List of books on history of number systems

This is a list of notable books that explore the history and development of number systems across different civilizations and time periods. These works cover topics ranging from ancient numeral systems and arithmetic methods to the evolution of mathematical notations and the impact of numerals on science, trade, and culture.

Overview

Number systems have played a crucial role in the development of mathematics, commerce, and communication. From tally marks and Roman numerals to the binary system and the widespread Hindu–Arabic numeral system, the evolution of numerical notations reflects the intellectual and cultural advancements of societies around the world. The following books provide historical, cultural, and mathematical insights into these developments.

List of notable works

• Conant, Levi Leonard (1896). The Number Concept: Its Origin and Development. Macmillan and Company. An early study of cultural number systems.
• Cajori, Florian (1928). A History of Mathematical Notations. Open Court Publishing. A foundational work tracing the development of mathematical and numerical symbols in Europe and beyond.
• Dantzig, Tobias (1930). Number: The Language of Science: A Critical Survey Written for the Cultured Non-Mathematician. Macmillan. An interesting book on the evolution of mathematics, including numbers.
• Zaslavsky, Claudia (1973). Africa Counts: Number and Pattern in African Culture. Lawrence Hill Books. Discusses the contributions of African cultures to the science of mathematics, focusing on number systems and patterns.
• Flegg, Graham (1983). Numbers: Their History and Meaning. Schocken Books. Traces the evolution of counting systems, from ancient techniques to computers.
• Ifrah, Georges (1985). From One to Zero: A Universal History of Numbers. Viking Press. An earlier version of his later, more comprehensive work focusing on numeral systems (originally published in French in 1981).
• Flegg, Graham (1989). Numbers Through the Ages. Macmillan. A fascinating, well-illustrated account of the early history of counting, numerals and elementary calculation.
• Crump, Thomas (1992). The Anthropology of Numbers. Cambridge University Press. An engaging examination of numbers and culture.
• Joseph, George Gheverghese (1992). The Crest of the Peacock: Non-European Roots of Mathematics. Princeton University Press. Highlights mathematical contributions from non-European civilizations, including number systems.
• Menninger, Karl (1992). Number Words and Number Symbols: A Cultural History of Numbers. MIT Press. A classic study of how cultures create and use number words and symbols (originally published in German in 1957).
• McLeish, John (1994). The Story of Numbers: How Mathematics Has Shaped Civilization. Penguin Books. Explores how various number systems have shaped different cultures throughout history.
• Ifrah, Georges (2000). The Universal History of Numbers: From Prehistory to the Invention of the Computer. Wiley. A comprehensive global history of number systems from ancient to modern times (originally published in French in 1994).
• Plofker, Kim (2009). Mathematics in India. Princeton University Press. Explores India's historical contributions to mathematics, including the invention of zero and place-value.
• Chrisomalis, Stephen (2010). Numerical Notation: A Comparative History. Cambridge University Press. An academic analysis of numeral systems across societies with a focus on their cultural context.
• Devlin, Keith (2011). The Man of Numbers: Fibonacci's Arithmetic Revolution. Walker & Company. A biography of Fibonacci and how his work changed European mathematics.
• Overmann, Karenleigh A. (2023). The Materiality of Numbers: Emergence and Elaboration from Prehistory to Present. Cambridge University Press. Discusses the role of the devices used in numbers – fingers, tallies, tokens, and notations – in the ways numbers are conceived, structured, and organized across cultures.

The History of Zero

• Rotman, Brian (1987). Signifying Nothing: The Semiotics of Zero. Stanford University Press. A thoughtful examination of the history and cultural context of the emergence of zero.
• Kaplan, Robert (1999). The Nothing That Is: A Natural History of Zero. Oxford University Press. A poetic and historical exploration of the concept and symbolism of zero.
• Seife, Charles (2000). Zero: The Biography of a Dangerous Idea. Viking Press. Tells the story of zero's controversial and transformative journey through history.

Children’s Books on the History of Numbers

• Anno, Mitsumasa (1983). Anno's Mysterious Multiplying Jar. Philomel Books. Inspired by historical mathematical puzzles with roots in factorial numbers.
• Lasky, Kathryn (1994). The Librarian Who Measured the Earth. Little, Brown and Company. While primarily about Eratosthenes, includes the historical use of numbers and measurement.
• Schmandt-Besserat, Denise (1999). The History of Counting. HarperCollins. Introduces how ancient civilizations developed counting systems.
• D’Agnese, Joseph (2010). Blockhead: The Life of Fibonacci. Henry Holt & Co. Tells the story of Fibonacci and his influence on number systems.
• Reimer, David W. (2014). Count Like an Egyptian: A Hands-On Introduction to Ancient Mathematics. Princeton University Press. An interesting introduction to Egyptian mathematics and calculating methods.
• Adler, David A. (2016). Place Value. Holiday House. A child-friendly look at how numbers evolved over time.
• Chakrabarti, Nandini (2022). Who Owns the Numbers?. Blueberry Illustrations. A simplified and engaging introduction to the history of our number system for young readers.

Historical texts

• Euclid. The Elements. (300 BCE). Laid foundations for number theory and geometry using axiomatic methods.
• Aryabhata (499). Aryabhatiya. Described place-value numerals and concepts foundational to Indian mathematics.
• Brahmagupta (628). Brahmasphutasiddhanta. Defined zero as a number and explained rules for its arithmetic.
• Al-Khwarizmi (825). On the Calculation with Hindu Numerals. Early Arabic work spreading Hindu numeral use in the Islamic world.
• Fibonacci (1202). Liber Abaci. Introduced Hindu–Arabic numerals and arithmetic to Europe.
• Ibn al-Banna. Talkhis amal al-hisab. (13th century CE). Arabic treatise integrating and synthesizing the Indian and Greek arithmetic traditions.
• Chuquet, Nicolas (1484). Triparty en la science des nombres. One of the earliest European texts using exponents and large numbers.
• Boethius (1488). De Institutione Arithmetica. Preserved Greek number theory in Latin during the early Middle Ages (from the work Introduction to Arithmetic written by Nicomachus of Gerasa in the 6th century CE).
• Stevin, Simon (1585). De Thiende. Promoted the use of decimal fractions in European mathematics.
• Napier, John (1614). Mirifici Logarithmorum Canonis Descriptio. Introduced logarithms, aiding calculation with large numbers.
• Frege, Gottlob (1884). The Foundations of Arithmetic. A philosophical treatise exploring the concept of number and investigating logic as the foundations of arithmetic. Originally published in German as Die Grundlagen der Arithmetik.
• Peano, Giuseppe (1889). Arithmetices principia, nova methodo exposita. An influential work introducing Peano's axioms, principles for deriving the natural numbers.
• Whitehead, Alfred North; Russell, Bertrand (1927). Principia Mathematica. Defined numbers using set theory, starting with zero, and then constructing the natural numbers through iteration.

See also

• Numerical notation
• History of mathematics
• Hindu–Arabic numeral system
• List of numeral systems
• Computer number formats
• History of ancient numeral systems
• History of numbers