Back in 2008, Chaim Goodman-Strauss and Heidi Burgel, together with the late John Conway, wrote a book called The Symmetries of Things, which covered a range of topics around mathematical symmetry and the symmetries of geometric objects.
Now the first two authors have a new book, The Magic Theorem, due for publication this week. We spoke to Heidi and Chaim about where this book has come from and what it’s about.
This is a review of the book The Big Bang of Numbers by Manil Suri. We were kindly sent a copy of the book to look at, and Ashleigh Ratcliffe shares her thoughts.
In this book, Suri sets out to build the whole of modern mathematics from its foundations, and has chosen to do this by mirroring the Christian 7-day creation story – along with a persistent running joke about the author’s entirely fictional personal rivalry with the Pope, which at times is slightly distracting. Despite this, it’s a clever conceit and allows the story of creation of maths to unfold gradually.
The author takes a holistic approach to the field of mathematics – the book demonstrates the importance of mathematics in the universe, and how it would not be possible to exist without mathematics. Whilst the main story is about building the universe from mathematics, you also get an idea of the historical building and progress of mathematics as a field. I find it such a beautiful concept that in any universe, we would have maths.
On day 1 (my personal favourite) we have arithmetic. This chapter starts with thinking about what numbers are and why we need them. After constructing sets and numbers, we start playing games with numbers and then obtain the different operations. This is a fun way to approach arithmetic, especially as each number gets its own personality. By the end of day 1, we have the building blocks of the universe.
On day 2, we have geometry. Using our building blocks and some abstract ideas, we make space for the universe. We first get lines, then planes, and then space. The chapters in this section are littered with useful diagrams, images and ideas – such as getting points to act as lights to switch on and off, which in turn create shapes. This is a very imaginative and beautiful concept, and an approach to this topic I have never seen before. We also see appearances of geometry in nature, and some fabulous crochet creations.
On day 3 we have algebra, and we get further in touch with nature. We can view the things we already made, but now in terms of algebra – which surprisingly includes teaching mother nature how to draw!
On day 4 we have patterns, which introduces us the wonderful concept of symmetry. We also meet some more occurrences of maths in nature through the golden ratio, spirals and fractals. On day 5 we have physics, and the idea of spacetime from which we can build a simplistic gravitational model.
On day 6 we have infinity. The author builds an intuition for the concept of infinity through a sci-fi tale featuring Georg Cantor.
Finally, on day 7, we have emergence: the day of rest, where we sit back and admire what we have created. The ending is left open, which aligns with the exploratory and investigative nature of the book. However, as a reader, I felt slightly annoyed to have followed the path of building the universe for it to all then be questioned.
The first few days are very easy to follow and there are nice images and applications of mathematics throughout the book. The importance of mathematics is well portrayed throughout, especially through its occurrences in nature – for a large section of the book, the narrator is mother nature.
The further into the book we get, the more abstract the ideas become and in parts it is hard to follow. Some bits of the story are a little far-fetched, and there were some explanations that I struggled to get my head round – so I would expect it to be hard for a non-mathematician to completely understand, despite the book’s description on publisher Bloomsbury’s website: “an accessible introduction for enthusiastic novices”.
The endnotes have further content for more advanced readers to find/read more details on certain areas or ideas. In my opinion, some things in the text could have been put in the endnotes, and vice versa, allowing the main story to be easier to follow and understand.
Overall, this is a very unique and interesting book and one I very much enjoyed reading. A truly different maths book, which shows mathematics in a different light.
This is a review of the book Mapmatics: How we Navigate the World through Numbers by Paulina Rowińska. We were kindly sent a copy of the book to look at, and Elinor Flavell shares her thoughts.
Do you love maps? Do you hate maps? Have you never given much thought to maps but are now worried that it might be good to know how to navigate if your phone dies? Well, Mapmatics is for you!
Do you know a geography nerd who is always bringing up maps? Do you know someone who always seems to get lost, despite it being easier than ever to get around? Or do you have that one friend who still doesn’t believe that everything can be related to maths? Well, Mapmatics is for them!
Mapmatics is for everyone!
Mapmatics is for you, and for anyone in your life who would like to more deeply understand the connections between maths and the world around them. On the surface Mapmatics is a book about how we create and use maps to interpret the world around us. But Rowińska shows that the reason we can do all of these things with maps is because of mathematics.
Over eight chapters, Rowińska talks us through problems that humans have wrestled with through the centuries – from “how can we take a 3D globe and turn it into a 2D map?” to “how can we map the inside of our planet without actually going to the centre of the earth?”. And with each problem she takes us through the underlying mathematics. Each chapter explores a different aspect of maps, and includes a diverse range of topics, from gerrymandering to the London Tube map.
