The Maya were one of the largest and most advanced civilizations in Mesoamerica and the world. Mayan culture endures in the Yucatán Peninsula, Mexico, and parts of Guatemala. Undoubtedly, one of the most striking aspects of the Maya was their advanced knowledge compared to other peoples, including extensive astronomical understanding and a very comprehensive numerical system . In this article, we will focus on Mayan numbers and teach you the basics.
The Mayan numerical system is remarkable because it was so complete and sophisticated, despite having been developed independently. This civilization had a clear concept of zero , something Europeans didn't grasp until the Hindus introduced it to them.
All Mayan numbers
Below we will list all the Mayan numbers from 1 to 1000. There are several images that you can download to your computer, mobile phone, and even print to study them in more detail.
the 1 to 100
the 1 to 500
the 1 to 1000
We hope you find this list useful. You can download it as a PDF by clicking here . If you have any questions about a number, please leave a comment at the end of this article.
The history of Mayan numbers
Experts believe the Mayan writing system was hieroglyphic , due to its resemblance to the system used in Ancient Egypt. Their writing consisted of a combination of ideograms and phonetic symbols, making its content quite difficult to decipher.
There is not much information about Mayan writing because the Spanish priests ordered all Mayan books to be burned.
An interesting detail about the Mayan numbering system is that they invented it to measure time, not to perform mathematical calculations. Thus, Mayan numbers have a direct connection to days, months, and years , which is why the Mayan calendar is one of their most famous achievements and one of the most complete and accurate in the world.
Furthermore, the Mayan numerical and mathematical system was the first to develop a positional system. That is, the value of a digit or number depended on its position. I will explain this in more detail below.
How to write Mayan numbers
The Mayan numbering system is very easy to understand. This is because there are only three symbols , although their forms can vary depending on their use. Some numbering systems were for codices, others for monuments, and still others even included human representations.
The three basic symbols that we can find in the Mayan numbering are: A dot (1), a line (5) and a snail/seed/shell (0).
By combining these three symbols, the Mayan numbers from 0 to 20 could be obtained. From here on, it is important to keep in mind that in Mayan numeration, quantities are grouped in 20s.
What happens with Mayan numbers from 21 onwards? This is where the Mayan positional system can be appreciated , in which the value of a number or digit varies depending on its position, depending on the vertical position the number occupies.
At the bottom are the numerals (those from 0 to 20), while at the top the numbers are worth the numeral multiplied by 20.
For example, in the number 25: at the bottom there is the 5 (the line that equals 5), and the top part equals 20 (the dot equals 1, but being at the top it is multiplied by 20).
If the number has a third level, then the number located at the 3rd level will be multiplied by 400 (20 x 20). When a fourth level is used, then the number located at the 4th level will be multiplied by 8000 (20 x 20 x 20).
Characteristics of Mayan numeration
As I mentioned earlier, one of the reasons the Mayan numbering system has attracted the attention of experts is that it had a high level of complexity for having been created individually and more than 2.000 years ago, since research has revealed that it was created hundreds of years BC. On the other hand, it stands out for being the first culture in the entire American continent to have the concept of "nothing" or "zero".
Contrary to what one might initially think, the Maya did not invent their numerical system to perform mathematical operations, but rather to measure time . This is known because archaeologists have found artifacts where the numbering system is geared towards measuring time and its division into fractions. Of course, they also used it to count other things.
The Mayan vigesimal system is considered one of the most accurate in the world . Furthermore, it is believed that the Mayan calendar is more accurate than the Gregorian calendar and even as precise as modern measurement systems.
Although the main use of their numbering system was to measure time, thanks to it they also made great advances in geometry, astrology and mathematics.
Regarding geometry, it is known that the Maya had a very clear understanding of the concepts of triangle, square, rectangle, circle, and circumference , and they could also measure angles. They were familiar with a large number of geometric figures and volumes, and they had the ability to measure and use them as needed.
The Mayan numbering system we are talking about is the main and best known, but it is not the only numbering system that the Maya used.
Mayan “heads” numbering system
This other numbering system they used is very distinctive because they used the heads of different deities to represent numbers, which is why it is known as the head-based numbering system . It is also a vigesimal system, and its main number is 20.
In this numbering system, the maximum number of deities that could be represented was 14 , so they were only enough to cover numbers from 0 to 13. How did they represent the 6 missing numbers up to 19? They placed the Mayan numbers from 4 to 9 at the bottom of the chin of the deity that represented 10.
Without a doubt, it is a more complex and very incomplete system, which is why it was not used in many Mayan communities; most used the system of dots, lines, and shells.
The Maya were one of the most prodigious and astonishing civilizations in the world, possibly the most advanced for their time in many aspects. Their advances in mathematics, their numbering system, their calendar, their architecture, their knowledge of the universe, etc., surpassed most of these aspects of any other contemporary civilization.
Next, we're going to watch a very interesting video about Mayan numbers:
Its disappearance and future
Experts believe the Mayan civilization disappeared between the 8th and 9th centuries AD, one of the greatest mysteries in human history . To this day, the reason for the gradual abandonment of the great Mayan cities, which had become enormous urban centers with significant cultural and technological advancements, remains unknown. Historians continue to search for clues to their demise.
Currently, some of the hypotheses regarding the abandonment of Mayan cities include natural disasters, attacks from more powerful empires, or even a depletion of resources that forced them to migrate to areas with more fertile land. However, none of these theories have been proven.
But what did this collapse mean for the Mayan numbering system, their calendar, and all the advances they had made? All this knowledge was far superior to that of contemporary Europe and perhaps the world.
When the Spanish arrived in Yucatán in the 16th century, the collapse of the Mayan civilization had occurred several centuries earlier, so the contact of the Spanish with the rest of the Mayan culture was not as important as the contact they had with the Aztecs and other civilizations that still preserved great buildings.
The mathematical legacy of the Maya was taken up by peoples who settled in the same geographical space as them, especially the Aztecs, who also stood out for their great use of mathematics, although the Aztec mathematical system had several differences with respect to the Mayan system.
With the end of the Aztec civilization and other great Mesoamerican civilizations, the remnants of Mayan culture were lost to history. The remains that survive for study and our understanding are very scarce and extremely valuable . Among the surviving Mayan artifacts, the Dresden Codex stands out as the oldest book in all of the Americas, containing an entire section dedicated to the calendar and its numerical system.
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