Mathematics in South America

SUMMARY: Long before European settlement, mathematics flourished in South America. 

South America includes Argentina, Bolivia, Brazil, Chile, Colombia, Ecuador, French Guiana, Guyana, Paraguay, Peru, Suriname, Uruguay, and Venezuela. The history of South American mathematics began with pre-Columbian developments such as the Nazca lines and quipus (“KEE-poos”) and continued through the astronomy boom of the colonial period to work by modern mathematicians and ethnomathematics studies in Brazil. 

Quipus

The Incan empire , with its capital in Cuzco, Peru, dominated pre-Columbian South America. The Incan civilization emerged from the highlands in the early thirteenth century and extended over an area from what is now the northern border of Ecuador, Peru, western and south central Bolivia, northwest Argentina, northern and central Chile, and southern Colombia. The Incas reached a high level of sophistication with remarkable systems of agriculture, textile design, pottery, and administration. Since the Incas had no written records, the quipu (or khipu) played a pivotal role in keeping numerical information about the population, lands, produce, animals, and weapons.

Quipus were knotted tally cords that consisted of a main cord from which hung a variable number of pendant cords containing clusters of knots. These knots and their clusters conveyed numerical information in base-10 representation. For example, if the number 365 was to be recorded on the string, then five touching knots were placed near the free end of the string followed by a space, then six touching knots for the 10s, another space, and finally three touching knots for the 100s. Specific information was conveyed via the number and type of knots, cluster spacing, color of cord, and pendant array. Inca administrators and accountants employed this complex system for numerical storage and communication. Quipus were mathematically efficient and portable. Unfortunately, the Spanish destroyed many quipus, potentially hiding clues to understanding Incan architectural processes, irrigation, and road systems.

Nazca Lines

The Nazca lines are a set of figures that appear engraved in the surface of the Nazca desert in southern Peru. The lines include hundreds of geometric shapes and renderings of animals and plants, including birds, a spider, a monkey, flowers, geometric figures, and lines—some of them miles long. The Nazca lines, best appreciated from an airplane, are one of the world’s enduring mysteries. It is hard to explain how the ancient people of Nazca (900 B.C.E.–600 C.E.) achieved such geometrical precision in an area over 300 square miles. German-born mathematician and archaeologist Maria Reiche spent five decades studying and preserving these lines. She, like many other scientists, believed that the Nazca lines represented an astronomical calendar and observatory, while other theories suggest that they map areas of fertile land.

Mathematics in the Colonial Era

The accidental arrival of navigator Christopher Columbus in the Americas in 1492 marked the beginning of a 300-year period of Spanish and Portuguese colonial rule in South America that ended in the early nineteenth century. Under the Treaty of Tordesillas (1494), Portugal claimed what is now Brazil, and Spanish claims were established throughout the rest of the continent with the exception of Guyana, Suriname, and French Guiana. Roman Catholicism and an Iberian culture were imposed throughout the region, and mathematical systems and practices of ancient cultures were replaced by the Hindu-Arabic decimal system used by the Spanish.

Mathematical activity in Spain between the sixteenth and nineteenth century decisively influenced mathematical thinking and practices in South America. In sixteenth-century Spain, two lines of mathematical thought existed: the arithmeticians (calculators, interested in the uses of mathematics) and the algebraists (abstract or pure mathematicians). Because the European countries used the colonies to enhance their trade and economic resources, the emphasis in South America was on applied mathematics.

Later, the Spanish and the Portuguese established schools—mostly run by Catholic religious orders—which concentrated mathematics teaching on economic applications related to trade. There was also an interest on mathematics related to astronomical observations. The first nonreligious book published in the Americas was an arithmetic book related to gold and silver mining printed in 1556.

Astronomy was a major area of interest in South America in the seventeenth century. In Brazil, research on comets was of major importance, as exemplified by the work of Valentin Stancel (1621–1705), a Jesuit mathematician from Prague who lived in Brazil from 1663 until his death (his astronomical measurements are mentioned in Newton’s Principia). As in many cultures, most astronomical interpretations attempted to explain divine messages to humankind. Other developments in Brazil included the first aircraft known to fly: the Passarola, invented by Bartolomeu de Gusmão, a Brazilian priest and scientist from Sao Paulo. De Gusmão, also known as the “Flying Priest,” studied mathematics and physics at the Universidade de Coimbra in Portugal. The Passarola was an aerostat heated with hot air and flew in Lisbon, Portugal, in 1709.

Mathematics in the Era of Independence

In the first quarter of the nineteenth century, many successful revolutions resulted in the creation of independent countries in South America. Mathematical activity increased throughout Latin America in the twentieth century. For instance, Argentinian mathematician Alberto P. Calderon (1920–1998) developed new theories and techniques in classical and functional analysis. Professor Calderon worked at the University of Chicago for many years. He was awarded the National Medal of Science in the United States.

Research by Professor Ubiritan D’Ambrosio and his students in the slums and indigenous communities in Brazil focused on ethnomathematics—a sub-field of mathematics history and mathematics education. The goal of ethnomathematics is to understand connections between culture and the development of mathematical processes and ideas. Other researchers have explored specific mathematical habits and methods in South American cultures. In the 1980s, Terezinha Nunes and her collaborators studied differences between street mathematics and school mathematics in Brazil by comparing how street vendors (including children) and farmers solve problems compared to those who encounter similar problems in formal school situations.

For example, in their study of young street vendors in Recife, the interviewers acted as customers and asked questions that required the use of arithmetic skills (such as making change). The children did much better in this “real” situation than on a formal test given a week later that used similar numbers and operations. One possible explanation is that the children were better able to keep the meaning of the problem in mind in the “real” situation. Many others, such as Geoffrey Saxe, have found similar results. An implication of these studies is that the essence of school mathematics, which the Recife children were not as successful at, is highly symbolic and possibly devoid of meaning. These studies have been important in advancing the goal of mathematics education that students must initially construct appropriate meanings for the various concepts and methods they encounter.

Contemporary Latin American and LatinX Mathematicians

In 2018, Forbes Magazine recognized contemporary and distinguished Latin American mathematicians. They included the following:

• Colombian-born Iván Contreras, who was a visiting professor at Amherst College in Massachussetts and who specialized in research, specificially on the intersections of geometry, topology, and physics
• Imelda Trejo, a Mexican graduate student who studied in Texas and who researched the healing relationship between immune and bone cells as a person recovers from a bone fracture
• American LatinX professor Selenne Bañuelos, who was cited for her work on differential and difference equations as well as applications for mathematical biology

In 2023, Argentine-born mathematician Luis Caffarelli was the recipient of the Abel Prize, often called the "Nobel Prize of Math." Caffarelli achieved the recognition for his work on "Regularity Theory," which is a subset of nonlinear partial differential equations. Caffarelli was also a professor at the University of Texas-Austin.

Bibliography

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D’Ambrosio, Ubiritan. “Ethnomathematics and Its Place in the History and Pedagogy of Mathematics.” For the Learning of Mathematics, vol. 5, no. 1, 1985.

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Ansede, Manuel. "Argentina’s Luis Caffarelli Wins ‘Nobel’ of Mathematics for Illuminating What Happens in a Glass with Ice." El Pais, 22 Mar. 2023, english.elpais.com/science-tech/2023-03-22/argentinas-luis-caffarelli-wins-nobel-of-mathematics-for-illuminating-what-happens-in-a-glass-with-ice.html. Accessed 3 Oct. 2024.