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

The book 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: Hardback
Length: 456 pages
Publication date: 08 October 2019
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. In his book, 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 problems. He highlights how their explorations led to significant mathematical discoveries, including the theory of real and complex numbers, analytic geometry, algebra, and calculus.

However, the solutions to these problems remained elusive until the nineteenth century, when mathematicians developed the necessary tools and theories to address them. It was during this time that Pierre Wantzel, a little-known mathematician, and Ferdinand von Lindemann, through his work on pi, definitively determined that the problems were impossible to solve.

Along the way, Richeson provides entertaining anecdotes and historical context related to the problems. For instance, he mentions 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: 800g
Dimension: 241 x 130 x 30 (mm)
ISBN-13: 9780691192963