Beyond Infinity (mathematics book)
| Company type | Book |
|---|---|
| Industry | Mathematics, Popular science |
| Founded | 2017 |
| Founder | Eugenia Cheng |
| Products | Book on infinity in mathematics |
Beyond Infinity: An Expedition to the Outer Limits of Mathematics is a widely read mathematics publication authored by Eugenia Cheng that delves into the concept of infinity. Released in 2017 by Basic Books and Profile Books, with a subsequent paperback version in 2018, the book earned a place on the shortlist for the 2017 Royal Society Insight Investment Science Book Prize.
Topics
Structured in two main sections, the initial part investigates ideas related to actual infinity, discussing number systems, set theory, cardinal numbers, ordinal numbers, transfinite arithmetic, and varying magnitudes of infinite sets. Important topics include Hilbert's paradox of the Grand Hotel, Cantor's diagonal argument, and the undecidability of the continuum hypothesis.
The latter section focuses on potential infinity, exploring how finite values can be attributed to infinite procedures such as growth rates, limits, and infinite summations. It also examines Zeno's paradoxes, Dedekind cuts, spatial dimensions including those of infinite-dimensional spaces, and briefly introduces aspects of higher category theory, which aligns with Cheng's academic expertise.
Complex mathematical notions are rendered approachable through relatable stories involving elements like the Loch Ness Monster, puff pastry, boating, dance competitions, footwear, as well as "Legos, the iPod Shuffle, snorkeling, Battenberg cakes and Winnie-the-Pooh."
Audience and reception
The Royal Society characterized Beyond Infinity as "a very engaging introduction to a forbidding subject." Critics highlighted its captivating and accessible narrative style; Wall Street Journal remarked that its "chatty tone" maintains reader interest. Targeted at general readers without advanced mathematical training—including inquisitive individuals and students—the book might be considered "too elementary for mathematicians or mathematics students."
Andrew James Simoson suggests this work alongside titles such as The Book of Numbers by John Horton Conway and Richard K. Guy, One Two Three... Infinity by George Gamow, and Really Big Numbers by Richard Schwartz.