How did the Ancient Mayans Discover Zero?

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In the history of mathematics, the concept of the number zero is a real revolution and has only been discovered a handful of times. The Ancient Greeks did not have a number for zero and the ancient civilizations of Sumeria and Babylon only used it partially. How did the Mayans happen upon it 2,000 years ago?

Why do we need a number for nothing?

Zero is a debatable concept and was famously debated by Ancient Greeks (who ultimately decided against the entire idea) all the way down through the medieval period. However, all modern numerical systems depend on it.

Zero is important because of its use as a placeholder, at least initially. In any numerical system with a base, a number indicating no numbers for that placeholder value is important so that the numerical system can easily expand.

Mayan numbers, using a base-20 system.

For example, if I have a base-10 system, like we use today, and I say that I want 1 tens of horses but not eleven horses or nine horses, I need to be able to place a number indicating no ones in that column.

We famously use the Arabic numbering system and zero came to us through the Arabic-Indian system in the 11th century via the Islamic scholar Al-Andalus, who was living in Muslim occupied Spain at the time. Prior to that, Westerners had been using the Roman numeral system, which was inferior in many ways.

The Mayan Numerical System

Rather than using a base-10 system, the Mayans used a base-20 system to count. For their calendars, they adapted it to a base-18 system since it would fit more closely with their calendar year.

The Mayan system was very easy to use since adding and subtracting was as simple as transposing dots or lines.

Addition in Mayan.

In fact the oldest example of the use of the system is found outside of the Mayan territory. Known as Stela 2 at Chiapa de Corzo.

Diagram of Stela 2.

However, they realized that they needed a placeholder to indicate no value for that position and they chose to use a seashell for this position. The reason for the seashell may be unclear but it could represent an empty shell, which could have contained a pearl or oyster. This was a part of their numerical system as far back as the very beginnings of their civilization and some scholars think that it may have come to them through the Olmec civilization, a civilization older than the Mayan.

The Mayan Calendar

The numerical system used by the Mayans was used extensively and most commonly used for dates. They believed that the beginning of time occurred on August 11, 3114 BC (according to our calendar) and marked all dates relative to that prehistoric date.

Through an elaborate and complex astrological-calendrical system, they devised what is now known as the Long Count Calendar System which was possibly used by the Olmecs but definitely in the early Mayan period and was later used by the Aztecs in Northern Mexico.

Bizarrely, we now visualize the Mayan calendar system as a series of turning wheels, even though the Mayans themselves never discovered the wheel or axle. They did, however, have extremely advanced astronomical knowledge, famously exemplified by the fact that their estimation of the solar year at 365.2422 days is much more accurate than anything used until the 20th century and is much more accurate than our current leap-year system.

A Destroyed History

The Mayan writing system, a hieroglyphic system, was the most advanced of the writing systems in the Americas. The Spanish conquest of the “New World” was particularly brutal on Mesoamerica. As missionaries, led primarily by Bishop Diego de Landa, tried to convert the indigenous peoples of the region, they worked tirelessly to destroy their works of art and records.

Example page from the Dresden Codex, one of the only surviving books from the Mayans.

We found a large number of books in these characters and, as they contained nothing in which were not to be seen as superstition and lies of the devil, we burned them all, which they regretted to an amazing degree, and which caused them much affliction.

Bishop Diego de Landa

It is estimated that Mayans had thousands of codices, chronicling their history for 800 years. Many missionaries from the time reported that there were still priests who could read the books to them. However, every known codex was destroyed except for four that remain and all of them are from the post-classical period. We may never know how they discovered zero or many of the details of their works since so much was lost to religious intolerance.

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