History of Mathematics


    General, West and the Middle East

Karl Menninger, Number Words and Number Symbols : A Cultural History of Numbers, Dover Publications, Reprint edition, 1992.

Menninger compares number words from several languages. Included is also finger counting and the abacus. This is a great book to learn about the development of numbers.

Ronald Calinger, Joseph E. Brown, Thomas R. West, A Contextual History of Mathematics, Prentice Hall, 1999.

The authors present mathematics in a historical context. The book presents a broad survey of mathematics from the ancient beginnings to Euler. The topics include Babylonian and Egyptian mathematics, India, China, Islamic world, Latin West, and Maya America.

Carl B. Boyer, Uta C. Merzbach, A History of Mathematics, Wiley; 2 edition, 1991.

The material is arranged chronologically beginning with its archaic origins, then continuing through Egyptian, Mesopotamian, Greek, Chinese, Indian, Arabic and European contributions through the present day. There are revised references and bibliographies and revised and expanded chapters on the nineteenth and twentieth centuries.

Lucas N. H. Bunt, Phillip S. Jones, Jack D. Bedient, The Historical Roots of Elementary Mathematics, Dover Publications, 1988.

Exciting, hands-on approach to understanding fundamental underpinnings of modern arithmetic, algebra, geometry and number systems, by examining their origins in early Egyptian, Babylonian and Greek sources. Students can do division like the ancient Egyptians, solve quadratic equations like the Babylonians and more.

O. Neugebauer, The Exact Sciences in Antiquity, Dover Publications, second edition, 1969.

Contents: Numbers, Babylonian Mathematics, The sources; their Decipherment and Evaluation, Egyptian Mathematics and Astronomy, Babylonian Astronomy, Origin and Transmission of Hellenistic Science, The Ptolemaic System, On Greek Mathematics, The Zodiacal and Planetary Signs, Chronological Table, Index.

Joran Friberg, Unexpected Links Between Egyptian and Babylonian Mathematics, World Scientific Publishing Company, 2005.

The author observed that two Old Babylonian tablets from Mari had clear Egyptian parallels. In this book Joran Friberg presents the results of his research and presents arguments that support the existence of links between Egyptian and Babylonian mathematics.

Ubiratan D'Ambrosio, H. Selin (Editor), Mathematics Across Cultures: The History of Non-Western Mathematics, Kluwer Academic Publishers, 2001.

Collection of essays dealing with the mathematical knowledge and beliefs of cultures outside the United States and Europe. In addition to articles surveying Islamic, Chinese, Native American, Aboriginal Australian, Inca, Egyptian, and African mathematics, among others, the book includes essays on Rationality, Logic and Mathematics, and the transfer of knowledge from East to West. The essays address the connections between science and culture and relate the mathematical practices to the cultures which produced them.


    Asia and Islam

J. L. Berggren, Episodes in the Mathematics of Medieval Islam, Springer (December 4, 2003).

From the reviews: The book is, in spite of the author's more modest claims, an introductory survey of main developments in those disciplines which were particularly important in Medieval Islamic mathematics.
The book will hence not only be an excellent textbook for the teaching of the history of mathematics but also for the liberal art aspect of mathematics teaching in general. - Jens H°yrup, Mathematical Reviews

Jean-Claude Martzloff, A History of Chinese Mathematics, Springer; 1 edition, 2006.

The book is made up of two parts, the first devoted to the general, historical and cultural background, and the second to the development of each subdiscipline that together comprise Chinese mathematics. This makes the book uniquely accessible, both as a topical reference work, and also as an overview that can be read and reread at many levels of sophistication by both sinologists and mathematicians alike.

David Eugene Smith, Yoshio Mikami, A History of Japanese Mathematics, Dover Publications, 2004.

One of the first books to show Westerners the nature of Japanese mathematics, this survey highlights the leading features in the development of of the wasan, the Japanese system of mathematics.
The text traces the development of wasan from the earliest period to the introduction of Western Mathematics.

Shen Kangshen, John N. Crossley, Anthony W. -C. Lun, The Nine Chapters on the Mathematical Art : Companion and Commentary, Oxford University Press, 2000.

The Nine Chapters was the standard mathematics textbook in China for about two thousand years. This volume contains an English translation of the Nine Chapters, together with the commentary of Liu Hui (third century). The translators provide useful comments on the text and relate it to the mathematical texts in other countries.


    Africa

Marshall Clagett, Ancient Egyptian Science, A Source Book, Volume Three, American Philosophical Society (1999).

In part one the author discusses Egyptian Mathematics in general. He then describes several mathematical papyri in detail. Included are Rhind and Moscow papyri, Kahun Mathematical Fragments, Berlin Papyrus, and the Leather Roll. The book has over 130 pages of illustrations.

Ron Eglash, African Fractals: Modern Computing and Indigenous Design, Rutgers University Press, 1999.

Ron Eglash investigates fractals in African culture. Fractals are characterized by the repetition of similar patterns at ever-diminishing scales. This repetition, as documented by Ron Eglash, can be often seen in architecture, arts and crafts of Africa.

Richard J Gillings, Mathematics in the Time of the Pharaohs, Dover Publications, 1982.

In this carefully researched study, the author examines Egyptian mathematics, demonstrating that although operations were limited in number, they were remarkably adaptable to a great many applications-solution of problems in direct and inverse proportion, linear equations of the first degree, and arithmetical and geometrical progressions.

Claudia Zaslavsky, Africa Counts: Number and Pattern in African Culture, Lawrence Hill Books, 1999.

This study of mathematical thinking among sub-Saharan African peoples covers counting in words and in gestures; measuring time, distance, weight, and other quantities; number systems; patterns in music, poetry, art, and architecture; number magic and taboos, and much more. African games such as mankala are described. An invaluable resource for those interested in African cultures and multiculturalism, this third edition includes an introduction covering two decades of new research in the ethnomathematics of Africa.


    Americas

Michael P. Closs, Native American Mathematics, University of Texas Press, 1996.

There is no question that native cultures in the New World exhibit many forms of mathematical development. Unlike modern mathematics in which numbers and concepts are expressed in a universal mathematical notation, the numbers and concepts found in native cultures occur and are expressed in many distinctive ways. Focus of this collection of essays is the mathematical development indigenous to the New World.

Gary Urton, with the collaboration of Primitivo Nina Llanos, The Social Life of Numbers: A Quechua Ontology of Numbers and Philosophy of Arithmetic, University of Texas Press, 1997.

The book is based too a large extent on fieldwork in communities near Sucre, south-central Bolivia. This is a study of the origin, meaning, and significance of numbers. For example in Quechua there is no symbol for zero. It was represented by not making a knot on a string.