[5] The book is divided into two parts, with the first exploring notions leading to concepts of actual infinity, concrete but infinite mathematical values.

Topics used to illustrate these concepts include Hilbert's paradox of the Grand Hotel, Cantor's diagonal argument,[4] and the unprovability of the continuum hypothesis.

[1][2] The mathematics is frequently lightened and made accessible with personal experiences and stories,[3][6][7] involving such subjects as the Loch Ness Monster, puff pastry, boating, dance contests, shoes,[3] "Legos, the iPod Shuffle, snorkeling, Battenberg cakes and Winnie-the-Pooh".

[6] The Royal Society judges called Beyond Infinity "a very engaging introduction to a forbidding subject".

[2] As similar reading material, reviewer Andrew James Simoson suggests placing this book alongside The Book of Numbers by John Horton Conway and Richard K. Guy (1996), One Two Three... Infinity by George Gamow (1947), and Really Big Numbers by Richard Schwartz (2014).