Mathematical Traditions

by Chris Landon


American Indians generally have had a pragmatic orientation to the use and study of mathematics. In most Indian cultures, mathematics traditionally was practiced by most of our ancestors, when and if they used it, for its value in daily life rather than for its own sake or as an intellectual challenge. Counts and record-keeping relating to economic activities have long been the major use for mathematics among most American Indian cultures, so far as ethnologists and other specialists have been able to learn.

American Indians did integrate mathematics into other areas of daily life. As is true of most cultures, we found the principles of this discipline broadly useful as a way to think about and describe many parts of human experience, especially those with quantitative and relational aspects. Our native ancestors also developed an esthetic regard for what their counts and calculations revealed about order and pattern in the world. Certain American Indian cultures well appreciated the usefulness and beauty of mathematics in activities related to history, engineering, architecture, astronomy, calendrics and the religious practices associated with these fields.

However, accessible written records of American Indian techniques in mathematics are extremely rare. Also rare are other forms of Indian records in this field of human knowledge. This is due to a number of causes.

Many American Indian cultures did not record their knowledge, or recorded only parts of it, in the visual form of a system of writing or symbols. Traditionally, our ancestors preferred to rely on the intimacy and interactive characteristics of the oral tradition as a teaching and storage medium for what they knew of numbers, order and pattern. When a great many elders died prematurely during the epidemics and wars that were part of the conquest of the Americas, we lost a significant portion of our mathematical traditions. Modern Indians and others wishing to know the American Indian traditions in mathematics have encountered many gaps in what knowledge remains in the oral tradition.

Indian and non-Indian scholars alike are also still learning how to decipher the surviving “written” materials pertaining to American Indian mathematics. Very recent advances have occurred in the translation of the Maya glyphs, to cite a major example. Great numbers of these symbols were carved onto monuments or were painted into books, a handful of which survived the Conquest. Mathematical content is a significant part of the matters recorded in this most advanced of American Indian writing systems. These new translations are leading to increased knowledge of Mayan thought and mathematics, and scholars may soon be able to make this information more generally accessible.

Reports of 16th and 17th century Spanish scholars and surviving pre-Contact documents are evidence that a great deal of recorded Indian knowledge, some of it pertaining to mathematics, was lost in the destruction of Mesoamerican and Incan libraries in those centuries. This tragedy resulted from the misguided attempts of colonial religious, military and civil authorities to erase the native cultures of the Indian nations that came under Spanish domination in that era.

Thus, what remains today of traditional American Indian mathematics are fragments of the living oral tradition and a very few surviving texts. Scholars can supplement these remains with the accounts of some early European observers and those of a few bilingual Indian historians from the period shortly after Contact. There is also a recent body of knowledge. This comes from scientific reconstruction of Indian mathematics deduced from art works, buildings, monuments, engineering works and other archaeological remnants. Each source has its limitations for purposes of general study.

We can read parts of some of the native texts while others have yet to be translated. Much of the remaining oral tradition is only shared among family, clan and tribal members and is not available for consideration outside those circles. Some parts of the oral tradition and Indian literary sources have been transcribed into modern books; while some of these can be helpful, others contain errors, misunderstandings, and misinformation. Many contemporary Indians who know something of the traditions caution that the materials in the books can’t always be taken as accurate accounts of how things were done or understood within the culture. Unfortunately, it is difficult to sort these matters out without significant “insider” knowledge from the particular culture(s) involved.

The accounts of explorers and colonial officials generally share these limitations. As concerns Indian mathematics, few contain much clear and useful information. (Most of the accounts I have examined over the years reveal the authors’ lack of attention to or incomprehension of Indian mathematical techniques. Actually, only a few explorers or colonial writers give much evidence of familiarity with mathematics in general.) The works of Indian historians, like Guamán Poma de Ayala of the Inca or the numerous Mexica (“Aztec”) collaborators of Father Bernhardino de Sahagún, give a better picture of Indian achievements. Yet even they discuss mathematics as a minor matter compared to other concerns of their time.

The interpretations and reconstructions of modern scientific researchers are the most accessible materials from which a reader can gather some sense of American Indian mathematics. Here one must keep in mind the shortcomings of the interpretive methods of one culture when applied to fragmentary materials from another.

Traditional Indian mathematics is thus a discipline in which much of the original richness is lost, much remains to be relearned, and much which we think we understand may have to be revised as new insights become available. What is offered below is an introduction to some of the better understood Indian mathematical achievements for teachers who wish to offer their students access to this aspect of American Indian cultures.

Appeared in This Land: Summer 2016. Courtesy Title VI Indian Education Department of Portland Public Schools.