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Recommended Further Reading

This is a list of books and articles that have been invaluable in this project and which further explore related topics.

The Crest of the Peacock, Non-European Roots of Mathematics by George Gheverghese Joseph (Book)

'From the Ishango Bone of central Africa and the Incaquipu of South America to the dawn of modern mathematics, The Crest of the Peacock makes it clear that human beings everywhere have been capable of advanced and innovative mathematical thinking. George Gheverghese Joseph takes us on a breathtaking multicultural tour of the roots and shoots of non-European mathematics. He shows us the deep influence that the Egyptians and Babylonians had on the Greeks, the Arabs' major creative contributions, and the astounding range of successes of the great civilizations of India and China.'

Mathematics Across Cultures, The History of Non-Western Mathematics edited by Helaine Selin (Book)

'Mathematics Across Cultures: A History of Non-Western Mathematics consists 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. Each essay is well illustrated and contains an extensive bibliography. Because the geographic range is global, the book fills a gap in both the history of science and in cultural studies. It should find a place on the bookshelves of advanced undergraduate students, graduate students, and scholars, as well as in libraries serving those groups.'

Mathematics in (central) Africa before colonization by Dirk Huylebrouck (Article)

'The paper provides a summary of (black) African ethnomathematics, with a special focus on results of possible interest to eventual mathematical properties of the Ishango rod(s). The African diversity in number names, gestures and systems (including base 2 of the Bushmen, probably related to the early Ishango people) shows frequent decompositions of numbers in small groups (similar to the carvings on the rod), while the existence of words for large numbers illustrates counting was not merely done for practical reasons. A particular case is the base 12, with its straightforward finger counting method on the hands, and used in Nigeria, Egypt and the Ishango region. Geometric representations are found in traditional sand drawings or decorations, where lines and figures obey abstract rules. Number lines drawn in the sand (using small and long lines as on the rod) make anyone immediately remind the Ishango carvings. Knotted strings and carved counting sticks (even looking like exact wooden copies of the Ishango rod) illustrate an African counting practice, as confirmed in written sources of, for instance, a gifted American slave. Finally, mancala mind games, Yoruba and Egyptian multiplication (using doublings as on the Ishango rod) or kinship studies all show ethnologists may have ignored for too long Africans were talking the mathematical language, ever since.'

Mathematics Elsewhere: An Exploration Of Ideas Across Cultures by Marcia Ascher (Book)

'Mathematics Elsewhere is a fascinating and important contribution to a global view of mathematics. Presenting mathematical ideas of peoples from a variety of small-scale and traditional cultures, it humanizes our view of mathematics and expands our conception of what is mathematical.

Through engaging examples of how particular societies structure time, reach decisions about the future, make models and maps, systematize relationships, and create intriguing figures, Marcia Ascher demonstrates that traditional cultures have mathematical ideas that are far more substantial and sophisticated than is generally acknowledged. Malagasy divination rituals, for example, rely on complex algebraic algorithms. And some cultures use calendars far more abstract and elegant than our own. Ascher also shows that certain concepts assumed to be universal--that time is a single progression, for instance, or that equality is a static relationship--are not. The Basque notion of equivalence, for example, is a dynamic and temporal one not adequately captured by the familiar equal sign. Other ideas taken to be the exclusive province of professionally trained Western mathematicians are, in fact, shared by people in many societies.'