A number system is defined as any of various sets of symbols used to express quantities as the basis for counting, determining order, comparing amounts, performing calculations, as well as representing value. Numeration systems include binary, ternary, quaternary, quinary, senary, septenary, octal, nonary, decimal, undernary, duodecimal, hexadecimal, vigesimal, and sexagesimal. These systems correspond to values of 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 16, 20, and 60, respectively.

Throughout the course of history, the decimal system overshadowed all other systems. It is not, however, found in Mexico or Central America where the number 20 has become firmly implanted due to it's use in astronomy. It was their interest in time and chronology which led them to develop their mathmatics to such a great degree of sophistication. It was discovered, through early Spanish expeditions, that the Mayans had a well-developed positional system, including a symbol for zero. The Mayans were, in fact, very familiar with the concept of zero (which did not appear in the west until the 12th century). Based on the value 20, Mayan arithmetic was worked in dots (representing the value of one) and bars (representing the value of five). It was both a flexible and fast system of calculating even large numbers.

Mayan mathmatics included two outstanding developments which may be considered among the most brilliant accomplishments of the human mind:

• positional numeration
• zero

Such proficient use of the vigesimal numeration system may account for the amazing accuracy with which the solar year had been calculated. The Mayan number system seems to have been used primarily for the calendar rather than commercial computation.