How the elusive imaginary number was first imagined, and how to imagine it yourself
Imagining Numbers (particularly the square root of minus fifteen) is Barry Mazur's invitation to those who take delight in the imaginative work of reading poetry, but may have no background in math, to make a leap of the imagination in mathematics. Imaginary numbers entered into mathematics in sixteenth-century Italy and were used with immediate success, but nevertheless, presented an intriguing challenge to the imagination. It took more than two hundred years for mathematicians to discover a satisfactory way of "imagining" these numbers.
With discussions about how we comprehend ideas both in poetry and in mathematics, Mazur reviews some of the writings of the earliest explorers of these elusive figures, such as Rafael Bombelli, an engineer who spent most of his life draining the swamps of Tuscany and who in his spare moments composed his great treatise "L'Algebra". Mazur encourages his readers to share the early bafflement of these Renaissance thinkers. Then he shows us, step by step, how to begin imagining, ourselves, imaginary numbers.
"A clear, accessible, beautifully written introduction not only to imaginary numbers, but to the role of imagination in mathematics."
George Lakoff, Professor of Linguistics, University of California, Berkeley
"This absorbing and in itself most imaginative book lies in the grand tradition of explanations of what mathematical imagination is--such as those of Hogben, Kasner and Newman, and Polya's How to Solve It. But it is unique in its understanding of and appeal to poetic thought and its analogues, and will appeal particularly to lovers of literature."
John Hollander
"A very compelling, thought-provoking, and even drmataic description of what it means to think mathematically."
Joseph Dauben, Professor of History and History of Science, City University of New York
