99 Variations on a Proof - by Philip Ording (Paperback)

About the Book

"This book offers a multifaceted perspective on mathematics by demonstrating 99 different proofs of the same theorem. Each chapter solves an otherwise unremarkable equation in distinct historical, formal, and imaginative styles that range from Medieval, Topological, and Doggerel to Chromatic, Electrostatic, and Psychedelic. With a rare blend of humor and scholarly aplomb, Philip Ording weaves these variations into an accessible and wide-ranging narrative on the nature and practice of mathematics. Inspired by the experiments of the Paris-based writing group known as the Oulipo - whose members included Raymond Queneau, Italo Calvino, and Marcel Duchamp - Ording explores new ways to examine the aesthetic possibilities of mathematical activity. 99 Variations on a Proof is a mathematical take on Queneau's Exercises in Style, a collection of 99 retellings of the same story, and it draws unexpected connections to everything from mysticism and technology to architecture and sign language. Through diagrams, found material, and other imagery, Ording illustrates the flexibility and creative potential of mathematics despite its reputation for precision and rigor. Readers will gain not only a bird's-eye view of the discipline and its major branches but also new insights into its historical, philosophical, and cultural nuances. Readers, no matter their level of expertise, will discover in these proofs and accompanying commentary surprising new aspects of the mathematical landscape"--Back cover.

Book Synopsis

An exploration of mathematical style through 99 different proofs of the same theorem

This book offers a multifaceted perspective on mathematics by demonstrating 99 different proofs of the same theorem. Each chapter solves an otherwise unremarkable equation in distinct historical, formal, and imaginative styles that range from Medieval, Topological, and Doggerel to Chromatic, Electrostatic, and Psychedelic. With a rare blend of humor and scholarly aplomb, Philip Ording weaves these variations into an accessible and wide-ranging narrative on the nature and practice of mathematics.

Inspired by the experiments of the Paris-based writing group known as the Oulipo--whose members included Raymond Queneau, Italo Calvino, and Marcel Duchamp--Ording explores new ways to examine the aesthetic possibilities of mathematical activity. 99 Variations on a Proof is a mathematical take on Queneau's Exercises in Style, a collection of 99 retellings of the same story, and it draws unexpected connections to everything from mysticism and technology to architecture and sign language. Through diagrams, found material, and other imagery, Ording illustrates the flexibility and creative potential of mathematics despite its reputation for precision and rigor.

Readers will gain not only a bird's-eye view of the discipline and its major branches but also new insights into its historical, philosophical, and cultural nuances. Readers, no matter their level of expertise, will discover in these proofs and accompanying commentary surprising new aspects of the mathematical landscape.

Review Quotes

"[99 Variations on a Proof] is certainly beautifully produced and invites dipping into rather than reading from cover to cover."---Nick Lord, Mathematical Gazette ​​​​​​​

"[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

"A deep and thoughtful examination of the nature of mathematical arguments, of mathematical style, and of proof itself."---Chris Sangwin, London Mathematical Newsletter

"A Choice Outstanding Academic Title of the Year"

"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 ​​​​​​​

"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 book is an insightful addition to mathematical literature."---Robert Maddox-Harle, Leonardo Reviews

"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."---Jürgen Appell, Zentralblatt MATH

"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"

About the Author

Philip Ording is professor of mathematics at Sarah Lawrence College. He is the coeditor of Simplicity: Ideals of Practice in Mathematics and the Arts.