What is infinity? What is proof?

These are two of the biggest questions mathematicians have grappled with over the years. In this well-written and fascinating book, John Stillwell takes us on a tour through some of the answers to these questions — and the surprising ways that the answers are related — discovered over the past 100 years. Diagonal arguments, transfinite ordinals, the continuum hypothesis, formal computational systems and the halting problem, incompleteness and unprovability, formal arithmetic and proof strength…

This book is somewhat above the usual level of books I review here. Readers will need a well-developed sense of logic to follow all the threads. But this is by far the most engaging and accessible exposition of these topics that I’ve ever seen, and I couldn’t resist reviewing such a well-written book about such beautiful and surprising mathematics.