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“Nik” — The Zero in Vigesimal Maya Mathematics

Presentation #336.03 in the session “Collaboration with Integrity: Partnerships with Indigenous Communities in the Americas and Polynesia”.

Published onJan 11, 2021
“Nik” — The Zero in Vigesimal Maya Mathematics


The Maya zero, as both a philosophical and a mathematical concept, implies the beginning and the end, the absence of quantity, and a bridge between the past and the future. From a philosophical perspective, the zero is understood through a Maya worldview, and from a mathematical perspective, the zero is a well-defined concept and symbol within the Maya vigesimal system. In various expressions—including stone sculpture, painted codices, and decorated pottery, among other media—the Maya zero is represented as a flower, a seed, a human head in profile, or a conch shell. The seed is typically used in arithmetic calculations while the flower appears most often in representations of the Long Count Maya calendar. The oldest representation of the Mesoamerican zero, dating from the year 31 BCE, is found in Stela C in the ancestral Olmec site of Tres Zapotes in Veracruz, Mexico. This presentation will share cultural and calendric connections of the Maya zero, as represented in the written and artistic record as well as the oral tradition of the living cultures of the Maya people in Guatemala.


Today, more than seven million Maya live in our original homelands of Mesoamerica and globally. Our communities continue to generate new knowledge, uninterrupted despite the legacy of colonization and the pressures of globalization. Two thousand years ago, my Maya ancestors built monumental cities, developed a written language of hieroglyphs,and invented the mathematical concept of zero, or “Nik.” The source of knowledge for this study emerges from Maya epigraphy — the study and interpretation of ancient hieroglyphic inscriptions (Coe and van Stone 2005). The Maya writing system contains knowledge revealing the unique and original understanding that our ancestors had about science and mathematics. In 1880, Ernst Forestmann, while studying the pre-Columbian Maya Codex housed in Dresden, Germany, was the first to identify the Maya symbols for the number one (a dot), the number five (a bar) and the Maya zero (a conch shell). Additional symbols representing the Maya zero include Nik, a flower, discovered in Maya stelae, the carved stone columns found in many ancestral Maya cities, in the 1960s. Archaeological research reveals the antiquity of such symbols. The oldest stelae with number symbols are found in Chiapa de Corzo, Chiapas, Mexico, with a date of 36 BCE and in Tres Zapotes, Veracruz, Mexico, with a date of 31 BCE.

In the context of Maya mathematics, it is important to consider the Maya worldview of time, which is cyclical. All events are destined to repeat themselves, as some of our colloquial expressions indicate: “Everything that has happened, will happen again” and “Every beginning will have an end, and every end will have a new beginning.” These expressions come from our observations of nature and the cosmos. We perceive cycles in the seasons of the year, which repeat indefinitely, and in the daily motion of the Sun and other celestial objects. The Moon has four main phases: new, first quarter, full, and third quarter. The Moon is perceived as dying, to be reborn every time it passes between the Earth and the Sun. Therefore, the zero point, or Maya Nik, represents that singular instance in the cyclical motion of the Moon. The Moon does not die, but reappears, cyclically, forever. The same happens with the planets and constellations.

All living things in nature go through cycles. The life cycle of a plant serves as an illustrative example. The seed, when placed underground, germinates, and with time it develops leaves, then it will produce flowers and bear fruit. The fruit will give forth the same seed as the seed that was planted, in an endless cycle. The seed is in concert with the life cycle of the plant; therefore, one of the symbols for the Maya zero is a seed. Nik, the Maya zero, is represented by several symbols: a seed, a snail, a seashell, a flower, a human head, and a headless torso. In this document, we only discuss the flower—Nik.

The representation of the Mesoamerican ritual calendar, found in pre-Columbian codices of both the Maya and the Aztec or Mexica civilizations, is shown in Figure 1. The fascinating thing about this design, is that it clearly depicts a flower, which is a symbol for the Maya zero. This realization inspired me to continue my investigations about the vigesimal Maya zero with new vigor, encouraged by the thought that the meaning of zero had a deeper philosophical underpinning. The question that emerged is “Why did my ancestors, the wise Maya artists, express the ritual calendar in the form of the Maya zero?”