Rowińska does a great job at explaining some rather complicated ideas while talking about lots of other researchers, giving you plenty of resources to go and learn more about a certain subject, if you so wish; and she includes some very helpful diagrams! She is very good at defining and explaining geography jargon in terms which a geography novice such as myself could understand. However, I would have found it helpful to include a glossary in the book so I could refer back to them. I also found it rather refreshing that in her examples she does not stick to the gender neutral “he” when talking about a random person experiencing something.
I have two primary criticisms of the book: Rowińska starts off the book by talking about her first experience of maps, but I would love to know more about her link to maps and geography and what prompted her to write the book in the first place. Secondly, I would love to see even more diagrams – in colour- in the book as I think this would support some of the more difficult mathematical ideas included. However, I realise this is the eternal struggle between author and publisher.
This book would suit anyone who loves understanding the mathematics behind things that we use every day. From a technical point of view, I would recommend having at least done mathematics in your final years of secondary school, as some of the mathematics presented would be challenging otherwise.
Overall, this is an engaging book that covers a huge variety of applications – from earthquakes to animation, and will be of interest to anyone who likes to understand the intersection between maths and other topics.
Mapmatics, at Pan Macmillan
Mapmatics, at Bookshop.org
Mapmatics, at Waterstones.com
Our own Katie and Peter have collaborated on a new popular maths book, along with friends of the site Alison Kiddle and Sam Hartburn, which is out today. Short Cuts: Maths is an “expert guide to mastering the numbers behind the mysteries of modern mathematics,” and includes a range of topics from infinity and imaginary numbers to mathematical modelling, logic and abstract structures. We spoke to the four authors to see how they found it writing the book and what readers can expect.
Peter: From my point of view, Katie approached me to ask if I’d like to be involved, which was very exciting! She’d worked on a couple of books with the same publisher and was asked to commission authors for this one.
Katie: The publishers wanted to make this book – one of a ‘Short Cuts’ series which needed a maths title – and asked me to be commissioning editor, which meant I could write some of it and ask others to write the rest. I chose some people I’ve worked with before who I thought would have something interesting to say about some topics in maths (in particular, the topics I know less about, so they could help me with those bits!)
Alison: As I was the last of the four of us to come on board, I think everyone had already expressed a preference for their favourite bits to write about, but luckily that left me with the two best topics, logic and probability.
Alison: I’ve been involved in writing a book before but that one was about maths education, for an audience of mainly teachers, so this was a different sort of challenge, writing for a general audience with different levels of maths prior knowledge and enthusiasm.
Sam: I’ve worked on many books in the same genre as a copyeditor and proofreader, but this was my first time as an author. I enjoyed seeing how the publishing process works from the author’s point of view – it’s definitely had an impact on my editorial work!
Peter: My first time in popular book form, though I felt it used a bunch of skills I’ve developed in other work. And Katie is so great at organising projects that it went really smoothly.
Sam: It’s a book you can dip into – you don’t need to read it from front to back. Each page is self-contained and answers a question, and we tried to make the questions as interesting as possible (two of my particular favourites are ‘Is a mountain the same as a molehill?’ and ‘Do Nicholas Cage films cause drownings?’).
Alison: We had quite a strict word limit to write to, which was a bit hard to get used to at first as I have a tendency to use ten words when two will do – but this turned out to be a blessing because it focussed us all on what the really important concepts were, and we found ways to express those concepts in a concise manner.
Katie: I love how the style of the book builds in these gorgeous illustrations – we worked with the illustrator to make sure they fit with the text, but also bring out fun aspects of the ideas we’re talking about.
Sam: I’d like to think that anyone who has a vague interest in maths would get something out of it. Even though it delves into some deep mathematical topics, we’ve (hopefully!) written it in such a way that it’s understandable to anybody with school-level maths. But I’d hope that experienced mathematicians would also be able to find something new, or at least fun, in there.
Alison: I’m definitely going to be recommending it to the students I work with. The bite-size dipping in and out model is great for them to skim read so they can find out a little bit about the mathematical ideas that appeal to them. Particularly useful for people preparing for university interviews where they want to show off that they know some maths beyond the usual curriculum!
Katie: My mum’s definitely getting a copy for Christmas – and not just because I was involved in writing it: she’s not from a mathematical background but I think she’d enjoy the straightforward explanations and discovering new ideas.
Sam: The publisher did commission some lovely illustrations. The bear in the modelling cycle is a particular delight!
