Before we can understand how the Maya tracked time with such incredible precision, we first need to learn how they counted. While we use a base-10 system, likely because we have ten fingers, the Maya used a base-20, or vigesimal system. This elegant system relies on just three simple symbols: a dot for one, a bar for five, and a shell for zero.

Combining these symbols allows for the creation of any number from 1 to 19. Dots are placed above bars. You never need more than four dots (since five dots would become one bar) or more than three bars (since four bars would equal 20, which moves to the next place value).

Here’s where Maya mathematics becomes truly powerful. Instead of writing numbers horizontally like we do (e.g., 2024), the Maya stacked them vertically. Each level represents a different place value, with the lowest value at the bottom.

In our base-10 system, the places are 1s, 10s, 100s, and so on (powers of 10). In the Maya vigesimal system, the places are 1s, 20s, 400s ($20^2$), 8000s ($20^3$), and upwards. This structure was essential for managing the vast timescales of their calendars, especially the Long Count calendar.

To read a Maya number, you multiply the value of the symbol(s) in each level by that level's place value, then add the results together. The presence of a shell symbol for zero was a revolutionary concept, allowing the Maya to handle place values with no remainder, just as we use 0 in a number like 205.

Adding and subtracting with Maya numerals is surprisingly intuitive. You simply combine or remove symbols within each place value level, simplifying as you go. For example, to add 7 and 5:

1. Start with the symbols for 7 (two dots, one bar) and 5 (one bar).
2. Combine them: you now have two dots and two bars.
3. This gives you a value of 12 (two dots = 2, two bars = 10).

If the combination results in five or more dots, you convert five dots into one bar. If it results in four or more bars (a value of 20), you convert them into a single dot in the next highest place value.

This system allowed Maya scribes and astronomers to calculate dates and astronomical events far into the future with complete accuracy, all without calculators or computers. This mathematical foundation is the engine that drives the complex, interlocking cycles of the Maya calendars.

Now that you've seen how the Maya count, you have the basic tools to understand how their calendars work.