The History of Mathematics

Early Counting and Numbers

How did certain ancient cultures count large numbers?

It is not surprising that one of the earliest ways to count was the most obvious: using the hands. And because these “counting machines” were based on five digits on each hand, most invented numbering systems used base 10. Today, we call these base numbers—or base of a number system—the numbers that determine place values. (For more information on base numbers, see “Math Basics.”)

However, not every group chose 10. Some cultures chose the number 12 (or base 12); the Mayans, Aztecs, Basques, and Celts chose base 20, adding the ten digits of the feet. Still others, such as the Sumerians and Babylonians, used base 60 for reasons not yet well understood.

The numbering systems based on 10 (or 12, 20, or 60) started when people needed to represent large numbers using the smallest set of symbols. In order to do this, one particular set would be given a special role. A regular sequence of numbers would then be related to the chosen set. One can think of this as steps to various floors of a building, in which the steps are the various numbers—the steps to the first floor the “first order units”; the steps to the second floor the “second order units”; and so on. In today’s most common unit (base 10), the first order units are the numbers 1 through 9, the second order units are 10 through 19, and so on.


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