# Religion in Mayan Math

### Introduction

The Mayans had a rich culture, which included substantial mathematical knowledge. They had a written number system, advanced knowledge of astronomy and an incredibly accurate calendar. Unknown to many, all of these things were heavily influenced by Mayan religion. In fact, priests were the ones who performed the majority of Mayan mathematics (Joseph, 2011, p.68).

### Religion in Mayan Numbers

The Mayan number system was relatively simple, and very effective. It utilized a dot as a one and a line as a five. These were paired together to create all numbers up until twenty, as this picture shows.

(Jackson, 2022)

In addition, there was also an alternative method for writing the numbers one through nineteen using heads that are believed to be Mayan deities, as shown in this picture.

(Montgomery, 2014)

Once the numbers reached twenty they began to group the dots and lines into groups that symbolized different numbers. from right to left the groups symbolized the amount of 1's, the amount of 20's, the amount of 360's, the amount of 7,200's. They also had a symbol to represent zero when there was not any in a group. This is an early form of zero, which is really fascinating! This is one of the earliest forms of any kind of zero! The Mayans did not use zero as a number like we do today, but they did use it as a placeholder. Learning about this is very interesting because it allowed them to differentiate between numbers like 67 and 6,0007, something other cultures had difficulty with. The numbers each group represents are not arbitrary. The first one is one, which makes sense, as does twenty if this was a base twenty system, which it is. The next number is found by taking eighteen times twenty, and after that each number is found by taking that times twenty an additional time. This picture illustrates the concept very well.

(Unknown, 2016)

The eighteen may seem completely random and useless, especially considering it makes calculations more difficult. It had a reason though. According to Joseph (2011), "the rationale behind the Mayan numeration system was not its effectiveness as a system for calculation but the calendrical requirement of counting the days of eighteen months, each of twenty days" (p. 68). These calendars were heavily influenced by religion in Mayan society, and astronomy was required to make them, as is discussed in the next section.

### Religion in Mayan Astronomy

Mayans had surprisingly accurate astronomy, despite not having modern devices. They had extremely close calculations for the length of a solar year, a lunar cycle, and even calculations on the orbit of Venus, and detailed information about eclipses'. The Mayan had religious reasons for many of their astronomical pursuits. According to Aldana (2007), "The Mayan saw the night sky as a reflection of the Underworld." (p.11). This religious correlation led them to be very attentive to the night sky, as they used it to know what was occurring in the Underworld. There are also correlations between Mayan gods and the cycles and orbits of different planets, especially Venus. Mayans had Venus tables, with very accurate calculations for Venus cycles. On each page of the table there is also three pictures. The first one is the god associated with the Venus cycle. The second is a spear-thrower, representing Venus, and the final one is a representation of the victims of the spear-throwers. The Venues tables also include what the Mayans believed to be different manifestations of Venus, and victims of Venus' rising (Closs, 1986, p.206) Here is a picture of what the Mayan Venus tables looked like.

(Santa, 2016)

It is clear to see that religion was greatly intertwined into Mayan astronomy. Another thing that is very interesting to ponder is how the Mayans came to such accurate calculations without the modern devices we have. We do not know, but we do know it must have taken a lot of thought and work. There are many ways in which we should be in awe of ancient cultures. However they came about it, Mayan astronomy was used to make calendars, so it is no surprise that calendars also had a lot of religious aspects to them in Mayan culture.

### Religion in Mayan Calendars

Mayan numbers and astronomy are both necessary for creating Mayan calendars. The Mayan had three separate calendars all with different uses. The first one is a 260 count calendar called the chol qiij, which means ordering of days (Aldana, 2022, p.39). It is commonly known as the tzolkin, meaning sacred year (Joseph, 2011, p.68), the reason for which will be discussed soon. This calendar was created with a mixture of Day signs and numerical coefficients. At the beginning of the year both would start at the first one, and each would repeat once all had been used. This sequence would come to an end and restart once the first Day sign and numerical coefficient were paired together again. This took 260 days, thus creating a 260 day calendar that looked something like this easy to understand rendition.

(Furian, 2024)

Now, the reason this one was considered the "sacred year" is because this was the calendar used by priests for religious rituals. Each one of the Day signs "was considered a god to whom prayers and other supplications were to be made" (Joseph, 2011, p.69). In addition, "Each of the thirteen numbers could represent one of the thirteen gods of the Superior World or one of the thirteen gods of the Inferior World" (Joseph, 2011, p.70). This was a very useful calendar for religious purposes, but not very helpful to the normal person. Thus, the Mayan devised a second calendar system. "The haab’ was a 365-day approximation to the solar year" (Aldana, 2007, p.xxix). This calendar was used to measure the years and seasons. It consisted of eighteen twenty day months with an additional five day month at the end, and would have looked something like this illustration.

