MiSciNet's Ancestors of Science: Mayan Mathematics

With a network of city-states that stretched from southern Mexico to Honduras, ancient Mayan civilization was rampant with technological advances, but arguably none were more vital than their achievements in mathematics.Mayan civilization began near 300 B.C.E. and lasted until 1200 C.E. Because many of their writings were destroyed in the sixteenth century by Spanish conquistadors, experts are unsure when the Maya developed their mathematical system. But surviving texts demonstrate that they developed an adaptable and simple-to-use mathematical system.

The Maya used a base 20 (vigesimal) numerical system, unlike our current base 10 or the Babylonian base 60 system that we still use for time-keeping. Consequently, instead of counting, as we do, in multiples of 1, 10, 100, and so on (10 raised to the power of 0, 1, and 2, respectively), the Maya counted in 1s, 20s, 400s, and so on (20 raised to the power of 0, 1, and 2, respectively).

Another difference between the Mayan system of counting and our system is that, whereas we have a unique symbol for each numerical value (0-9), the Maya used only three symbols to form all their numbers (which were only positive integers): a dot representing one, a bar representing five, and a shell representing 20 or zero, depending on its placement.

Here's an exercise in Mayan math. Using the Mayan system, solve the following problem, then translate it into our modern, base-10 system. You'll find the answer at the end of the article.

The most noteworthy trait of Mayan mathematics was an awareness of zero. The concept of zero in mathematics was unknown in most places during the time of the early Maya, with the Gupta Empire in India being an exception. Zero days and zero years exist in Mayan calendars, unlike the standard Gregorian calendars.

The Maya also understood the value of zero in positional notation (place holding). Without zero, one cannot distinguish 12 from 120 or 43 from 403. The use of zero also provides the ability to manipulate and estimate huge numbers. In contrast, the Greeks used words instead of numerals for noting large numbers. For example, to the Greeks the word "myriad" meant 10,000.

The sophisticated Mayan system of math enabled them to develop accurate time measurements (among the most accurate ever developed), erect huge step-pyramids, and control a vast system of trading with neighboring civilizations.

Here's the answer to the problem above: 7 + 12 = 19


  • Canadian Museum of Civilization Corporation, Mayan Civilization: Mathematics, available at http://www.civilization.ca/civil/maya/mmc01eng.html (Canadian Museum of Civilization Corporation, 2001)

  • D. Teresi, in Lost Discoveries: The Ancient Roots of Modern Science -- from the Babylonians to the Maya, (Simon & Schuster, 2002), pp. 75-87.

  • W. Kuhn. Auburn University Department of English: Classical India available at http://www.auburn.edu/english/gb/gbsite/india/classical/classicalindia.html (2001)

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