In the history of mathematics not enough attention is devoted to developments in ancient America. Perhaps this is a consequence of trying to understand only a portion of the present. No one denies the importance of the ancient civilizations of the Near East in the line that leads up to the western European tradition, but to appreciate the background of human intellectual accomplishments it is necessary to pass beyond the restrictive frame and biases of western man. We (mankind) entered the Americas about 20,000 years before the present. By 10,000 B.P., man had spread into the Americas so that traces of activities such as hunting are found thinly scattered from the northern lands to the hemisphere's southern tip. The style of civilization that eventually developed was distinctive with one region in particular seeing the rise of monumental architecture, recorded numeration, dense settlements, centralized authority, and so forth. This so-called nuclear regionon elliptic area with the valley of Mexico at one focus and the Peruvian Andes at the othercontained configurations of cultures that changed often in the course of a thousand years. When Europeans first reached the Andes in the third decade of the sixteenth century they credited themselves with the "discovery" of an ancient civilization. This civilization known as the Incasthey destroyed almost without issue. Some Europeans wrote down their observations of Inca life. These observations, usually called chronicles, together with what can be salvaged with the archaeological shovel, form the basis of what we can know. One can hardly expect a fair and accurate appraisal of the intellectual attainments of the native Andeans by a group that rationalized its destructive acts on the grounds of cultural superiority. To get closer to the truth of the matter, the archaeological materials have to be analyzed for the most they can yield. We know, first of all, that in Inca times there were cities with quarters for thousands of inhabitants. A road network linked these places; the disused roads stand out sharply today on air photographs. To maintain a population that may have reached six million, knowledge of food production is indispensible. And in a land of steep mountains, knowing how to get enough food means discovering the altitudes where particular animals and plants flourish. We must postulate, and indeed have evidence for, thousands of years of experimentation and the accumulation of information about plants, animals, and vertical land-scapes as they relate to basic human requirements. The native Andeans dug irrigation canals, built bridges, and constructed community store houses. Clearly technical knowledge