Vector: a surprising story of space, time, and mathematical transformation
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My thanks to Robyn Arianrhod (Monash Univ.) for producing perhaps the best historical text about a topic in mathematics. Arianrhod is a great storyteller who gently leads the reader through important yet deep mathematical content via her provision of context--historical and mathematical--while also revealing personal motivations, problems-to-be-solved, disappointments, intellectual disputes, and primacy arguments. Though the book's goal is to tell the story of vectors and tensors, the story is necessarily woven within the histories of algebra, calculus, imaginary numbers, quaternions, matrices, non-Euclidian geometry, differential geometry, physics, electromagnetism, and the Theory of Relativity. In turn, Arianrhod cleverly introduces a wide range of mathematicians, with a focus on their commitment to creativity and human imagination as they helped advance and use the concepts of vectors and tensors. To further help and educate the reader, Arianrhod provides an extensive timeline, extensive notes for each chapter, and a comprehensive index. Readers are encouraged to give the book a try. Let Arianrhod tell her story and expect to be captivated, as it is a demanding book that is difficult to put down before the story is finished…though Arianrhod claims the story continues to evolve. Summing Up: Essential. Upper-division undergraduates, graduate students, researchers, and professionals. --Jerry Johnson, emeritus, Western Washington University