Beyond Infinity: An Expedition to the Outer Limits of Mathematics

Mathematics is a scenic journey where we travel toward the destination and stop and admire the g-i-raphs and probability trees along the way. Our destination here is infinity itself. We will meet Hilbert’s Hotel, a hotel with an infinite amount of rooms; infinite cookies, a demonstration of how something finite can be split infinitely; and Mobius strips, which have only one side. Once you reach the end, you will have both the satisfaction that comes from looking back on a beautiful vacation and, simultaneously, realizing how much you have learned.

Often, when a writer attempts to write a book about an esoteric topic, he or she makes one or two mistakes. Either they try to dumb down the topic too much, resulting in condescending baby talk, or they end up writing a scientific-paper-style tome, inaccessible for people who don’t study the topic. Although Cheng does occasionally err on the side of being too baby-ish, she totally avoids condescension. For the most part, she strikes a nice balance. This book is a fun exploration of infinity, with advanced concepts explained at a beginner’s level. Best of all, it highlights the excitement that comes from mathematical discovery.