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
Labels:

Comments

Post a Comment

Popular posts from this blog

Beyond Belief - Helen Pearson *****

Apparently it comes as a surprise to many that medicine was not particularly scientific until the end of the twentieth century (to be honest, it's no surprise to me - we had a GP who used homeopathy in the 90s). Instead it was based on anecdotal guidance - the kind of thing that appeared to work. Evidence-based medicine has since improved the field, trying where possible to base decisions on evidence, ideally based on randomised controlled trials. The first part of Helen Pearson's book covers this well - though I think it's by far the least interesting part of what we discover. Instead what's truly fascinating is the rest of it, looking at a wide range of other fields where evidence was rarely properly used and that are only now starting to dip a toe in the water. These include social policy, policing, conservation, business and education. The main part of the book gives us examples of how bad these areas have been in terms of basing decisions on what's always been ...
Post a Comment
Read more

The Infinite Book – John D. Barrow ****

Authors are often asked to review books on a topic they’ve written on themselves. The reasoning is sensible – they ought to know something about the subject – but there’s always that uneasy suspicion that there’s going to be a bit of bias creeping in. So I think it’s only fair to admit up front that I have written a book on infinity (of which more later). Infinity is a wonderful subject, because it’s intimately mind-bending (if the combination sounds paradoxical, that’s what infinity is all about) and gives you the chance to pull in all sorts of different concepts and assocations along the way, something Barrow does with great gusto. There’s a surprisingly large amount of coverage here for God, and for the universe, and the book jumps around from Aristotle to Hilbert’s Infinite Hotel (explained at great length), from the paradoxes of infinite sets to the paradoxes of time travel. Overall it’s an enjoyable journey that gives plenty of opportunity to be amazed and surprised. The...
Post a Comment
Read more

Adventures of a Computational Explorer - Stephen Wolfram ***

Stephen Wolfram, the man behind the scientist's mathematical tool of choice, Mathematica, plus a whole host of other software products, including the uncanny Wolfram Alpha knowledge engine, is undoubtedly a genius of the first order. In this book, we get an uncensored excursion into the mind of genius - which is, without doubt, a fascinating prospect. The book consists of a collection of essays and speeches that Wolfram has produced over the last ten to fifteen years, covering an eclectic range of topics. Like all such collections, the result is something that lacks the coherence of a book with a narrative that runs through it, inevitably introducing a degree of repetition and a mix of interesting and not-so-interesting topics - but there's likely to be something to catch the attention anyone who is into computing or mathematics. One of the most interesting pieces is the opening one, where Wolfram describes being a consultant on the SF movie Arrival. He seems to hav...
Post a Comment
Read more