Skip to main content

Is Maths Real? - Eugenia Cheng ****

As soon as I saw this book, I knew I had to read it, if only because I wrote a book called Are Numbers Real?. The maths content of Eugenia Cheng's book is brilliant: where I was covering the history of mathematics, she focuses on what real, pure mathematicians do. (Funnily, I had called my book Is Maths Real?, but it was changed to the less accurate Are Numbers Real? so we wouldn't need different covers for the UK and US editions.)

The mathematical journey that Cheng takes us through is mesmerising. She starts by showing the power of abstraction - how by thinking about the nature of, say, something basic like addition or multiplication it is possible to extend the concept into something other than numbers. We also discover that, in some ways, the answer '2' is the least interesting response to 'What is 1 + 1?' - real maths isn't about the answer per se, but about digging into the processes, mechanisms and definitions to get a deeper understanding of the underlying logic.

From these simple beginnings, we are then helped to get over what has proved a stumbling block for many: the abstraction of what we'd call variables in computing. Using an x (say) instead of a specific number. I loved algebra at school, because it felt like code breaking, but I absolutely understand why this step is one that defeats many young people in their exposure to mathematics. We then get on to formulae and their relationship to other mathematical structures like geometric ones, and different visual representations. And this was all a delight.

I wouldn't entirely agree with Cheng on why so many people aren't interested in, or openly dislike, maths. I suspect a lot of it is about the very thing that makes it attractive to her - that abstraction. If we look at the rest of STEM, engineering and medicine give us practical things. Physics and chemistry tells us how the world works. Biology tells us about interesting animals and feeds into medicine. But most of maths is neither useful in ordinary life nor telling us anything about the world, because it exists within its own abstracted universe. This book makes clear how beautiful that can be - but it's a hard sell to teenagers.

Originally, I was going to give this book five stars, because the maths coverage is brilliant, but most of Cheng's books I've read have the flaw of containing (for me, at least) too much about her and her opinions. I want to read about maths, not Cheng's interest in food, her politics or her cultural inclinations. I do want to know about why mathematicians find maths interesting - but that’s a very different thing. This sort of personal content does appeal to some readers, just as, say, reading a magazine about celebrities is fascinating for some, but it puts me off.

Overall, then, do read it if you want to know more about the nature of pure mathematics and about being a mathematician - the mathematical content is great - but you may need to occasionally grit your teeth over the rest.

Hardback:   
Kindle:  
Using these links earns us commission at no cost to you
Review by Brian Clegg - See all Brian's online articles or subscribe to a weekly email free here
Labels:

Comments

Post a Comment

Popular posts from this blog

The Decline and Fall of the Human Empire - Henry Gee ****

In his last book, Henry Gee impressed with his A (Very) Short History of Life on Earth - this time he zooms in on one very specific aspect of life on Earth - humans - and gives us not just a history, but a prediction of the future - our extinction. The book starts with an entertaining prologue, to an extent bemoaning our obsession with dinosaurs, a story that leads, inexorably towards extinction. This is a fate, Gee points out, that will occur for every species, including our own. We then cover three potential stages of the rise and fall of humanity (the book's title is purposely modelled on Gibbon) - Rise, Fall and Escape. Gee's speciality is palaeontology and in the first section he takes us back to explore as much as we can know from the extremely patchy fossil record of the origins of the human family, the genus Homo and the eventual dominance of Homo sapiens , pushing out any remaining members of other closely related species. As we move onto the Fall section, Gee gives ...
Post a Comment
Read more

The Autobiography – Charles Darwin ****

I have to confess to putting off reading this book until the last moment, as I expected it to be a typical piece of Victorian sentimental unreadable stodge. I was wrong. Darwin’s little book (only 150 small pages with appendices) was originally written for his own children, and displays a very personal style of writing – though, as son Francis comments, his style was always more populist than was common then: “In writing he sometimes showed the same strong tendency to strong expressions that he did in conversation. Thus in the Origin, p440, there is a description of a larvel [sic] cirripede ‘with six pairs of beautifully constructed natatory legs, a pair of magnificent compound eyes and extremely complex antennae’. We used to laugh at him for this sentence, which we compared to an advertisement.” The main book is delightful because it demonstrates Darwin’s self-depreciating modesty, and the fascinating path he took from enthusiastic shooter of game, to amateur geologist (still his...
Post a Comment
Read more

Zero Degrees of Empathy [The Science of Evil] – Simon Baron-Cohen ***

I’ve been a real fan of previous books by Simon Baron-Cohen like  The Essential Difference , so opening this was one was a pleasant prospect. What I found was a book that wasn’t  bad … but that could have been a lot better. I got the impression of a book that had been rushed out without a lot of work going into it. The thesis at the heart of the book – that one of the important ‘circuits’ of the brain is the one dealing with empathy, and that individuals sit on an empathy spectrum, with some residing at zero degrees of empathy – is an interesting one. Baron-Cohen introduces us to three key personality types he defines as ‘zero-negative’ including psychopaths, plus types that are ‘zero-positive’ like those with Asperger’s. In a way both of these definitions are odd, in that his zero-negatives can actually have a lot of the kind of empathy that involves being able to read another person’s emotional state, and his zero-negatives can have a lot of the kind of empathy i...
Post a Comment
Read more