List of books on history of number systems

This list compiles notable works that explore the history and development of number systems across various 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 been central to the development of human civilization, enabling record-keeping, commerce, astronomy, and scientific advancement. Early systems such as tally marks and Roman numerals gradually gave way to more abstract and efficient representations like the Babylonian base-60 system and the Hindu–Arabic numerals, now standard worldwide. The invention of zero, positional notation, and symbolic mathematics has had profound philosophical and technological implications.

Notable works on the history of number systems

Author	Title	Year	Publisher / ISBN	Summary
Levi Leonard Conant	The Number Concept: Its Origin and Development [1]	1896	Macmillan	One of the earliest anthropological studies of how cultures form number concepts.
Florian Cajori	A History of Mathematical Notations	1928	Open Court Publishing	A pioneering historical account of numeric and algebraic notations.
Tobias Dantzig	Number: The Language of Science	1930	Macmillan	A popular introduction to the philosophical and historical aspects of numbers.
Claudia Zaslavsky	Africa Counts [2]	1973	ISBN 978-1-61374-115-3	Groundbreaking work on mathematical practices in African cultures.
Graham Flegg	Numbers: Their History and Meaning [3]	1983	ISBN 978-0-8052-3847-1	A reader-friendly overview of counting and numeral systems.
Georges Ifrah	From One to Zero [4]	1985	ISBN 978-0-14-009919-5	Condensed history of number systems, preceding his later comprehensive volumes.
Thomas Crump	The Anthropology of Numbers [5]	1992	ISBN 978-0-521-43807-0	Connects number use to linguistic and cultural patterns.
George Gheverghese Joseph	The Crest of the Peacock	1992	ISBN 978-0-14-012529-0	Highlights mathematical contributions from non-Western societies.
Karl Menninger	Number Words and Number Symbols [6]	1992	MIT Press	A cultural history of how societies develop number systems.
John McLeish	The Story of Numbers [7]	1994	ISBN 978-0-449-90938-6	Discusses how number systems shaped civilization.
Georges Ifrah	The Universal History of Numbers [8]	2000	ISBN 978-0-471-37568-5	Comprehensive global history of numbers.
Kim Plofker	Mathematics in India	2009	ISBN 978-0-691-12067-6	Documents India’s contribution to mathematics, including place-value and zero.
Stephen Chrisomalis	Numerical Notation: A Comparative History	2010	ISBN 978-0-521-87818-0	Academic analysis of numeral systems across cultures.
Keith Devlin	The Man of Numbers [9]	2011	ISBN 978-0-8027-7812-3	Biography of Fibonacci and his impact on European numeracy.
Karenleigh A. Overmann	The Materiality of Numbers [10]	2023	ISBN 978-1-009-36124-8	Investigates how fingers, tallies, tokens, and notations influence the content, structure, and organization of numerical concepts.

Works on the history of zero

Author	Title	Year	Publisher / ISBN	Summary
Brian Rotman	Signifying Nothing: The Semiotics of Zero [11]	1987	ISBN 9780312012021	Explores the semiotic significance of zero.
Robert Kaplan	The Nothing That Is: A Natural History of Zero [12]	1999	ISBN 9780713992847	A poetic, historical account of zero’s conceptual journey.
Charles Seife	Zero: The Biography of a Dangerous Idea	2000	ISBN 978-0-670-88457-5	Popular science exploration of zero's impact on math and culture.

Children's books on the history of numbers

Author	Title	Year	Publisher / ISBN	Summary
Mitsumasa Anno	Anno's Mysterious Multiplying Jar [13]	1983	Philomel Books	Introduces factorials through a visual and narrative journey.
Kathryn Lasky	The Librarian Who Measured the Earth [14]	1994	Little, Brown and Company	Biography of Eratosthenes, who calculated Earth's circumference.
Denise Schmandt-Besserat	The History of Counting [15]	1999	HarperCollins	Chronicles the evolution of counting systems across cultures.
Joseph D’Agnese	Blockhead: The Life of Fibonacci [16]	2010	Henry Holt & Co.	Story of Fibonacci and his influence on number systems.
David Reimer	Count Like an Egyptian [17]	2014	Princeton University Press	Engaging introduction to Egyptian mathematics and calculating methods.
David A. Adler	Place Value [18]	2016	Holiday House	Child-friendly explanation of place value and number evolution.
Nandini Chakrabarti	Who Owns the Numbers? [19]	2022	Blueberry Illustrations [20]	Simplified introduction to the history of our number system for young readers.

