The History of Mathematics

Early Counting and Numbers

What were the two fundamental ideas in the development of numerical symbols?

A numeral is a standard symbol for a number; numerical symbols in various cultures represent numbers. For example, XXII is the numerical symbol—also called a Roman numeral—that corresponds to 22—also a numerical symbol—in the standard Hindu-Arabic numerals. In the Mayan system, a combination of two symbols, a dot (.) and a dash (-), were used to define numbers.

There were two basic principles in the development of numerical symbols: First, a certain standard sign for the unit is repeated over and over, with each sign representing the number of units. For example, III is considered 3 in Roman numerals (see the Greek and Roman mathematics section for more about Roman numerals). In the other principle, each number has its own distinct symbol. For example, “7” is the symbol that represents seven units in the standard Hindu-Arabic numerals. (See below for an explanation of Hindu-Arabic numbers; for more information, see “Math Basics.”)


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