Forgotten Mathematicians: Mayan Maths

The Mayan civilisation settled in the region of Central America from around 2000 BCE. At its peak, it was one of the most densely populated and culturally dynamic societies in the world.

Map of the Mayan Civilisation

Due to the importance of astronomy and calendar calculations in Mayan society, their mathematicians constructed a very sophisticated number system. They used a vigesimal number system (based on base 20, and to some extent 5), which is said to have originated from counting on fingers and toes. Their numerals consisted of only 3 symbols: a dot representing 1, a bar representing 5 and a shell representing 0. The fact the the Mayans knew the value of 0 is incredible, as most of the world’s civilisations had no concept of 0 at that time.

These three symbols were used in various combinations so that even uneducated people could do simple arithmetic for trade and commerce, as addition and subtraction was done by adding up the dots and bars, which is relatively simple. Numbers larger than 19 were represented by the same kind of sequence, but a vertical place system format was used to show each power of 20, as shown in the image below.

Mayan numerals

In the Mayan society, mathematics was an extremely important discipline and appears in Mayan art, such as wall paintings, where mathematics scribes or mathematicians are depicted by number scrolls which trail from under their arms. Interestingly, the first mathematician identified in one of these paintings was a female figure.

Furthermore, despite not having the concept of a fraction, Mayan mathematicians produced extremely accurate astronomical observations using no tools other than sticks. For example, they were able to measure the length of the solar year to a far higher degree of accuracy than that used in Europe  – their calculations gave an answer of 365.242 days, compared to the modern value of 365.242198 – as well as the lunar month – their value was 29.5308 days, compared to the modern value of 29.53059. That’s incredibly accurate!

However, due to their geographical disconnect from other civilisations, their mathematical discoveries had no influence on the European and Asian numbering systems or mathematics.

Let me know what you think! M x




  1. The Mayans are generally known to be one of the most advanced ancient civilizations. As is evident from this post, they had developed a commendable Math system. They used it to study the patterns in the sky and came up with accurate calendars that would count for thousands of years! They believed, “the future was in the present”. πŸ™‚


  2. Mayans also independently discovered/invented zero. The Mayans used an eyelike character to denote zero. Source:

    Recently, Babylonian mathematics was in news :

    Will you write about Babylonian math?

    Also, please do add references at end of your posts to support your writing and photos used.

    Enjoyed reading.


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