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Ancient Mayan Math

Gary Todd on Flickr

In the last issue, we talked about how ancient Egyptians worked with numbers in a way similar to binary numbers. The Mayans are another fascinating culture that created a mathematical system to track events in the night sky, trade things, and use math in other everyday ways.

(Fun Fact: As children of European descent, we learn to count with our fingers. Mayan kids apparently counted with their fingers AND toes.)

The most intriguing detail about Mayan math is that they only used three characters to work within a vigesimal Base-20 system: a conch shell for zero, a dot for one, and a bar for five. Our decimal Base-10 system uses 10 characters: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. The Mayan system is more efficient than our system. And where we write numbers from left to right, Mayans stacked their numbers into rows counted from bottom to top.

How does Mayan math actually work? Take the number 39. In our decimal system, 39 translates to (3 x 10) + 9, or 39 with the 3 on the left to indicate that there are 3 instances of 10 in the number. In a Base-20 number system, 39 is 20 + 19. Here’s how Mayans represent 39:

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The single dot in the top position represents 20 while the bottom four dots and three bars represent the remainder of 39 – 20, which is 19.

Mayans break numbers down into groups of 20 with any remainder accounted for as a number less than 20. In our decimal system, we break numbers down into groups of ten with any remainder accounted for as a number less than 10.

Can you figure out how we express this Mayan number as a decimal number?

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The Mayans are also one of only two ancient cultures to use the number zero. Using zero allowed the Mayans to do more complicated math than the Romans despite Roman engineering skills in building roads, buildings, and aqueducts. To Mayans, zero also represented the end of a natural cycle and the beginning of a new cycle, whether describing the phases of the moon, the rotating positions of stars, or the life cycle of plants and humans.

Can you come up with your own mathematical system? Pick a base number, say 2 or 5 or 50, and then figure out how to represent a variety of decimal numbers. Then figure out how to add numbers and subtract numbers. Can you make a system that does all three?

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Learn more

Maya Archaeologist


“Nik” — The Zero in Vigesimal Maya Mathematics


Maya Numerals


Maya Numerals Converter