Did the Maya Really Invent the Concept of Zero?

The Maya did invent zero, and the strongest evidence for that claim is internal to the Maya record itself: the shell glyph, the modified Long Count, and the unbroken tradition of use from the Late Preclassic through the colonial period. The harder questions — whether the invention was independent, whether it was borrowed from outside Mesoamerica, and how it compares with the parallel Indian invention of the fifth or sixth century CE — remain live in the scholarly literature. This page follows the article format of the site, working outward from the Maya number system and the concept of zero pages and linking to related topics in Maya writing, language, and books and the Maya codices and surviving books.

The internal evidence: the shell glyph, the Long Count, and the position-of-zero function

The case for Maya invention of zero rests on three pieces of internal evidence. First, the Maya had a sign for zero — the shell glyph, sometimes read as a cowrie shell, sometimes as a half-flower — that they used in three different notational systems: the bar-and-dot system, the head-variant system, and the Long Count calendrical system. Second, the zero was used positionally, as a true placeholder, in all three systems, and not merely as a “nothing” mark. Third, the zero was in continuous use for more than a thousand years, from the Late Preclassic through the Spanish conquest, with no major change in its form or function.

The Tres Zapotes Stela C is the earliest securely dated use of the shell-glyph zero in a Long Count inscription. Tres Zapotes is an Olmec-Maya site in the Tuxtla Mountains of southern Veracruz, and the monument carries the Long Count date 7.16.6.16.18, which corresponds to 32 BCE in the proleptic Gregorian calendar. The shell-glyph zero appears in the tun (360-day) position of the date. The Tres Zapotes Stela C is the subject of a separate article in the history of the Maya civilization pillar, and the Tuxtla Statuette, another early Long Count monument, also uses the shell-glyph zero at a date of 8.6.2.4.17 = 162 CE. The tradition of zero as a positional sign is therefore attested in Mesoamerica at least 360 years before the conventional date of 357 CE for the Indian mathematician Brahmagupta’s first explicit statement of zero as a number in its own right.

Within the Maya area, the shell-glyph zero is attested on a number of Late Preclassic and Protoclassic monuments, including the Chiapa de Corzo stela, the Mojarra Stela (La Mojarra Stela 1, which is Isthmian-script, not Maya, but uses a similar numerical system), and a handful of lowland Maya examples. The tradition is unbroken into the Classic period, when shell-glyph zeroes become universal in Initial Series inscriptions at Tikal, Palenque, Copan, and Quirigua.

The shell glyph itself: an iconographic argument

The shell-glyph zero in the Maya script is usually a stylized nautilus or a cowrie shell, sometimes painted with a fleshless lower jaw and identified with the death’s-head or with the Earth Lord of the night. The iconographic reading of the sign as a shell is supported by its appearance in non-numerical contexts — for example, in the “jester god” headdress of Maya kings, where the shell sits in a position of cosmological importance. The shell, in the pre-Columbian Mesoamerican world, was a symbol of moisture, fertility, and the watery underworld; the choice of a shell as the sign for “nothing” is consistent with the Maya tendency to use a specific, identifiable image rather than an abstract mark.

The head-variant zero — used in the Supplementary Series and the Lunar Series — is a fleshless human head, sometimes with the visual identifier of the Earth Lord, sometimes with a death’s-head jaw. The head-variant zero is conceptually parallel to the shell-glyph zero, but iconographically distinct. The two forms are never mixed in the same numerical series. The dual existence of two visually different zero signs is itself evidence that the Maya had a clear concept of zero as a sign-meaning, not just a notational convenience.

The comparison with the Indian zero

The Indian zero has a separate and well-documented history. The use of a dot or a small circle to mark an empty position in a decimal place-value system is attested in the Bakhshali Manuscript, possibly as early as the third or fourth century CE, and becomes standard in the works of Aryabhata (fifth century) and Brahmagupta (seventh century). The first explicit statement of zero as a number that could be added, subtracted, and used in equations is Brahmagupta’s Brāhmasphuṭasiddhānta of 628 CE.

The comparison is suggestive but not conclusive. The Mesoamerican and Indian traditions are separated by a third tradition in Babylon, where a place-value sexagesimal system with an empty-position marker was used in cuneiform astronomical texts from at least the third century BCE. The Babylonian empty-position marker was not a true zero — it was a contextual convention, not a number that could be operated on — but it does suggest that the conceptual breakthrough of marking an empty place in a positional system was not unique to the Maya.

