I am very pleased to announce that The Book of Infinity is available for pre-order.
Check it out at your favorite booksellers.
From the preface:
Come, let us explore infinity! We shall visit all my favorite paradoxes and conundrums. The ancient puzzles, confounding or intractable, will yield at times to our analysis. And what a joy it is to experience those Aha! moments—a flash of clarity lights the way out of the labyrinth. But alas, having escaped one maze, we shall often find ourselves immediately lost in another—a new paradox with new questions to answer. The puzzles of infinity are endless riddles nestled within one another.
The Book of Infinity was the original motivation for me to begin my substack Infinitely More. When I first arrived a few years ago at the University of Notre Dame from Oxford, I was asked by my new department what course I would most want to teach. My answer was a new course on infinity that I had long dreamed about—what fun it would be to share my ideas and puzzles with enthusiastic students, tracing the concept from ancient times to contemporary issues. I set furiously to work preparing this book, a series of vignettes on infinity, and we offered the course. I serialized the chapters on Infinitely More as they were completed—see the section The Book of Infinity. I’ve since taught the course several more times, and with further polishing and editing, the book is finally completed.
400 pages and 26 chapters:
The Book of Numbers
The Sand Reckoner
Zeno’s Paradox
The Method of Exhaustion
Supertasks
The Infinite Coastline Paradox
The Paradox of Giants
The Paradox of the Largest Tweetable Number
Potential Versus Actual Infinity
Equinumerosity and Comparison of Size
What Is the Infinite?
Hilbert’s Grand Hotel
Uncountable Infinity
How to Count
Transfinite Recursive Constructions
Slaying the Hydra
The Continuum Hypothesis
Throwing Darts at the Real Line
The Orders of Infinity
The Surreal Numbers
The Axiom of Choice
Infinitary Hat Puzzles and the Aftermath
The Guessing-Box Puzzle
We Can Predict the Future
Infinite Liars
Common Knowledge
Here are a few snippets from the index, to give you an idea of what’s covered…
The book is packed with full-color mathematical figures—over 200 color figures, of my own design, which I produced in LaTeX using TikZ. Here are a few samples:
And many others! Each figure is woven into the text to help explain a mathematical or philosophical idea.
Meanwhile, I am serializing all my other books-in-progress here on Infinitely More—subscribe for full access to all my current work, including the surreal numbers, games, logic, philosophy of mathematics, and more.