Imagining Numbers (particularly the square root of minus fifteen) is Barry Mazur's invitation to those who delight in the imaginative work of poetry—and who may or may not have a background in math—to leap into the world of imaginary numbers. Such numbers are strange and fascinating mathematical entities, as this accessible book shows, ideas whose meanings have evolved in richly telling ways. (Indeed, imaginary numbers were sometimes called "impossible" when first recognized and brought into use in 16th-century Italy; it took over 200 years for mathematicians to become thoroughly comfortable using them.)
Discussing the function of the imagination, as well as that of imagery, in both poetry and mathematics, Mazur reviews the ideas and writings of some of history's key mathematical explorers, such as Rafael Bombelli, an engineer who composed his great treatise L'Algebra while engaged in the project of draining Tuscany's Chiana swamp. In an entertaining work of explanation and exposition, of theory and play, Mazur encourages us to grasp the initial bafflement of such Renaissance thinkers—the how and why of their confusion—while also encouraging us to think more creatively about math in all its guises. Finally, this unique book shows us, step by step, how to begin imagining such uncanny numbers ourselves.