History Mystery: Mayans Number System!

I think this is the right time to discuss about the Mayan calendar and hence this post for your views. Before going to discuss the Mayan mathematics and numbers it is very important to know how we came to know all about them.

Here is a small briefing: Diego de Landa a Spanish Franciscan aged 17 landed in Yucatan peninsula and helped the Mayan people to resist the invasion of Herman Cotes of Spain. Remember that the people of the Yacatan peninsula were the descendants of the ancient Mayan civilization which was declined after 900 AD. Landa tried his best to protect the people from the Spanish masters and he visited all the ruins of the great Mayan cities of ancient civilization and learnt their customs and their history. Since he is a Franciscan a stunt follower of Christianity he abhorred their religious practice and sentiments he ordered for the Mayan idols and books should be destroyed. Later he has regretted for his action and he did mention in his book “Relación de las cosas de Yucatán” In that book he describes the hieroglyphics , Mayan customs, their temples and temple practices etc. Few Mayan documents which survived after Landa’s destruction were Dresden codex, Madrid Codex and Paris Codex. In the all above the Dresden Codex is believed to be copied from the original documents of Seventh century AD and it is a treatise of Astronomy. Knowledge of Mayan civilization has been greatly increased in the recent years due to the modern technology such as aerial photography, satellite imaging and high resolution radar imaging etc. The Mayan people constructed temples, palaces, shrines, thatched houses, terraced buildings causeways and huge dams to store rain water and the rulers were the high priests and possessed high knowledge in astronomy field. The farming was carried over in the raised fields with the help of the irrigation system.

 They were the highly cultured and civilized people who used calendar for their routine and religious life. Since they are masters in astronomy and calendar it is evident that they are masters in Mathematics too. The Mayan followed a very refined number system. It is assured that their mathematical system was the very advanced one of those times. Mayan number system is based on twenty (it is worth remember we are following number system based on ten). Most of the scholars give the following reason for their d vigesimal (twenty) system. Ancient people used both of their fingers and toes for calculation hence it is. Though it is of base twenty it has only three symbols for representing a particular number amazing isn’t it? They had the number zero and it was represented by a shell. Though the number system looks like positional, it is not actually so.

 The Mayan number mentions the unit numbers from one to nineteen in the first place and in the second place twenties up to nineteen and in the third place it denotes the numbers up to 360’s instead of 400’s after that the system reverts to the multiples of twenties ( i.e. 202 , 203 204 so on…)

 Let us see one example:

Consider one Mayan numeral: [9; 8; 9; 13; 7]

It actually represents the following number : + 13 × 20 + 9 × 18 × 20 + 8 × 18 × 202 + 9 × 18 × 203 =1357107

The above example was derived using the Dresden Codex. Some of the historian argued that they have followed different systems for astronomy, calendar and merchandizing but there is no written evidence for that.

 Let us discuss about the Mayan Calendars, they followed two calendars namely ritual calendar and civil calendar. The ritual calendar was known as the Tzolkin based on 260 days and it contained thirteen months of twenty days each. Each month was named after their gods and the days were numbered from zero to nineteen. The Haab, namely civil calendar consisted of 365 days and it had eighteen months of twenty days each and the remaining last five days were mentioned as wayem. According to Landa’s “Relación de las cosas de Yucatán” this last five days were considered as unlucky period for them and during those days they won’t wash comb and not even do any hard work. A satisfactory reason for why they followed two calendars could not be found. The years coincide after every 18980 days in other ward after every 52 civil years or 73 ritual years. Mayan astronomers accurately calculated the movements of Venus. Apart from these calendars the Mayans measured the time in another way also. It was an absolute time scale based on the creation date. 12th August 331 BC is taken as creation day but some historians differ from this Long count. The long count based on 360 days in a year is nothing but the count of days in Mayan number system hence it is more accurate than the other two calendars. Most of the inscriptions available from the Mayan towns are in terms of long count only.

Let us see one example for this:

 This [8; 14; 3; 1; 12] date is mentioned in a Plate found from the town Tikal.

 Let us calculate the year of inscription. 12 + 1 × 20 + 3 × 18 × 20 + 14 × 18 × 202 + 8 × 18 × 203 = 1253912 That is it was made 1253912 days after the creation date of 12th August 3113 BC. Hence the plate was carved in the year 320 AD.


The Mayans astronomical measurements are outstanding and more accurate. They don’t have any instruments other than sticks. They made a cross like shape with the help of two sticks both tied together at 90 degrees and through this they observed celestial bodies and their movements. Many of the historians believe that The Caracol building at Chichen Itza to be a Mayan observatory. Many of the windows in Caracol follow certain rules with respect the movement of moon and Sun. With their crude instrument namely with sticks the Mayans accurately calculated the length of a year as 365.242 days. Our modern scientific world recorded the same as 365.242198 days. In the similar manner Mayan accurately calculated the lunar month as 29.5302 days and latest findings displays it as 29.53059 days.