The Mayan civilization, which flourished in Mesoamerica from around 2000 BCE to 1500 CE, developed an advanced numerical system that was both efficient and unique. The Mayans used a vigesimal (base-20) numbering system, which was distinct from the decimal system (base-10) used in many modern cultures. Their numerical representations were based on three symbols: a dot (1), a horizontal bar (5), and a shell-like symbol (0). These symbols were used to construct numbers and perform calculations.
The Mayan numerical system was positional, meaning the value of a symbol depended on its position relative to others. This approach allowed for the representation of very large numbers with relatively few symbols, much like the modern decimal system but based on powers of 20 rather than powers of 10.
The Mayans wrote their numbers vertically, with the lowest value at the bottom and increasing in value as the positions ascended. Each level represented an increasing power of 20, with the first position signifying units (1-19), the second position representing multiples of 20 (20, 40, 60, etc.), the third position representing multiples of 400 (20×20), and so forth.
The first position in the Mayan numbering system held numbers from 0 to 19. These numbers were represented using combinations of dots and bars, with the special shell symbol denoting zero. This early concept of zero was a remarkable mathematical achievement, as few ancient civilizations had a defined symbol for it.
The second position represented multiples of 20. For example:
Beyond the second position, each additional level increased in powers of 20:
With this system, the Mayans were able to express large numbers compactly, facilitating record-keeping, astronomy, and trade.
The Mayans had words for numbers, much like modern languages. Here are some of their number names:
Beyond 10, they used a combination of words, similar to how we say “twenty-one” in English. For example, 20 was “Jun kal” (one score), 21 was “Jun kal jun” (one score and one), and so forth.
The Mayan numbering system was unique, but it was not the only sophisticated numerical system in history. Other civilizations had their own numeral representations:
The Mayan system stands out for its early use of zero and its ability to efficiently represent large numbers with simple symbols.
To better understand the Mayan numbering system, try the following exercises:
(•• + —) + (• + —) = ?
Understanding Mayan numbers offers insight into the intellectual achievements of this ancient civilization and their contributions to mathematics.
How did the Mayans use their number system in daily life?
The Mayans used their numerical system for various practical purposes such as keeping track of time, trade, taxation, and astronomical calculations.
Why did the Mayans use a base-20 system instead of a base-10 system?
Some researchers suggest that the base-20 system may have originated from counting on fingers and toes, unlike the base-10 system, which is based only on fingers.
Did the Mayans have a written way to perform mathematical operations like addition or multiplication?
While no detailed mathematical treatises have survived, Mayan inscriptions suggest they used their numbers for calculations, especially in relation to the calendar and astronomy.
How does the Mayan concept of zero compare to other ancient civilizations?
The Mayan civilization was one of the first to develop and use a distinct symbol for zero, while many other ancient cultures either lacked zero or used placeholder symbols.
Are there any modern applications of the Mayan numbering system?
Although the system is no longer widely used, it is still studied in the fields of archaeology, mathematics, and history, and is occasionally used for educational purposes in teaching positional notation.
