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We have discovered a pattern for cultural bifurcations involving artists making significant contributions to the history of mathematics.How much of this material would you recognize as mathematics on the basis of your school education? How much appears on standard tests? And what kind of training best supports the development of your natural mathematical skills? How is the integration of mathematics and culture faring today? The six stories of this book-in addition to being examples of cultural ecologies, mathematical mentalities, and bolts from the blue-exhibit the integration of math and cultural history, the basis of a new way of teaching math in school.