabetic numeral system is a useful example of how alphabet and number notation can intertwine. It illustrates the reuse of linguistic elements for numeric purposes, the persistence of archaic letterforms for technical reasons, and the ways in which older numeric conventions coexist with modern decimal notation.