*This guest review is written by Sophie Maclean. Math Without Numbers will be released on 7th January.*

I think it’s safe to say that all fans of The Aperiodical like maths. I would also be confident in saying that there’s a shared feeling of “the more the merrier”, and we want as many people as possible to share our love of maths. In this respect, Milo Beckman would fit right in. In fact, I’d go as far as to say that his book *Math Without Numbers* is precisely the kind of book that could get more people to realise how fun maths can be.

*Math Without Numbers* starts with topology, then goes on a whistle stop tour through analysis and algebra to arrive at mathematical modelling. The huge variety of topics means that nothing is covered in much depth, but it gives a great overview and allows the reader to decide for themselves what they’d like to look into more.

My favourite chapter is about automata, as there is an opportunity to do some thinking and playing with the maths. Fans of Conway’s Game of Life, game theory, the Four Colour Theorem, and Hilbert’s “infinite hotel” will also find sections of this book very appealing. There is a real “wow” moment in the last chapter, about science. I won’t spoil it but I guarantee every reader at some point will think to themselves “I see where this is going” and then very soon afterwards think “That is SO cool”.

The aim of *Math Without Numbers* is to demystify maths, and to help everybody to see the true beauty of the subject. Part of the struggle you may have faced when trying to enthuse others about maths is getting them to give it a chance. Beckman’s solution is to make the idea of a maths book less scary, by promising that “the only numbers in this book are page numbers”. Does he stick to this promise? If we’re being pedantic, no (you only need to reach the second page of writing to find the word “million”, and “two” appears on the following page). Does this means he fails in his goal of making maths more accessible and less intimidating? Emphatically not.

Beckman (by and large) avoids using jargon and intimidating words like “integration”, instead using terms which he builds up to (in this case “continuum-sum”). This succeeds in making complex ideas seem significantly less daunting to those who are apprehensive. He accompanies each idea with a whole host of real-life examples and analogies. This both serves to make the mathematics seem more familiar, and to ensure a wide variety of audiences have a reference point.

If I were being critical, there are times when Beckman seems inconsistent in his use of jargon and analogies. Sometimes I felt he tried too hard to avoid using mathematical terms, and that the analogies felt a bit forced. There are other times when Beckman did use more mathematical words, without explaining the meaning. There were also a couple of proofs that I don’t think I would have been able to easily follow if I didn’t already know them (indeed, I asked a non-mathematical friend to read and she agreed). These are few and far between though, and both my friend and I doubt they would detract from any enjoyment.

One of the things I love most about this book is how Milo Beckman guides the audience to thinking more mathematically. He demonstrates the process of coming up with wrong ideas and working out which parts to keep. He shows how you may not know the path to the solution when you first come to tackling a problem, but that’s okay – and the first step needs only to be to work out what you can do.

When reading this book, it felt like a friend was telling me about their latest hobby, and it was difficult not to get swept along with the excitement. Like an overly excited friend, Beckman is occasionally prone to going off on tangents, to jumping to and fro a bit, and introducing ideas that are potentially beyond the scope of the book. Occasionally this does give the impression of an identity crisis. For example, the chapter on mathematical foundations is written as a dialogue, which is a wonderful idea, but just doesn’t fit with the rest of the book.

At this point I have to give a huge amount of credit to the illustrator, M Erazo. The illustrations in the book really help to explain what is going on – in fact, I’d go as far as to say that on some occasions I would still be able to understand what was going on if the text was removed and only the drawings remained. They’re an integral part of the book, and all help to break up what can sometimes feel like a large block of writing.

Though Beckman never says as much himself, I would say this book is perfect for somebody who loves learning about mathematics, but doesn’t want anything technical – perhaps a keen school student, or somebody that enjoys maths but hasn’t formally studied it for a while. It also serves as a good advert for Mathematics, so could make a good gift for anybody you’re trying to convert!

Math Without Numbers is published in the UK by Penguin.

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