Maya numerals (bar and dot)
The Maya wrote numbers with a dot for one, a bar for five and a shell for zero, counting in twenties. Stacked in levels, the signs could record very large numbers and long spans of time.
Meaning
Maya numbers count by twenties, not tens. The NMAI’s Living Maya Time gives the three signs: a dot is 1, a bar (“a stick”, in the museum’s words) is 5, and a shell is 0. Dots and bars together write every number from 1 to 19. Joyce Marcus explains that from about 600 BC to AD 900 most peoples of Mesoamerica wrote numbers this way, and that among the Gulf Coast peoples after 50 BC and the Lowland Maya the position of a sign also counted: each level up is worth twenty times the one below, 1, 20, 400, 8,000 and 160,000, where our places are 1, 10, 100 and 1,000. With place value came a sign for zero. The museum adds that not long ago traditional people in Yucatán still did sums with seeds, sticks and shells.
Origin and history
Who first wrote zero is put differently by different scholars. The NMAI says plainly that the Maya “invented the concept of zero”. Marcus credits “the peoples of southern Mexico”, who invented positional numbering “and with it established the mathematical concept of zero”. Guillermo Bernal Romero is most specific: the epi-Olmecs of the Gulf Coast, in the first century BC, built the Long Count on place value, and that required “an extraordinary invention: the value zero”.
In the calendar the rule of twenty bends once. The third level of the Long Count is not 400 days but 360, 18 × 20, so that it comes close to the year; then the counting goes on by twenties to the k’atun and the bak’tun. Mark Van Stone, writing for FAMSI, explains the base of twenty simply: in the tropics people went barefoot and “counted on their fingers and toes”.
Numbers as faces
Besides bars and dots, Maya scribes could write a number as the head of a god. The head of the Maize God, Tomás Pérez Suárez writes, was used in inscriptions for the number eight, waxak, so that he can be called its patron.
See also
Maya calendar, Kukulkan, Chaac, Itzamna, Maize God.
Sources
- Maya Math Game (Living Maya Time), Living Maya Time, Smithsonian National Museum of the American Indian, National Museum of the American Indian, Smithsonian Institution, Maya Math Game
- Maya Sun (Living Maya Time), Living Maya Time, Smithsonian National Museum of the American Indian, National Museum of the American Indian, Smithsonian Institution, Maya Sun
- Los calendarios prehispánicos (Joyce Marcus, Arqueología Mexicana), Joyce Marcus, “Los calendarios prehispánicos”, Arqueología Mexicana no. 41, pp. 12–19 (translated by Elisa Ramírez), Arqueología Mexicana (Editorial Raíces / INAH), article text, “Los numerales”
- La cuenta larga y la máquina del tiempo (Guillermo Bernal Romero, Arqueología Mexicana), Guillermo Bernal Romero, “La cuenta larga y la máquina del tiempo”, Arqueología Mexicana no. 118, pp. 30–37, Arqueología Mexicana (Editorial Raíces / INAH), article text
- Nal. El Dios del Maíz (Dios E) (Tomás Pérez Suárez, Arqueología Mexicana), Tomás Pérez Suárez, “Dioses mayas”, Arqueología Mexicana no. 88, pp. 57–65, Arqueología Mexicana (Editorial Raíces / INAH), article text
- 2012: Science and Prophecy of the Ancient Maya, Part 4: Appendix (Mark Van Stone, FAMSI), Mark Van Stone, 2012: Science and Prophecy of the Ancient Maya, Part IV, Appendix: Technicalities of the Calendars (PDF), Foundation for the Advancement of Mesoamerican Studies (FAMSI), Long Count example
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Last reviewed October 3, 2026 by Rory Hansen. How we research
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