The Mayan civilisation flourished in and around the region of Mesoamerica, particularly during their Classic Period which extended from 250AD to 900AD. During this era, they made several advancements in arts, culture, architecture, and other domains of life and knowledge. They also developed an efficient number system of their own which was subsequently used by other Mesoamerican civilisations, most notably the Aztecs, although with some variations. It was a number system that predominantly made use of dots and bars to represent numerals.

The history of Mayan number system actually extends far beyond the Classic Period of the Mayans. For instance, the use of a shell glyph to represent zero has been found from as early as 36 BC. According to some scholars, the use of zero was actually invented in Mesoamerica by the Olmecs, a civilisation which preceded the Mayans and had already come to an end around 4th century BC. Mayans borrowed certain elements from the Olmecs and made their original contributions as well.

The Mayan number system is basically a vigesimal number system which means that it uses 20 as its base. The use of 20 as base is also found in later civilisations such as the Aztecs. However, the number system of the Mayans was a bit more complex in that they used base 5 within the base 20. In other words, this means that number up to 19 could be represented in a certain way while after that the representation method changed.

The Mayan number system revolved around the use of dots and bars in addition to the use of a shell glyph to represent zero. The dot was used to represent 1 and the bar was used to represent 5. Thus, for instance, 1 was represented with a single dot, 2 with two dots, three with three dots, and so on. Further, “5” was represented with a single horizontal bar and 10 with two horizontal bars. However, “20” was not represented with four bars and instead a shell glyph along with a single dot was used to represent the figure of 20.

One of the most interesting aspects of Mayan number system is the use of zero as a placeholder. This was particularly important for the Mayan Long Count calendar which counted the total number of days since the creation of the world according to Mayan mythology. Thus the symbol of shell glyph was used to represent zero and it frequently appears on the Long Count dates. It is generally thought that it was actually the Olmecs who invented zero and the Mayans took over the concept from them.

The Mayan number system was quite efficient and counting with the Mayan number system was not a very complex process. Using the simple symbols of dots, bars, and a shell glyph for zero, they could count any given numbers. Starting from 1 with a single dot, the number went up to 19 for which three horizontal bars and four dots were used. The three bars represented 15 and the four dots represented the additional four numbers. From 21 to 40, the counting process was quite similar with the addition of an extra dot. For instance, while “11” was represented with two bars and a dot, 31 could be represented with two bars and two dots. After 40, another dot was added in the counting and it went on. A large figure like 5124 could be represented in base 20 using the symbols of 12 (multiplied twice by 20), 16 (multiplied once by 20), and 4.

Addition and subtraction in Mayan number system was also performed using the same dot and bar notations. As an example, consider the addition of 5 into 8 to get 13. For this a bar representing 5 is added into a bar and three dots representing 8 to get two bars and three dots representing 13. The exact reversal of this process can be used for subtraction in Mayan number system. In certain ways, use of symbols made addition and subtraction of large numbers easier.

The Mayans actually had two number systems joined together to form one complete system. The first number system used 5 as its base and it only represented the numbers from 1 till 19. The second number system used 20 as its base and was used to represent numbers starting from 20. For instance, in base 5, 20 would be presented with four bars. But instead of that, in base 20, it is represented with a shell glyph for zero in addition to a single dot, thus using 20 as base. Interestingly, Mayans sometimes used a very peculiar number system which used images for numbers. This system was sometimes used on calendars and to date buildings and was clearly more difficult to manipulate than the former.

There were certain advantages of the Mayan number system which made use of symbols instead of actual numerals. To being with, it made simple arithmetic very easy compared to the one which involved the actual numerals. While dealing with the symbols instead of numbers, it is easy to handle the sums since only the symbols have to be manipulated instead of performing the actual calculations. Second advantage is that large numbers can be easily expressed and this made representation of large time period on Mayan Long Count simple.

Mayan civilisation made impressive advancements in different domains of culture, art and knowledge during its Classic Period which extended from 250AD to 900AD. They also developed their own number systems which used 5 and 20 as its bases. The use of zero used in the Mayan number system was probably taken over from the previous Olmec civilisation. It was used as a placeholder in Mayan number system in addition to the use of dots and bars for representation of numbers. The Mayan number system made addition and subtraction relatively simple since only symbols had to be manipulated instead of doing the actual calculations.