Most books on the history of mathematics concentrate their attention on Western mathematics. There is usually some mention of other cultures, but it is not extensive. Mathematics Across Cultures is an attempt to tell the rest of the story. It collects articles on the mathematics of non-Western cultures and on the historiographical issues raised by studying this mathematics.
The articles can be divided into three groups. First, there are several methodological articles. These deal with how mathematics is (or can be) communicated across cultures, with what is usually called "ethnomathematics", with philosophical issues about rationality and logic and how they might vary from one culture to another, etc. D'Ambrosio's article, proposing a broad historical framework for understanding the relationship between Western and Non-Western mathematics, is particularly interesting.
The second group of articles discuss the mathematics of cultures that are often discussed in history books: Ancient Iraq (aka Mesopotamia), Ancient Egypt, Medieval Islam, India, China. What is particularly interesting here is the point of view: the authors insist on viewing these mathematical traditions in their own terms, and not in terms of how they anticipated or influenced Western mathematics. The articles by Robson and Ritter are particularly nice.
Third, there are articles on cultures that are discussed much less often: the Hebrew mathematical tradition, the Incas and other Mesoamerican cultures, the Sioux, Pacific cultures, Australia, Subsaharan Africa, Korea, Japan. These are fascinating, and mostly new to me.
Overall, we have here a valuable corrective and supplement to the usual history books.
Fernando Q. Gouvêa (firstname.lastname@example.org) is the editor of FOCUS and MAA Online.
Introduction; H. Selin. Acknowledgments. List of Contributors. Communicating Mathematics Across Culture and Time; L.N. Wood. Anthropological Perspectives on Ethnomathematics; R. Eglash. East and West; E.J. Van Kley. Rationality and the Disunity of the Sciences; D. Turnbull. Logics and Mathematics: Challenges Arising in Working across Cultures; H. Verran. A Historiographical Proposal for Non-Western Mathematics; U. D'Ambrosio. The Uses of Mathematics in Ancient Iraq, 6000-600 BC; E. Robson. Egyptian Mathematics; J. Ritter. Islamic Mathematics; J. Sesiano. The Hebrew Mathematical Tradition; Y.T. Langermann, S. Simonson. Inca Mathematics; T.E. Gilsdorf. Mesoamerican Mathematics; M.P. Closs. The Ethnomathematics of the Sioux Tipi and Cone; D.C. Orey. Traditional Mathematics in Pacific Cultures; W.S. Sizer. Australian Aboriginal Mathematics: Disparate Mathematics of Land Ownership; H. Verran. On Mathematical Ideas in Cultural Traditions of Central and Southern Africa; P. Gerdes. Accounting Mathematics in West Africa: Some Stories of Yoruba Number; H. Verran. Chinese Mathematical Astronomy; J.-C. Martzloff. The Mathematical Accomplishment of Ancient Indian Mathematicians; T.K. Puttaswamy. The Dawn of Wasan (Japanese Mathematics); J. Shigeru. Developments of Materials for Ethnomathematics in Korea; K.S. Hwan.Index.