Tales of Impossibility: The 2000-Year Quest to Solve the Mathematical Problems of Antiquity

Tales of Impossibility explores the fascinating story of four famous and studied questions in the history of mathematics: squaring the circle, trisecting an angle, doubling the cube, and inscribing regular polygons in a circle. These problems were first posed by the ancient Greeks and have served as ever-present muses for mathematicians for more than two millennia. David Richeson investigates how celebrated luminaries, including Euclid, Archimedes, Viète, Descartes, Newton, and Gauss, labored to understand these problems and how many major mathematical discoveries were related to their explorations. Although the problems were based in geometry, their resolutions were not until the nineteenth century, when mathematicians developed the theory of real and complex numbers, analytic geometry, algebra, and calculus. Pierre Wantzel and Ferdinand von Lindemann determined the problems were impossible to solve.

Format: Paperback / softback
Length: 456 pages
Publication date: 02 November 2021
Publisher: Princeton University Press

Tales of Impossibility is a captivating exploration of four of the most famous and studied problems in the history of mathematics. These ancient compass and straightedge problems, which include squaring the circle, trisecting an angle, doubling the cube, and inscribing regular polygons in a circle, have been a source of inspiration for mathematicians for over two millennia. David Richeson delves into the origins and proofs of these problems, demonstrating how they have played a crucial role in the growth of mathematics.

Richeson examines the contributions of renowned mathematicians such as Euclid, Archimedes, Viète, Descartes, Newton, and Gauss to understanding these complex problems. He highlights how their explorations led to significant mathematical discoveries, including the theory of real and complex numbers, analytic geometry, algebra, and calculus.

Despite the geometric basis of these problems, their solutions did not emerge until the nineteenth century, when mathematicians developed the necessary tools and theories. Pierre Wantzel, a little-known mathematician, and Ferdinand von Lindemann, through his work on pi, finally determined that these problems were impossible to solve.

Along the way, Richeson provides entertaining anecdotes related to the problems, such as how the Indiana state legislature passed a bill setting an incorrect value for pi and how Leonardo da Vinci made elegant contributions to his own study of these problems.

Tales of Impossibility takes readers on a journey from the classical period to the present, chronicling how these four unsolvable problems have captivated mathematical thinking for centuries. It is a must-read for anyone interested in the history, philosophy, and beauty of mathematics.

Weight: 422g
Dimension: 204 x 135 x 35 (mm)
ISBN-13: 9780691218724