Figure 1

This image (left) of the Codex Fejérváry-Mayer, a pre-Columbian Aztec Codex of central Mexico, reflects one of the representations of Nik—the Maya zero as the flower—which becomes clearly apparent in juxtaposition (right).

The Days of the Maya Ritual Calendar

The Cholk’in (or Cholq’ij) Maya calendar is a ritual cycle of 260 days (13 numbers multiplied by 20 days). The names of the days in the K’iche’ Mayan language are as follows: Ajpu’(or Ajaw in Yucatec Mayan), Imox, Iq’, Aq’ab’al, K’at, Kan, Kame, Kej, Q’anil, Toj, Tz’I’, B’atz’, E, Aj, I’x’, Tz’ikin, Ajmaq, No’j, Tijax, and Kawoq. These days have an invariable numerical code, which goes from 0 to 19. The 0 corresponds to Ajaw (Ajpu’), 1 corresponds to Imox, and so on, until the last day Kawoq, corresponding to the number code 19, to start over again with Ajaw.

Another of my curious findings relates to the Tonalamatl Aztec or Mexica calendar of 260 days, which is equivalent to the Maya calendar described above. The symbols that the Aztecs used to represent the days vary in design, but not in meaning, compared to their maya equivalents. Ajaw in the Aztec calendar is called Xochitl, which translates literally to “flower,” and its symbol is indeed a flower. I deduced that the Maya zero, represented by a flower in both Maya and Aztec numerical and calendrical iconography, has a transcendental meaning, the depth of which has not been fully deciphered, awaiting a future time.

Today—the Maya zero

Another curious finding is that “today,” in the Maya worldview, is Nik,or the Maya zero. Speakers of Mayan languages know this, which becomes clear when we analyze how Mayan languages express future and past days with great ease and expanse, both into the past and towards the future. To name past and future days in my Kaqchik’el Mayan language, for example, we construct the word starting with the number of days we want to express plus a suffix implying past or future. Thus, "iwir,” or “yesterday,” in Mayan, literally means “one day into the past.” "Kabijir,” the day before yesterday, literally means 2 days into the past, and so on, indefinitely. To express future time, we say “chuwaq,” meaning “tomorrow,” meaning 1 day into the future. "Kabij," the day after tomorrow, literally means 2 days into the future, and so on, indefinitely. If yesterday and tomorrow are days with the numeral 1, then necessarily “today” is Nik, the Maya zero. It is noteworthy to point out that in Spanish or English, there are no expressions of time that go any further than two days into the past or the future; however, in Mayan languages, using the numerical construction on either side of Nik allows us to express these timeframes, past and future, ad infinitum.

To express the word “today” in the Q’anjob’al Mayan language, we say “nani,” which translates to “today,” or “center.” As a matter of fact, today is at the center of the past and the future. In the K’iche’ Mayan language, “today” is expressed as “kamik,” with a literal translation meaning “death.” The philosophical connection between the word “kamik” and = Nik, is that, when a person dies, the count of the days of his or her life on Earth ends, and a new count begins from the day the person died.


To summarize, the vigesimal Maya zero has the following meanings: (a) Beginning and end; (b) Center; (c) Seed; (d) Death; (e) Absence of quantity, among other variants, including “Mother.” More details about this research can be found in two publications by the author in 1996 and 1997, listed in the references.


  • Coe, M. D. and Van Stone, M. 2005, READING THE MAYA GLYPHS, Thames and Hudson, Inc. ISBN-13: 978-0-500-28553-4.

  • Mucía Batz, J. 1996. "Nik" Filosofía de los números mayas. Un aporte al rescate de la cultura maya, Centro de Documentacion e Investigacion Maya (Guatemala). Publisher: Guatemala CEDIM; Chimaltenango:Rutzijol. (Editorial Saqbe 2001).

  • Mucía Batz, J. 1997. JUNRAQAN, cosmovisión y los números mayas. Guatemala C. A.

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