We were sent a free copy of this book by the publisher, and invited irregular contributor Elinor Flavell to read and review it.

Been feeling finite recently? Bounded by life? Those larger numbers feeling out of reach? Then you need “A Guide to Infinity: Ten Mathematical Journeys” by Edward R. Scheinerman. Over ten chapters, Scheinerman takes the reader through the infinity at the end of the number line, that other infinity between zero and one, the other other infinity found in shapes, and many other other other infinities.

The book reads like a set of lecture notes – and like lecture notes, has its pros and cons. This is not the book to give your friend to convince them that maths is amazing. However, if it’s been a while since you studied infinity, or you are looking for something to fill your time before you start university in the autumn, or maybe you are currently studying topics around infinity, you may find this book helpful.

Like lecture notes, there are lots of definitions, which can be useful when building up your knowledge about infinity. However, like lecture notes there is also assumed knowledge, and use of words before formal definitions! Those who are more familiar with mathematical jargon may find it easier to peruse.

At the end of each chapter there are several questions to the reader – which I think are great! They clearly follow from the material in the chapter, but are quite open questions, and more than one question made me stop to properly think about it.

For me, “A Guide to Infinity” does not quite contain enough information on the wider context and history of infinity. Scheinerman does make a few mentions of names, but I wanted more! Of course, as a historian of maths I am biased towards including historical material in books, but I think it would have complemented the book well – without this, it reads, as I keep saying, like a set of lecture notes.

As anyone who has taken a lecture series can tell you, not all lecture notes are created equal – and as lecture notes go, “A Guide to Infinity” is good. However, it does not quite match its claim of being “An accessible Introduction to Mathematical Infinity for the Endlessly Curious”. Infinity is a hard topic to start with – and for me, “A Guide to Infinity” does not quite hit the spot.

A Guide To Infinity at Yale Books
A Guide To Infinity on Bookshop.org
A Guide To Infinity on Waterstones.com