The Book of Infinity

A rich, thorough exploration of infinity that combines mathematical precision with playful, accessible coverage of a fascinating variety of paradoxes and conundrums.

In this rich, thorough account of all things infinite, Joel David Hamkins combines playful thought experiments with mathematically precise exposition to explore the vast, fascinating spectrum of paradoxes and conundrums of infinity. Written with equal parts wonder and rigor, the book moves from classical paradoxes (Zeno, Hilbert’s hotel, Aristotle’s wheel) to Cantor’s transfinite arithmetic, the continuum hypothesis, surreal numbers, infinitesimals, epistemic logic puzzles, and contemporary debates about potential vs. actual infinity. Twenty-five lively, self-contained chapters are enriched by extensive illustrations, diagrams, figures, and Fermi-style estimation puzzles. Highly readable and pedagogically rich, The Book of Infinity is ideal for undergraduate philosophy and math students and enthusiasts of logical and mathematical curiosities alike.

Approaches a wide range of ideas with both rigor and delight Renders deep mathematical ideas accessible to beginners Emphasizes intuition and deep conceptual understanding Integrates historical perspectives and contemporary issues Suits anyone interested in paradoxes, large numbers, and conceptual puzzles