Beyond Infinity: An Expedition to the Outer Limits of Mathematics

Cheng (How to Bake π), a scientist in residence at the School of the Art Institute of Chicago and honorary fellow at Sheffield University, tackles some difficult concepts in this superb study of the mathematics of infinity. Beginning with the definition of infinity, Cheng moves through myriad mind-bending inquiries, including what the smallest infinity is, how to compare different infinities, whether you can subtract from infinity, and whether you can make an infinite number of cookies with a finite amount of dough. For each, she provides the mathematics behind the often counterintuitive answers. Cheng works hard at making these concepts accessible, employing menus and music playlists, among other things, to frame the challenging mathematical proofs. Acknowledging the difficulties the proofs present, Cheng wisely provides readers with reasonably accessible equations, useful graphics, and entertaining and straightforward explanations. Contemplating infinity is not trivial, even when following the lead of a writer as talented as Cheng, and readers will have to stop and wrestle with such recondite concepts as surjective and injective functions, harmonics, and factorials. Cheng’s enthusiasm for mathematics is infectious and readers curious about the mathematics of infinity will find her to be a worthy guide. Agent: George Lucas, Inkwell. (Mar.)