(Unknown)

Finally, there was the third calendar, the long count calendar. This calendar was used to count the time that had passed since the first Mayan day, which is theorized to be about August 13, 3114 BC. It was counted in different units. The first one was a kin, and it represented a day. The next was a uinal which was 20 kins. Then a tun, which was 18 uinals. Each unit after that denoted twenty of the units before it, similar to the Mayan numeral system. Here is an accurate description of what the Mayan long count calendar looked like.

(Quirigua)

Each unit had a hieroglyph that represented it, some of which were Mayans gods. In addition, the Mayans believed that when their long count calendar came back around to the beginning the Gods would return, which would have occurred in 2012 (von Däniken et al., 2010). This is quite fascinating, and even though no gods returned in 2012, perhaps scary to some. It is intriguing that the Mayan predicted the return of their Gods to a specific day. It is also fun to theorize as to what exactly they believed would happen when the gods returned. We do not know, but we do know that Mayan calendars were extremely important for the Mayan religion.

### Conclusion

Mayan religion has impacted Mayan math a lot. The main places it has impacted Mayan math are in numbers, astronomy and calendars. Math was something mainly done by Mayan priests and many Mayan gods appear as numbers. Religion also inspired the Mayans to explore astronomy, and create multiple different calendars. In the end, like many other ancient cultures, math and religion were intertwined in Mayan culture.

References

Aldana, G. (2007). The Apotheosis of Janaab’ Pakal : Science, History, and Religion at Classic Maya Palenque. University Press of Colorado. https://ezproxy.shsu.edu/login?url=https://search.ebscohost.com/login.aspx?direct=true&db=e000xna&AN=347940&site=eds-live&scope=site&ebv=EB&ppid=pp_Cover.

Aldana, G. (2022). Calculating Brilliance : An Intellectual History of Mayan Astronomy at Chich'en Itza. University of Arizona Press. https://ebookcentral.proquest.com/lib/shsu/reader.action?docID=28935672&ppg=1.

Closs, M. P. (1986). Native American Mathematics. University of Texas Press. https://ezproxy.shsu.edu/login?url=https://search.ebscohost.com/login.aspx?direct=true&db=e000xna&AN=2942907&site=eds-live&scope=site&ebv=EK&ppid=Page-__-1.

Furian, P. (2024). Tzolkin, a 260-day Mesoamerican calendar used by Maya civilization of pre-Columbian Mesoamerica. Gear with 13 numbers turning a gear with 20 day names [Photograph]. Alamy. https://www.alamy.com/tzolkin-a-260-day-mesoamerican-calendar-used-by-maya-civilization-of-pre-columbian-mesoamerica-gear-with-13-numbers-turning-a-gear-with-20-day-names-image613615001.html?imageid=59B6BE8A-687B-4C1A-A8C1-C71BED84FBEC&p=183153&pn=1&searchId=033cf23b6f4d446218ed8ae691e7ea8c&searchtype=0.

Jackson, J. (2022). Mayan Numerals [Photograph]. YouTube. https://www.youtube.com/watch?v=7BIo_uTPew0.

Joseph G. G. (2011). The Crest of the Peacock: Non-European Roots of Mathematics(3rd ed.). Princeton University Press.

Montgomery, J. (2014). Maya numerals - Head-Variant Glyphs [Photograph]. Planet Archaeology. https://planetarchaeology.co.uk/maya-number-system/.

Quirigua, S. Mayan Long Count [Photograph]. Mayan Calendar Time. https://www.mayan-calendar.org/index.html.

Santa, B. (2016). The Preface of the Venus Table of the Dresden Codex, first panel on left, and the first three pages of the Table [Photograph]. Science Alert. https://www.sciencealert.com/this-ancient-text-reveals-a-maya-astronomer-calculated-the-movements-of-venus-over-a-millennium-ago.

Unknown. (2016). Mayan Number System Explained [Photograph]. Stack Exchange. https://math.stackexchange.com/questions/1758155/mayan-number-system-explained.

Unknown. The Haab [Photograph]. Calendarr. https://www.calendarr.com/canada/.

von Däniken, E. (2010). Twilight of the gods : The Mayan Calendar and the Return of the Extraterrestrials. Red Wheel/Weiser. https://ebookcentral.proquest.com/lib/shsu/detail.action?docID=5531289.