Skip to main content

Cakes, Custard and Category Theory - Eugenia Cheng ****

Popular maths books are the most difficult to make interesting to those beyond the hard core readers who are happy to spend their time on mathematical puzzles and diversions, and the reason this book gets four stars despite a couple of problems is that is one of the most original and insightful books on the nature of mathematics for the general reader that I've ever seen.

Rather than simply throw mathematical puzzles and diversions at us, or weird and wonderful numbers, Eugenia Cheng takes us on something close to a journey through the mathematical mind, introducing us first to abstraction, then through the processes of mathematics, the way it generalises and the essential foundations of axioms. This is all as an introduction to the second half the the book on Cheng's speciality, category theory, which will I suspect be as unfamiliar to most non-mathematicians as it was to me.

So in terms of what it sets out to do and what, to some degree, it achieves it is absolutely brilliant. Cheng writes in a light, engaging fashion and really pushes the envelope on the way that you can explore mathematics. The basics are there - the inevitable doughnut/coffee cup topology comparison (though she prefers bagels, as doughnuts are not always toroidal), for instance, but this quickly then evolves into the much more challenging concept of 'taking the complement' of something by removing it from three dimensional space with an imaginary three dimensional eraser and examining what remains through topological eyes.

I can't totally ignore the issues. The lesser one is that as a gimmick, each section begins with a recipe which is then used to illustrate a mathematical point (though also to talk about food) - I found this a touch condescending and very irritating, though some readers will probably like it. The bigger problem is that the author isn't great at structuring a book. The first chapter particularly is all over the place, and she has a tendency to use concepts before they are explained. This is particularly true of category theory, which never really gets a clear, approachable definition, but rather is feinted at to begin with, and then introduced as example after example, which without a structure explaining just what it does is quite difficult to put together as a total picture of a discipline.

So, flawed it certainly is, but that doesn't get in the way of it being an unusually interesting attempt at doing something far more significant than most popular mathematics books do. I've always felt that pure maths was uncomfortably abstract and arbitrary, coming up with rules that have no obvious justification. This is the first book of read where it's possible to get a sense of, 'Hey, that kind of makes sense' - which surely is an impressive achievement. If you can look past the gimmicky aspect and the occasionally confusing structure you are in for a treat.


Paperback 

Kindle 
Using these links earns us commission at no cost to you
Review by Brian Clegg

Comments

Popular posts from this blog

Rakhat-Bi Abdyssagin Five Way Interview

Rakhat-Bi Abdyssagin (born in 1999) is a distinguished composer, concert pianist, music theorist and researcher. Three of his piano CDs have been released in Germany. He started his undergraduate degree at the age of 13 in Kazakhstan, and having completed three musical doctorates in prominent Italian music institutions at the age of 20, he has mastered advanced composition techniques. In 2024 he completed a PhD in music at the University of St Andrews / Royal Conservatoire of Scotland (researching timbre-texture co-ordinate in avant- garde music), and was awarded The Silver Medal of The Worshipful Company of Musicians, London. He has held visiting affiliations at the Universities of Oxford, Cambridge and UCL, and has been lecturing and giving talks internationally since the age of 13. His latest book is Quantum Mechanics and Avant Garde Music . What links quantum physics and avant-garde music? The entire book is devoted to this question. To put it briefly, there are many different link...

Everything is Predictable - Tom Chivers *****

There's a stereotype of computer users: Mac users are creative and cool, while PC users are businesslike and unimaginative. Less well-known is that the world of statistics has an equivalent division. Bayesians are the Mac users of the stats world, where frequentists are the PC people. This book sets out to show why Bayesians are not just cool, but also mostly right. Tom Chivers does an excellent job of giving us some historical background, then dives into two key aspects of the use of statistics. These are in science, where the standard approach is frequentist and Bayes only creeps into a few specific applications, such as the accuracy of medical tests, and in decision theory where Bayes is dominant. If this all sounds very dry and unexciting, it's quite the reverse. I admit, I love probability and statistics, and I am something of a closet Bayesian*), but Chivers' light and entertaining style means that what could have been the mathematical equivalent of debating angels on...

The Bright Side - Sumit Paul-Choudhury ***

When I first saw The Bright Side (the subtitle doesn't help), I was worried it was a self-help manual, a format that rarely contains good science. In reality, Sumit Paul-Choudhury does not give us a checklist for becoming an optimist or anything similar - and there is a fair amount of science content. But to be honest, I didn't get on very well with this book. What Paul-Choudhury sets out to do is to both identify what optimism is and to assess its place in a world where we are beset with big problems such as climate change (which he goes into in some detail) that some activists position as an existential threat. This is all done in a friendly, approachable fashion. In that sense it's a classic pop-psychology title. For me, Paul-Choudhury certainly has it right about the lack of logic of extreme doom-mongers, such as Extinction Rebellion and teenage climate protestors, and his assessment of the nature of optimism seems very reasonable, if presented at a fairly overview leve...