Katie: Yes! We love the modelling bear. I also liked being able to share ideas people might not otherwise encounter if they read about mathematics, like how mathematical modelling works, or what topology is, or some of the nitty-gritty of mathematical logic.
Peter: There are loads of quick summaries of areas of maths I know less about, which is really nice to have. The illustrations are great — the baby failing to manage a crocodile always makes me chuckle, and I can’t wait to show my son the game theory dinosaurs!
Short Cuts: Maths is available to buy today from all good bookshops.
A conversation about mathematics and literature inspired by a book. Presented by Katie Steckles and Peter Rowlett with special guest Sarah Hart, author of Once Upon a Prime: The Wondrous Connections Between Mathematics and Literature.
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This is a review of David Acheson’s new book, which we were kindly sent a copy of to read.
In The Spirit of Mathematics: Algebra And All That, David has pulled together a collection of what he refers to as ‘elegant mathematics using only simple materials’ – neat, short algebraic proofs and definitions, models of physical systems and mathematical tricks and curiosities.
He includes all the classics, from proof by induction to Fibonacci numbers to hitting a snooker ball, and each is presented with enthusiasm, alongside stories of mathematicians – and fearlessly including all the equations and derivations (if every equation really did halve your readership, as Stephen Hawking believed, this would be a very brave book to publish). But the maths is well-explained and very approachable, and it’s refreshing to see it featured so prominently outside of a textbook.
The book is also filled with helpful diagrams and illustrations, as well as humorous asides, cartoons and pictures of many mathematicians (sadly, only one female mathematician is featured, and she’s included only for her joke about how hard she’s found it to get a proof…) – but the book is well-produced and clearly laid out, with well-defined, short chapters each with a clearly defined topic.
The result is a compendium of intriguing ideas which would fascinate and compel a keen mathematician wanting to learn more, and provide hours of intrigue and jumping-off points for further investigation. Most topics are only covered briefly, so a deeper understanding would need research elsewhere, but for an enthusiastic reader this would happen naturally. Each discovery is motivated by a real-world example, or an interesting puzzle or curiosity, and all the key topics from algebra are touched on in one way or another.
However, this book wouldn’t suit an inexperienced mathematician – given which steps in the calculations are described as ‘simple’, a reasonable level of maths is assumed, and I’d imagine a strong GCSE or A-level student, particularly one already keen to learn more, would get much more out of it than a younger student. It’d also suit an adult wishing to refresh their mathematical knowledge from school and pick up some new ideas. But despite the blurb on the back claiming ‘for those who dread the subject, this book may be an eye-opener’, I suspect that such a reader might struggle in places.
Overall, this is a well-presented celebration of the best parts of mathematics, and showcases just how powerful maths can be.
We asked guest author Elliott Baxby to take a look at John Allen Paulos’ latest book, Who’s Counting.
Mathematics is an increasingly complex subject, and we are often taught it in an abstract manner. John Allen Paulos delves into the hidden mathematics within everyday life, and illustrates how it permeates everything from politics to pop culture – for example, how game show hosts use mathematics for puzzles like the classic Monty Hall problem.
The book is a collection of essays from Paulos’ ABC News column together with some original new content written for the book, on a huge range of topics from card shuffling and the butterfly effect to error correcting codes and COVID, and even the Bible code. As it’s a collection of separate columns, it doesn’t always flow fluently – I did find myself losing focus on some of the topics covered, particularly ones that didn’t interest me as much. This was mainly down to the content though – the writing style is extremely accessible and at times witty.
The book included some interesting puzzles and questions, which were challenging and engaging, and included solutions to each problem – very helpful for a Saturday night maths challenge! I even showed some to my friends, who at times were truly puzzled. I loved the idea of puzzles being a means of sneaking cleverly designed mathematical problems onto TV game shows. It goes to show maths is everywhere!
I enjoyed the sections on probability and logic as these are topics I’m particularly interested in. One chapter also explored the constant $e$, where it came from and where else it pops up – a very interesting read. It does deserve more attention, as π seems to be the main mathematical constant you hear about, and I appreciated seeing $e$ being explored in more depth.
This book would suit anyone who seeks to see a different side of mathematics – which we aren’t often taught in school – and how it manifests itself in politics and the world around us. That said, it would be better for someone with an A-level mathematics background, as some of the topics could be challenging for a less experienced reader.
It’s mostly enjoyable and has a good depth of knowledge, including questions to test your mind. While I didn’t find all of it completely engaging, there are definitely some points made in the book that I’ll refer back to in the future!