The key question is whether any of the three traditions influenced any other. Direct transmission between the Indian and Mesoamerican traditions is implausible across the Pacific in the relevant period; the transmission of the Babylonian idea to either is also unlikely. Most specialists in the field treat the Maya zero as an independent invention, while noting that the parallel development of place-value systems with zero markers in India, in Mesoamerica, and possibly in China is one of the great instances of convergent mathematical thought.

Olmec and Isthmian precursors

The Olmec of the Gulf Coast (c. 1500–400 BCE) are the cultural predecessors of the Isthmian and Maya lowland cultures and the probable originators of the Mesoamerican Long Count tradition. The earliest Long Count dates are at Tres Zapotes and at the Tuxtla Mountains, and the use of a positional count with an empty-position marker in the Olmec heartland is well attested. The Olmec themselves, however, did not use a distinctive zero sign; the empty position in an early Olmec or Isthmian Long Count was typically left blank, or marked with a small crescent or a half-eye, and the explicit shell-glyph zero seems to be a Maya innovation of the Late Preclassic period.

The Isthmian script, used in the Isthmian region of southern Mexico and western Central America, had a numerical system very similar to the Maya system but with a smaller set of head-variant numerals and a different set of month signs. The Mojarra Stela (Isthmian, c. 156 CE) uses a Long Count date in a system that is essentially Maya in form. The Isthmian numerical system did not use a distinctive zero sign, however, and the monuments that do mark an empty position in the Long Count typically use a small crescent or a half-eye that is not the same as the Maya shell glyph. The Maya invention of the zero is therefore a Maya innovation, not a borrowing from the Isthmian tradition.

Quirigua Stela E and the chronology of use

The single most spectacular use of zero in the Maya corpus is on the Quirigua Stela E, a Late Classic monument in the lower Motagua River valley of eastern Guatemala. Stela E was erected in 756 CE by the ruler K’ahk’ Tiliw Chan Yopaat (Cauac Sky), the great enemy of Copan. The monument’s Initial Series inscription records a Long Count date in the 9th baktun, and its Period Number, the multiple by which the date is projected forward to a future end-of-cycle, uses a 33-digit vigesimal number. The shell-glyph zero appears in multiple positions of the date, including the baktun (the 144,000-day cycle), the katun (7,200 days), and the tun (360 days). Quirigua’s use of the zero in these positions is the same as the use of the zero on monuments two centuries earlier, and the same as the use in the colonial-period codices.

The Quirigua monuments are surveyed in Maya stelae, altars, and stone monuments and the history of the Maya civilization pillar. The site’s dynastic history is treated in the page on Copan and the dynasty of the 18-Rabbit.

The case against independent invention

The argument against the independent-invention view, advanced by some Mesoamericanists in the 1970s and 1980s, holds that the Olmec Long Count tradition is best understood as a development of an even earlier, possibly South American numerical tradition. The argument is not widely accepted; the chronological evidence places the Olmec Long Count well after the late Paracas and early Formative traditions of the Central Andes, and the forms of the Olmec numerical signs are not directly comparable to anything in the early Andean record. The case for a South American origin of the Maya zero is therefore considered weak by most specialists, but the question is not closed.

A second argument against the independent-invention view holds that the concept of zero is so difficult that it must have a single origin and must have been transmitted to the Maya by a now-vanished cultural intermediary. The argument is not supported by any known cultural tradition, and the historical record of zero in different civilizations (Babylonian, Indian, Maya) suggests that the concept is in fact relatively easy to develop once a positional system is in place. The “single origin” view has few defenders today.

The current consensus

The current scholarly consensus, articulated in the works of David L. Webster, David Kelley, Michael Closs, and others, is that the Maya invented zero independently, that the shell-glyph zero is a Maya innovation of the Late Preclassic period, and that the invention was a necessary consequence of the Maya’s development of a true place-value number system. The Maya zero is functionally equivalent to the Indian zero and is one of only two or three independent inventions of true zero in human history. The question of how to date the first appearance of the zero glyph is an open research question, and the field continues to refine the chronology as new inscriptions come to light.

Sources

Aveni, A. F. (2001). Skywatchers of Ancient Mexico. University of Texas Press. — link
Saturno, W. A. et al. (2012). Ancient Maya astronomical tables from Xultun, Guatemala. Science 336 (6082), 714–717. — link
Berlin, E. A. & Berlin, B. (1996). Medical Ethnobiology of the Highland Maya of Chiapas, Mexico. Princeton University Press. — link
Sharer, R. J. & Traxler, L. P. (2006). The Ancient Maya (6th ed.). Stanford University Press. — link
Coe, M. D. (1993). The Maya (5th ed.). Thames & Hudson. — link