Maya math was the most sophisticated number system ever developed in the Americas. It allowed scholars, astronomers, and architects to make complex calculations, but it was simple enough to be used by market traders and illiterate farmers.

Where we use ten different symbols to represent numbers (1, 2, 3, 4 , 5, 6, 7, 8, 9, 0), the Maya used only three: a dot for a one, a bar for five, and a symbol (usually a shell) for zero. (The Maya were the first civilization to discover and understand the concept of zero.) Below are the Maya numbers from 0–19:

We use a decimal system, based on the number ten, but the Maya used a vigesimal system, based on the number twenty. So where we learn to count on our fingers, Maya children counted on their fingers and toes. In fact, the number twenty was very important to the Maya, so much so that the words for “human being” and “twenty” share the same root in most Mayan languages.

The Maya wrote their numbers from top to bottom rather than from left to right, but apart from that, their system was not so different from ours. For example, to write the number 34, we place a three in the tens column and a four in the ones column. The Maya put a one in the twenties column and a fourteen in the ones column.

Adding and subtracting in the Maya system is simply a matter of juggling the dots and bars. To calculate 36 + 13, for example, you start by adding the units (i.e., 16 + 13). This gives you 29, so you leave 9 in the ones column and carry the 20 up, giving you a grand total of 2 twenties and 9 ones = 49.

Clever, isn’t it? When you consider that the Ancient Egyptians never cracked the concept of zero and that complex calculations with Roman numerals were way too complicated for ordinary Romans.

The easiest way to practice Maya math is to use sticks, stones and shells. They function in a similar way to an abacus. To see how, watch the video demonstration in the sidebar.

A sophisticated, yet simple system

Maya math demo

Eclipse tables in the Dresden codex.

Note the columns of numbers

Lesson plans & activities to download:

You can download our full range of Maya lesson plans and resources: here