The ancient Maya had discovered, understood, and used zero.
They usually represented the value of zero or null with the symbol of an ovular shell.
The Long Count calendar requires the use of a zero as a place holder within its vigesimal numerical system. There have been many different glyphs that were used as a zero symbol by different scribes for marking Long Count dates.
Glyph writing was a respected form of art to the Maya. At Chiapa de Corzo, Mexico, the earliest known use of glyphs being used as zero was discovered on ‘Stela 2’ located there which dates to 36 BC.
The concept of zero is attributed to first being understood and utilized by the Hindus.
The Hindus were also the first to use the concept of zero in the way it is used today. A symbol was required in positional numbers to mark the place of a power at the base of a value that was not actually occurring. To mark no value in a value position. This was indicated by the Hindu by a small circle called a “Shunya.” This is the Sanskrit word for ‘vacant.’
By the middle of the second millennium BC, in the ancient civilization of Babylon the lack of a positional value for zero was indicated by a space between their symbols of numerals.
The Babylonians used a sexagesimal counting system that had the value of 60 at its base. This was the same sexagesimal system that was also used by the ancient Sumerians during the third millennium BC. They had passed down their system of mathematics to the ancient Babylonians.
In 498 AD, the Indian (Hindu) mathematician and astronomer Aryabhatta introduced the decimal system when he stated, “Sthanam sthanam dasha gunam.” This statement means, “place to place in ten times in value.” This may have been the origin of the modern tenbased decimal value system used today.
The ten number based system used with the Hindu decimal zero was adopted by Arabian mathematicians. They had further modified it and introduced the decimal system and the concept of zero to the Europeans during the Middle Ages.
There are two concepts of zero.
One concept is that as being a placeholder in the numbering system to indicate the absence of numbers in a numbering column. This usage was known by the ancient Babylonians and surprisingly, also by the Maya some centuries before. The zero representation used by the Maya civilization didn’t look like ours and was used slightly differently because their number systems stacked and wasn’t tenbased system.
The other concept of zero is that as being a “null number’, or what you get when you subtract 1 from 1. Instead of being a placeholder for the absence of a value, it is the value of nothing. This concept was not developed until some time later. It is estimated to have been realized by at least after 600 AD, but nobody knows exactly who had came up with this concept, or exactly when.
It is speculated that it could have been the Arabic mathematicians, but there is no documentation to be that certain.
Since the eight earliest Long Count dated artifacts appear outside of the main Maya homeland, it is assumed that the use of zero in the Americas predates the Maya civilization and was possibly the invention of the Olmecs. Many of the earliest Long Count dates were found located within the center areas of the Olmec civilization which had already ended by the 4th century BC. These Olmec artifact dates are several centuries before the earliest known Long Count dated artifact that has yet been found.
In addition to understanding the concept of ‘zero,’ there are some examples in the Mayan language that tell us that the Maya also understood the notion of infinity.
Here are some examples:

“Hun tso’dz’ceh,” to count the hairs a deer has.

“Maxocbin,” infinite in number.

“Hunhablat,” countless.

“Picdzaac(ab),” long number, countless.

“Ox’lahun D’zakab,” eternal thing.

“Hunac,” countless times.
The Maya used a vigesimal numerical system that’s based on sets of 20. In a true twenty based system, the first number denotes the number of units up to the value of 19. The next set would denote the number of 20’s up to 19 times until the sum value is 400. The next set of numbers are the 400’s up to 19 times and so forth up to the next set.
This rule of the vigesimal is followed by the Maya with the exception of when it was used for calendars in the third place value only the numbered of to the 360’s, instead of the number of the 400’s. This is because of the 18 20day uinals that make the 360 days in the Haab’ year.
This vigesimal mathematical system is used in the writing used by the scribes that wrote the Dresden Codex. It’s the only math system of the ancient Maya for which we have any written evidence of. This is the number system used by the Maya priests and astronomers for celestial and calendaric calculations.
Besides calendars and dating, the Maya needed a counting system they could easily use on a day to day basis. A counting system that would have been used by merchants and traders. This had to be a commonly known numbering system that was used in daily speech when communicating amounts.
The Maya commonly used a dot to represent one value using a cocoa bean or a pebble for counting. We can speculate that they may have perhaps used a stick as a horizontal bar to represent 5 and other special symbols to represent the values of 20, 400, or 8000, an amount of which we know they called a ‘pic’.
Although no trace of such a counting method remains, we can reasonably speculate that the Maya used a simple numbering type counting system of such as pebbles and sticks. The count could be higher with this method with higher numbers being calculated by repeating or removing the sticks and pebbles as many times as was needed to make the count.
The Maya vigesimal 20 based counting system has been found in use through numerous different archaeological discoveries. The Maya used mathematics for a wide spectrum of things. However, it should be noted that it is extrapolated by some that the Maya did not have methods of multiplication for their numbers and definitely did not use division of numbers. This cannot be true as the Maya counting system is certainly capable of being used for the operations of multiplication and division.
The Maya vigesimal system still tends to confuse people. Counting that goes 1, 20, 400, 8000, 160000, etc., can seem complicated and confusing when you’re trying to figure out how it was useful to anyone except to very ‘bright’ Maya?
As mentioned earlier, the decimal system is based on ten which we can get by counting our fingers, 1 – 10. Whereas, the Maya counted all the way to twenty by counting all their fingers AND toes to 20. We use the decimal system and count in sets of 10, the Maya used the vigesimal system and counted sets of 20. Each set of 20, goes up the next level and is then counted in sets of 20 again and so forth up each tier or level.
That can get rather confusing when you’re not used to counting like that. What about a way to count simple things in “Maya 20 count way” without being very good at it?
Article source:

This article is an excerpt from the book: Kane, Njord. “Chapter 12 – Ancient Maya Arithmetic.” The Maya : The Story of a People. 2nd ed. Yukon: Spangenhelm, 2016. ISBN: 9781943066032 Used by permission from the author and publisher exclusively for use on readicon.com only.
Sources:
 Kane, Njord. The Maya : The Story of a People. 2nd ed. Yukon: Spangenhelm, 2016. ISBN: 9781943066032
 Kane, Njord. Maya Math Simplified. 2nd ed. Yukon: Spangenhelm, 2016. ISBN: 9781943066087
 Georges Ifrah, “From One to Zero, a Universal History of Numbers”, Penguin Books, 1987.
 G Ifrah, A universal history of numbers : From prehistory to the invention of the computer (London, 1998).
 J B Lambert, B OwnbeyMcLaughlin, and C D McLaughlin, Maya arithmetic, Amer. Sci. 68 (3) (1980), 249255.
 Lounsbury, Floyd G. Maya Numeration, Computation, and Calendrical Astronomy. In Dictionary Of Scientific Biography. New York, New York. Charles Scribner’s Sons. Volume 15, Supplement 1. 1978. P. 759818.
 McAnany, A. Patricia (1998). “Ancestors and the Classic Maya Built Environment.”
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written by Njord Kane © 2016 Spangenhelm Publishing
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