Paradoxes: Guiding Forces in Mathematical Exploration

A Riveting Account of Paradoxes and their Impact on Mathematics

Does .999...=1? Can a sphere be reassembled into two identically sized spheres? Is the consistency of mathematical systems unprovable? Surprisingly, the answer to all of these questions is yes! And at the heart of each question, there lies paradox.

For millennia, paradoxes have shaped mathematics and guided mathematical progress. From the ancient paradoxes of Zeno to the modern paradoxes of Russell, paradoxes remind us of the constant need to revamp our mathematical understanding. It is for this reason that paradoxes are so important.

Paradoxes: Guiding Forces in Mathematical Exploration provides a survey of mathematical paradoxes spanning a wide variety of topics; delving into each paradox mathematically, philosophically, and historically. Readers will gain a full picture of how paradoxes have contributed to and guided the progress of mathematics in many ways. Paradoxes also provides the reader with a robust argument for the inclusion of paradoxes in education. This is all presented in a way that is accessible to anyone with a high school background in mathematics! Entertaining and educational, this book will appeal to any reader looking for a mathematical and philosophical challenge.