The Wikipedia page on Mayan numerals mentions the symbol for zero is an upside down turtle shell. It is not clear from the symbol itself that it is a turtle shell, and I'm not able to find any source explaining why we believe it is a turtle shell. I've seen other references (1 and 2) saying it is an olive (or oliva) seashell.

What is the evidence that this post-classical Mayan symbol for zero is a shell and is it actually a turtle shell or some other kind of shell?

The reason why I'm interested is that the Mayans used dots and bars for the rest of this variant of their number system, which could have come from calculating using rocks and sticks on the ground (this is just a conjecture by me). I can imagine they might have also picked up olive shells along the beaches and used that to represent zero. That would seem to be a better size to manipulate for calculations than a big turtle shell (as an avid seashell collector, it's neat to think that the olive shell could have been associated with an early concept of zero).

From the paper Anna Blume: "Maya Concepts of Zero" (March 2011, Proceedings of the American Philosophical Society 155(1)) I referenced above as (1) it says:

In his 1886 commentary on the Dresden Codex, Förstemann originally thought these oval forms “looked like a symbol for the human eye”. Twenty-four years later, in their 1910 study “Animal Figures in the Maya Codices,” it was Tozzer and Allen who identified the standard oval form that the Maya used to represent zero in the codices as a stylized oliva shell.

So it seems like there is some guesswork here, and I'm not sure where the turtle shell theory originated.

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    It is the shell's emptiness which signifies nothingness; or zero, as you put it.
    – Lucian
    Sep 28, 2021 at 12:13
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    @Lucian - that seems plausible that the Mayans associated the shell with emptiness but is there any proof of that? Sep 28, 2021 at 16:59
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    You mention "big turtle shell" twice. What makes you think it can't be a "small turtle shell"? Sep 29, 2021 at 13:08
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    @RayButterworth - that's a fair point. I just mean big relative to the rocks and sticks they might have used during calculations. Sep 29, 2021 at 21:25
  • Looks like the Wiki page on the Mayan number system has been updated. Thanks to whoever did that! I'm also trying to get it updated in en.wikipedia.org/wiki/0#Pre-Columbian_Americas - I can't edit the page on '0' directly so added suggestions in the Talk page. Oct 1, 2021 at 21:17

3 Answers 3


I've done some further research, and I'd like to post my findings in a form of an answer.

I could not find any authoritative source mentioning the symbol is a turtle shell, so that section in the Wikipedia article should probably be revised.

Throughout their history, the Mayans used different symbols for zero. In the Classic period, they used the Quatrefoil, Shell-in-hand, and a Head variant. In the Postclassic period (Dresden Codex) they used various seashell symbols (see pictures here). There's also a simpler, more informal form, found on the walls of Structure 10K-2 at Xultun (source)

The earliest source I can find that make the connection between the pointed, oval-shape symbol for zero and seashells is Animal Figures in the Maya Codices (Tozzer and Allen, 1910): "the glyphs for various molluscs which are used not to represent the shell but to give the value of zero to the numerical calculations." See Plate 1.

For examples of the shells used, page 64 of the Dresden codex (shown below and page 49 from here) gives two different symbols for zero, with one looking clearly like a seashell. multiple seashell symbols for zero

They further deduce that the oval-shaped symbol is that of the Oliva (olive) seashell. "This is doubtless a species of Oliva, a marine shell. Mr. Charles W. Johnson informs us that O. reticulata is the species occurring on the Yucatan shores, while O. splendidula is found in other parts of the Gulf of Mexico".

Note: O. reticulata is found in the Indian and Pacific Ocean, so it is doubtful this is the correct species. It is probably more likely to be the Lettered Olive, which is common in the Yucatan. O. splendidula has been reclassified recently. This species can be found in the Gulf Of California so is another possible candidate.


I am an oyster aquaculturist. I believe they use sea shells for zero because it has to do with the way the Fibonacci sequence is expressed along a shell. This is especially true for oysters. If you follow the curve of the shell from newest to oldest growth, the point of origin for the shell lies outside of the physical shell. So 0 is the starting point of a number line just like the place of origin for a shell is a starting point and also nothing or an absence of shell. That's really the first time I wrote that out and it's incredibly hard to explain without visuals.

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To me it's always looked like a closed fist. The dots are fingertips. The bar is the side of the hand (5 fingers outstretched)

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