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

The Infinity Machine - Sebastian Mallaby ****

It's very quickly clear that Sebastian Mallaby is a huge Demis Hassabis fan - writing about the only child prodigy and teen genius ever who was also a nice, rounded personality. After a few chapters, though, things settle down (I'm reminded of Douglas Adams' description of the Hitchhiker's Guide to the Galaxy ) and we get a good, solid trip through the journey that gave us DeepMind, their AlphaGo and AlphaFold programs, the sudden explosion of competition on the AI front and thoughts on artificial general intelligence. Although Mallaby does occasionally still go into fan mode - reading this you would think that AlphaFold had successfully perfectly predicted the structure of every protein, where it is usually not sufficiently accurate for its results to have direct practical application - we get a real feel for the way this relatively unusual company was swiftly and successfully developed away from Silicon Valley. It's readable and gives an important understanding of...
Post a Comment
Read more

The Laws of Thought - Tom Griffiths *****

In giving us a history of attempts to explain our thinking abilities, Tom Griffiths demonstrates an excellent ability to pitch information just right for the informed general reader.  We begin with Aristotelian logic and the way Boole and others transformed it into a kind of arithmetic before a first introduction of computing and theories of language. Griffiths covers a surprising amount of ground - we don't just get, for instance, the obvious figures of Turing, von Neumann and Shannon, but the interaction between the computing pioneers and those concerned with trying to understand the way we think - for example in the work of Jerome Bruner, of whom I confess I'd never heard.  This would prove to be the case with a whole host of people who have made interesting contributions to the understanding of human thought processes. Sometimes their theories were contradictory - this isn't an easy field to successfully observe - but always they were interesting. But for me, at least, ...
Post a Comment
Read more

Nanotechnology - Rahul Rao ****

There was a time when nanotechnology was both going to transform the world and wipe us out - a similar position to our view of AI today. On the positive transformation side there was K. Eric Drexler's visions in the 1986 Engines of Creation. Arguably as much science fiction as engineering possibilities, it predicted the ability to use vast armies of assemblers to put objects together from individual atoms.  On the negative side was the vision of grey goo, out of control nanotechnology consuming all in its path as it made more and more copies of itself. In 2003, for instance, the then Prince Charles made the headlines  when newspapers reported ‘The prince has raised the spectre of the “grey goo” catastrophe in which sub-microscopic machines designed to share intelligence and replicate themselves take over and devour the planet.’ These days the expectations have been eased down a notch or two. Where nanotechnology has succeeded, it has been with the likes of atom-thick mat...
Post a Comment
Read more