Historical texts

Author	Title	Year	Summary
Euclid	Elements	c. 300 BCE	Laid foundations for number theory and geometry using axiomatic methods.
Aryabhata	Aryabhatiya	499 CE	Described place-value numerals and concepts foundational to Indian mathematics.
Brahmagupta	Brahmasphutasiddhanta	628 CE	Defined zero as a number and explained rules for its arithmetic.
Muhammad ibn Musa al-Khwarizmi	On the Calculation with Hindu Numerals	c. 825 CE	Early Arabic work spreading Hindu numeral use in the Islamic world.
Fibonacci	Liber Abaci	1202	Introduced Hindu–Arabic numerals and arithmetic to Europe.
Ibn al-Banna	Talkhis amal al-hisab [21]	13th century	Arabic treatise integrating Indian and Greek arithmetic traditions.
Nicolas Chuquet	Triparty en la science des nombres [22]	1484	One of the earliest European texts using exponents and large numbers.
Boethius	De Institutione Arithmetica [23]	6th century CE (pub. 1488)	Preserved Greek number theory in Latin during the early Middle Ages.
Simon Stevin	De Thiende	1585	Promoted the use of decimal fractions in European mathematics.
John Napier	Mirifici Logarithmorum Canonis Descriptio	1614	Introduced logarithms, aiding calculation with large numbers.
Gottlob Frege	The Foundations of Arithmetic	1884	Philosophical treatise exploring the concept of number.
Giuseppe Peano	Arithmetices principia, nova methodo exposita	1889	Introduced Peano's axioms for the natural numbers.
Alfred North Whitehead and Bertrand Russell	Principia Mathematica	1910–1913	Defined numbers using set theory, constructing the natural numbers through iteration.

References

1. "The Number Concept: It's Orign and Development". 1896.
2. Africa Counts. Lawrence Hill Books. 1999. ISBN   978-1-55652-350-2.
3. Flegg, Graham (1984). Numbers: Their History and Meaning. Pelican Books. ISBN   0140225641 . Retrieved 8 May 2025.
4. Ifrah, Georges. "The Universal History of Numbers (excerpts)" (PDF). University of Kentucky. Retrieved 8 May 2025.
5. Crump, Thomas (1990). The Anthropology of Numbers. Cambridge Studies in Social and Cultural Anthropology. Vol. 70. Cambridge University Press. doi:10.1017/CBO9780511621680. ISBN   9780521380454 . Retrieved 8 May 2025.
6. Menninger, Karl (1992). Number Words and Number Symbols: A Cultural History of Numbers. Translated by Paul Broneer. Dover Publications. ISBN   0486270963.
7. The Story of Numbers.
8. Ifrah, Georges (2000). The Universal History of Numbers: From Prehistory to the Invention of the Computer. Translated by David Bellos and E.F. Harding. John Wiley & Sons. ISBN   9780471375685.
9. Bodanis, David (2011-11-27). "The Man of Numbers: Fibonacci's Arithmetic Revolution by Keith Devlin – review". The Guardian. Retrieved 2025-05-08.
10. dos Santos, César Frederico (2023-08-30). "Review of: "The Materiality of Numbers"". Academia.edu. Retrieved 2025-05-08.
11. Rotman, Brian. "Signifying Nothing: The Semiotics of Zero". ResearchGate. Retrieved 2025-05-08.
12. Publishers Weekly (October 25, 1999). "The Nothing That Is: A Natural History of Zero". Publishers Weekly. Retrieved 2025-05-08.
13. Masaichiro and Mitsumasa Anno (2023). "Anno's Mysterious Multiplying Jar". Meaningful Maths, Northern Territory Department of Education. Retrieved 2025-05-08.
14. Kirkus Reviews (August 15, 1994). "The Librarian Who Measured the Earth". Kirkus Reviews. Retrieved 2025-05-08.
15. Denise Schmandt-Besserat (2000). "The History of Counting" . The University of Chicago Press. 10 (4): 456–458. doi:10.1086/384858.
16. D'Agnese, Joseph (2010). Blockhead: The Life of Fibonacci. Illustrated by John O'Brien. Henry Holt and Company. ISBN   978-0805063059.
17. Department of Mathematics and Statistics, The College of New Jersey (2014-06-30). "Count Like an Egyptian — New Book by David Reimer". The College of New Jersey. Retrieved 2025-05-08.
18. Kirkus Reviews (2015-11-10). "Place Value". Kirkus Reviews. Retrieved 2025-05-08.
19. Goodreads. "Nandini Chakrabarti". Goodreads. Retrieved 2025-05-08.
20. "Blueberry Illustrations".
21. "Talkhis amal al-hisab" (PDF).
22. O'Connor, John J.; Robertson, Edmund F. "Nicolas Chuquet". MacTutor History of Mathematics Archive. University of St Andrews. Retrieved 2025-05-08.
23. Swetz, Frank J. (August 2014). "Mathematical Treasure: The Arithmetic of Boethius". Convergence. Mathematical Association of America. Retrieved 2025-05-08.