MoMath + Wolfram

Funding for this project generously provided by Overdeck Family Foundation

around 1400–1532

South American Quipu

Knots upon knots to count and record

Also known as a khipu or quipo, a quipu is a recording device using ropes, strings and knots. Quipus were used in South America primarily during the Incan Empire to record numeric data and events. Sewn and twisted, a quipu consists of a top cord with several other cords descending (or ascending) from it. The descending cords are then carefully knotted and altered using different-colored strands or other fibers in order to record the numeric information. Each knot denotes a different numerical value: an e-knot or figure 8 knot is 8, a long knot is 2 to 9 depending on how often it is wrapped and a single knot is 10 or powers of 10. A group of knots can also stand for powers of 10, so 5 knots grouped together would represent 500.

South American Quipu

Until the Spanish conquest of 1532, quipus were common in the Incan Empire. However, only an estimated one thousand quipus survive in museums and private collections. Dedicated researchers have been able to study various quipus to find similar ones and even duplicates. This work by mathematicians, archaeologists, computer scientists and textile preservationists has helped give a better understanding of how another culture counted and recorded data.

Artifact dimensions

67.5 cm × 59.5 cm

Artifact origin

Nazca, Ica, Peru

Current artifact location

Peabody Museum of Archaeology and Ethnology, Cambridge

Catalog number

PM 41-52-30/2938


Counting timeline Sumerian Earliest Known Math Table Sumerian 7 Quotient and 10 Product Tablet Babylonian School Multiplication Tablet Babylonian Reciprocals Tablet Rhind Papyrus Roman Stylus Tablet Bamboo-Strip Multiplication Table Venerable Bede's De temporum ratione South American Quipu Aztec Dates from Codex Mendoza Midewiwin Birchbark Scroll

Interactive Content

Computational Explanation

Other Resources

Additional Reading

  • Ascher, M. and Ascher, R. Mathematics of the Incas: Code of the Quipu. New York: Dover, 1997.
  • Ascher, M. "Mathematical Ideas of the Incas." Ch. 10 in Native American Mathematics (Ed. M. P. Closs). Austin, TX: University of Texas Press, pp. 261–289, esp. pp. 266–288, 1996.
  • d'Altroy, T. N. The Incas, 2nd ed. Chichester, England: Wiley Blackwell, 2015.
  • Day, C. Quipus and Witches' Knots: The Role of the Knot in Primitive and Ancient Cultures. Lawrence: University of Kansas Press, 1967.
  • Gaenger, S. Relics of the Past: The Collecting and Study of Pre-Columbian Antiquities in Peru and Chile, 1837–1911. Oxford, England: Oxford University Press, 2014.
  • Gilsdorf, T. E. Introduction to Cultural Mathematics: With Case Studies in the Otomies and Incas. New York: Wiley, 2012.
  • Joseph, G. The Crest of the Peacock: Non-European Roots of Mathematics. Princeton, NJ: Princeton University Press, 2011.
  • Locke, L. "The Ancient Quipu, a Peruvian Knot Record." American Anthropologist, Vol. 14, No. 2, pp. 325–332, 1912.
  • Miccinelli, V. and Animato, C. Quipu: il nodo parlante dei misteriosi incas. Genoa, Italy: Edizioni Culturali Internazionali Genova, 1989.
  • Minelli, L. L. and Domenici, D. Per Bocca D'altri:Inca, Gesuiti E Spagnoli Nel Peru' Del XVII Sec. Alma Digital Library, Università di Bologna, 2007.
  • Pappas, T. The Joy of Mathematics: Discovering Mathematics All Around You. San Carlos, CA: Wide World Publishing/Tetra, pp. 14–15, 1989.
  • Poma de Ayala. G. F. The First New Chronicle and Good Government: On the History of the World and the Incas up to 1615 (Trans. and Ed. R. Hamilton). Austin, TX: University of Texas Press, 2009.
  • Prem, D. Yupana Inka: Decoding the Inka's Math. English Edition Kindle, 2019.
  • Stone, R. Art of the Andes: from Chavín to Inca, 2nd ed. London: Thames & Hudson, 2002.
  • Urton, G. Signs of the Inka Khipu: Binary Coding in the Andean Knotted-String Records. Austin, TX: University of Texas Press, 2003.
  • Valera, B. Exsul Immeritus Blas Valera Populo Suo e Historia et Rudimenta Linguae Piruanorum Indios. Napoli: Archivio Miccinelli-Cera, 1618.