Skip to main content

Studying pre-Columbian math and science

MILLERSVILLE, Pa. - More than 1,000 years ago, in an empire that stretched from central Mexico through present-day Central America, a group of mathematicians and astronomers developed a system that, among other things, could have predicted an eclipse that would darken the skies over a thousand years in the future, without instruments, only by using the naked eye. These indigenous people were the Maya of the Classic Period, running from about 250 A.D. to 925 A.D.

In 2007, a scholarly descendant of the Huilliche people of southern Chile is teaching some aspects of Mayan mathematics and astronomy to college students in southeastern Pennsylvania.

Ximena Catepillan of Millersville University in Pennsylvania includes a pre-Columbian component in her Mathematics in Non-European Cultures course or Math 102. In a brief interview, Catepillan explained some aspects of the course, its cultural context and how she became interested in this unusual subject.

Indian Country Today: How did you become interested in pre-Columbian math and science?

Ximena Catepillan: I became interested in this because of my heritage; my paternal grandfather was Huilliche, from southern Chile, and after my own trips to Mexico and my own interest in the Mapuche of Chile, I thought, 'Well, I want to put this together.' There is so much on the history of the Mayan culture but very little with respect to the math and science ... I studied the archaeoastronomy. The Mayans were very highly developed.

ICT: You mentioned the prediction of eclipses. How did they do this and when were these methods being used?

Catepillan: The predictions can be made by observation and that requires years of observing the cycles of the sun and the moon. They were using this system during the time of the Classical Maya period. All of the astronomical discoveries and most of the construction took place then. [The Maya built their temples in connection to the observations of stars, sun and moon.]

ICT: How long would a Mayan astronomer have to observe the skies to be able to predict an eclipse?

Catepillan: I don't know. We talk with the archaeologists about this. For instance, it's just unbelievable in Chichen Itza, the way that the temple steps are positioned, that on a certain day of the year the shadow of a snake appears. It is amazing; if the construction had been off by even half an inch, it wouldn't work. And also in Chichen Itza, they were studying Venus. When you look at those buildings, the windows are all aligned with the path of Venus.

ICT: Is there a religious significance to Venus?

Catepillan: The synodic revolution of Venus has four phases, and the Maya kept track of them for religious and ceremonial purposes. Five cycles corresponds, almost, to eight years. The Maya were obsessed with Venus. ... Among the most interesting of the constructions were the stelae, which were pillars of stone on which they carved a lot of information, such as the crowning of a king. I teach students how to read the dates on the stelae and in order for them to do that, they have to learn how to read the symbols and about the long-term figures, and convert the numbers into our Gregorian calendar. That's where the math comes in. Without these systems you could not make the conversions ... They also learn to read the calendars: the Tzolkin calendar was used for spiritual and religious purposes and the Haab calendar for farming - knowing the right dates to plant and harvest, for example. The Tzolkin had 260 days and the Haab had 365, but they were used simultaneously, which made a total cycle of 18,980 days. It is the most elaborate calendar.

ICT: Do contemporary Mayans use these calculations or have this knowledge?

Catepillan: They do not, unfortunately. However, one of the archaeologists at the Maya Exploration Center of Mexico [with whom Catepillan works] found that present-day Mayans are using the Mayan version of the golden ratio in the construction of their huts. They didn't get that from the Greeks.

ICT: Are there any Mayan descendants studying these systems?

Catepillan: It's possible, but I'm not sure. This is a puzzle; they had so much knowledge. There are only four codices left [which were records of math, science, history, religion and other matters], and the contemporary Maya don't have this knowledge. Some of the information we have comes from the writings of the Catholic missionary who ordered the burning of the codices. He was Diego de Landa.

ICT: Are you researching any other pre-Columbian math or science?

Catepillan: I'm going with my colleagues at the [Maya Exploration] Center to Machu Picchu. My students will benefit from this visit. Their systems are different, too. I am very excited.