The Maya shell zero, and the Long Count it served
TL;DR — The Maya wrote zero as a shell glyph, in base-20 place-value use by AD 665; India’s first agreed dated zero is from 876.
The Maya had a zero of their own, written as a shell. “We know that by 665 they used a place-value number system to base 20 with a symbol for zero,” write J. J. O’Connor and E. F. Robertson in the MacTutor History of Mathematics at the University of St Andrews, adding that “their use of zero goes back further than this.” The first dated Indian zero that all scholars accept is from 876. The two zeros were invented separately; the Maya one, the same authors note, “did not influence other peoples.”
Quick facts
- When
- Earliest Long Count dates between 40 and 20 BC; a place-value system with zero in use by AD 665
- Where
- The Maya lands of southern Mexico, Guatemala and Belize, and their Isthmian neighbors to the west
- Who
- Maya and Isthmian scribes
- Outcome
- A shell-shaped glyph marked the empty place in base-20 numbers, centuries before the first agreed dated zero in India
Dots, bars and a shell
Maya numbers needed only three signs: a dot for one, a bar for five, and a sign for zero. Mark Pitts, in a guide for the Foundation for the Advancement of Mesoamerican Studies (FAMSI), shows four common ways the Maya wrote zero and points out that “the last two glyphs look like shells. Shells are often empty containers; they contain ‘nothing’, zero contents.”
The numbers ran in twenties. In a place-value system, each position is worth twenty times the one below it, and an empty position needs a mark, or the number collapses. The shell was that mark.
A day count from 3114 BC
The zero served the calendar. The Long Count counted days from a starting point that Pitts gives as “our date of August 11, 3114 B.C.,” the “creation date” of the current world. Mark Van Stone, also writing for FAMSI, notes that the date depends on the correlation used: the common one gives August 11, 3114 BC, while Floyd Lounsbury’s adjustment puts it two days later, on August 13.
The Long Count is older than the Classic Maya. “The earliest known Long Count dates (7.16.x.x.x, between 40 and 20 BC/BCE) come from Chiapa de Corzo, Tres Zapotes, and Takalik Abaj,” Van Stone writes. “The last is Maya, but the other two are Isthmian,” from west of the Maya lands, and in the majority view, Van Stone reports, the Long Count was “an Isthmian, not a Maya invention.”
Babylon, India and the Maya
Zero had more than one origin. MacTutor dates the first Babylonian placeholder to “around 400 BC,” when scribes “put two wedge symbols into the place where we would put zero.” In India, “in around 500 AD Aryabhata devised a number system which has no zero yet was a positional system.”
The first Indian zero with an agreed date is later. “The first record of the Indian use of zero which is dated and agreed by all to be genuine was written in 876,” MacTutor records: an inscription at Gwalior about a garden “187 by 270 hastas” that would provide “50 garlands per day” to the local temple. It was the Indian system, MacTutor adds, that passed west to the Islamic world.
The Maya did not vanish
The people who carved these numbers are still there. “Today’s population of six million may even surpass that of all the cities of the Classic period,” Van Stone writes, and “depending how you count, there are from 22 to 30 Maya languages in use.” Their “260-day sacred calendar has been in use without interruption for at least 2300 years.” The Classic Maya, by MacTutor’s dates, flourished between AD 250 and 900; the Maya use of the 584-day cycle of Venus is told in a separate article.
Key facts
- By AD 665 the Maya used a base-20 place-value system with a symbol for zero (MacTutor).
- Two of the four common Maya zero glyphs look like shells (Pitts, FAMSI).
- The Long Count starts on August 11, 3114 BC by the common correlation, or August 13 by Lounsbury’s (Van Stone, FAMSI).
- The earliest Long Count dates, 40–20 BC, come from Chiapa de Corzo, Tres Zapotes and Takalik Abaj (Van Stone).
- India’s first dated zero accepted by all is the Gwalior inscription of 876 (MacTutor).
- About six million Maya live today, speaking 22 to 30 Maya languages (Van Stone).
FAQ
Did the Maya invent zero?
They developed their own. By AD 665 they used a base-20 place-value system with a symbol for zero, and their use of zero goes back further. It was invented separately from the Indian zero.
What did the Maya zero look like?
It had several forms; two of the common ones look like shells, which, as Mark Pitts notes, are empty containers.
Was the Maya zero earlier than India's?
The Maya were using a place-value zero by 665. The first dated Indian zero that all scholars accept is from 876, at Gwalior, though Indian mathematicians used positional numbers earlier.
Did the Maya invent the Long Count?
Probably not. The earliest Long Count dates, from 40 to 20 BC, come from two Isthmian sites and one Maya site, and most scholars think it was an Isthmian invention.
Do the Maya still exist?
Yes. About six million Maya live today, speaking 22 to 30 Maya languages, and the 260-day calendar is still in use.
Sources
- J. J. O'Connor and E. F. Robertson, "A history of Zero," MacTutor History of Mathematics, University of St Andrews
- J. J. O'Connor and E. F. Robertson, "Mayan mathematics," MacTutor History of Mathematics, University of St Andrews
- Mark Pitts, "Book 2: Maya Numbers and the Maya Calendar," FAMSI
- Mark Van Stone, "2012 FAQ," FAMSI
Cite this article
- APA
- Song Letter. (2026, October 11). The Maya shell zero, and the Long Count it served. Our Earth's History. https://ourearthshistory.com/americas/classical/maya-shell-zero-before-india/
- Chicago
- Song Letter. “The Maya shell zero, and the Long Count it served.” Our Earth's History, October 11, 2026. https://ourearthshistory.com/americas/classical/maya-shell-zero-before-india/.
- MLA
- Song Letter. “The Maya shell zero, and the Long Count it served.” Our Earth's History, 11 Oct. 2026, https://ourearthshistory.com/americas/classical/maya-shell-zero-before-india/.
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