99 Variations on a Proof

Winner of the PROSE Award for Excellence in Physical Sciences and Mathematics, Association of American Publishers Winner of the PROSE Award in Mathematics, Association of American Publishers A Choice Outstanding Academic Title of the Year This book is an insightful addition to mathematical literature. ---Robert Maddox-Harle, Leonardo Reviews Ording presents ninety-nine proofs that a specific cubic equation has two real roots. The theorem itself is fairly uninteresting, but the proofs are the stars and each of them seeks to show a different aspect of the theory, history, or culture of mathematics. ---Geoffrey Dietz, MAA Reviews These proofs' playfulness at the boundary of sense and nonsense surely expands the limits of mathematical exposition as well as readerly response to mathematical ideas. I think Queneau would have been proud. ---Dan Rockmore, New York Review of Books This rather unusual book shows that . . . the essentials for communicating mathematical contents is not formulas, let alone numbers, but a more or less precise reasoning in a convincing language. ---Jurgen Appell, Zentralblatt MATH A deep and thoughtful examination of the nature of mathematical arguments, of mathematical style, and of proof itself. ---Chris Sangwin, London Mathematical Newsletter [A] fascinating book. . . . The book can be recommended as light reading and, in particular, for everyone who wants to become more aware of the different styles used in mathematical writing. ---C. Fuchs, International Mathematical News [99 Variations on a Proof] is certainly beautifully produced and invites dipping into rather than reading from cover to cover. ---Nick Lord, Mathematical Gazette In his marvelous book 99 Variations on a Proof, Philip Ording demonstrates in a creative, often amusing, and always illuminating way that there are many, many good styles for writing mathematical proofs. Mathematicians (in fact, almost all writers) have much to learn about their craft from this book, and mathematical literature much to gain. ---John J. Watkins, Mathematical Intelligencer