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.
The ideas discussed come from geographically varied cultures, including the Borana and Malagasy of Africa, the Tongans and Marshall Islanders of Oceania, the Tamil of South India, the Basques of Western Europe, and the Balinese and Kodi of Indonesia.
This book belongs on the shelves of mathematicians, math students, and math educators, and in the hands of anyone interested in traditional societies or how people think. Illustrating how mathematical ideas play a vital role in diverse human endeavors from navigation to social interaction to religion, it offers--through the vehicle of mathematics--unique cultural encounters to any reader.
"A useful reminder of how universal mathematical and logical structures are in any culture. Mathematicians will enjoy seeing the subject they love cropping up in apparently unexpected contexts. Non-mathematicians should be encouraged to realize that some of the processes that seem to appear naturally in everyday life do in fact have a mathematical content."--John O'Connor, Nature
"For a mathematician, Mathematics Elsewhere will expand the universe; for a non-mathematician, the expansion will just take a little more time. The book succeeds well in presenting and explaining very different ways of doing math both within particular cultural contexts and in terms of modern mathematics. . . . The author is clearly an excellent teacher and a wonderful explainer. Every time I felt a bit lost, the next sequence would present the same concept in different words or with another example. She is adept at moving from the general to the specific, from narrative to figurative."--Helaine Selin, Science
"This interesting book is a fundamental work in the area of ethnomathematics. . . . [T]he author opens numerous doors and directions in which one finds interesting, nontrivial mathematics. Persons interested in investigating the mathematics of non-Western cultures can use this book as a motivation to look beyond the obvious."--Thomas E. Golsdorf, Mathematical Reviews
"Ascher illustrates that non-Western cultures have developed sophisticated mathematical ideas often without having any formal concept of mathematics. This stimulating book deserves a wide audience, especially among those involved in teaching the subject."--Andrew Bowler, New Scientist
Table of Contents:
CHAPTER 1: The Logic of Divination 5
CHAPTER 2: Marking Time 39
CHAPTER 3: Cycles of Time 59
CHAPTER 4: Models and Maps 89
CHAPTER 5: Systems of Relationships 127
CHAPTER 6: Figures on the Threshold 161
CHAPTER 7: Epilogue 191
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