Skip to main content

Closing the Gap - Vicky Neale ***

Every now and then a working scientist will write a superb popular science book, but it's significantly rarer that mathematicians stray beyond recreational maths without becoming impenetrable, so I was cheering as I read the first few chapters of Vicky Neale's Closing the Gap about the attempt to prove the 'twin primes conjecture' that infinitely many pairs of prime numbers just two apart.

I'd say those first few chapters are far and above the best example I've seen of a mathematician getting across the essence of pure maths and why it appeals to them. Unfortunately, though, from then on the book gets bogged down in the problem that almost always arises, that what delights and fascinates mathematicians tends to raise a big 'So what?' in the outside world.

Neale interlaces attempts getting closer and closer to the conjecture, working down from a proof of primes several millions apart to under 600, adding in other, related mathematical work, for example on building numbers from squares and combinations of primes, but increasingly it's a frustrating read, partially due to necessary over-simplification. Time and again we're told about something, but effectively that it's too complicated for us to understand (or we'll come back to it in a later chapter), and this doesn't help make the subject approachable. I understand that a particular mathematical technique may be too complicated to grasp, but if so, I'm not sure there's any point telling us about it.

Part of the trouble is, most of us can only really get excited about maths if it has an application - and very little of what's described here does as yet. I'm not saying that pure mathematics is a waste of time. Not at all. Like all pure research, you never know when it will prove valuable. Obscure sounding maths such as symmetry groups, imaginary numbers and n-dimensional space have all proved extremely valuable to physics. It's just that while the topic remain abstract, it can be difficult to work up much enthusiasm for it.

At the beginning of the book, Neale draws a parallel with rock climbing, and that we are to the mathematicians scaling the heights like someone enjoying a stroll below and admiring their skill. And, in a way, this analogy works too well. We can certainly be impressed by that ability - but a lot of us also see rock climbing as a waste of time and consider it as interesting if you aren't actually doing it as watching paint dry.

It's not impossible to make obscure mathematics interesting - Simon Singh proved this with Fermat's Last Theorem. But that was achieved with writing skill by spending most of the book away from the obscure aspects. I'm beginning to suspect that making high level mathematics approachable is even more difficult than doing that maths in the first place.

Hardback:  
Kindle:  

Review by Brian Clegg

Comments

Popular posts from this blog

I, Mammal - Liam Drew *****

It's rare that a straightforward biology book (with a fair amount of palaeontology thrown in) really grabs my attention, but this one did. Liam Drew really piles in the surprising facts (often surprising to him too) and draws us a wonderful picture of the various aspects of mammals that make them different from other animals. 

More on this in a moment, but I ought to mention the introduction, as you have to get past it to get to the rest, and it might put you off. I'm not sure why many books have an introduction - they often just get in the way of the writing, and this one seemed to go on for ever. So bear with it before you get to the good stuff, starting with the strange puzzle of why some mammals have external testes.

It seems bizarre to have such an important thing for passing on the genes so precariously posed - and it's not that they have to be, as it's not the case with all mammals. Drew mixes his own attempts to think through this intriguing issue with the histor…

Foolproof - Brian Hayes *****

The last time I enjoyed a popular maths book as much as this one was reading Martin Gardner’s Mathematical Puzzles and Diversions as a teenager. The trouble with a lot of ‘fun’ maths books is that they cover material that mathematicians consider fascinating, such as pairs of primes that are only two apart, which fail to raise much excitement in normal human beings. 

Here, all the articles have something a little more to them. So, even though Brian Hayes may be dealing with something fairly abstruse-sounding like the ratio of the volume of an n-dimensional hypersphere to the smallest hypercube that contains it, the article always has an interesting edge - in this case that although the ‘volume’ of the hypersphere grows up to the fifth dimension it gets smaller and smaller thereafter, becoming an almost undetectable part of the hypercube.

If that doesn’t grab you, many articles in this collection aren’t as abstruse, covering everything from random walks to a strange betting game. What'…

Karl Drinkwater - Four Way Interview

Karl Drinkwater is originally from Manchester, but has lived in Wales half his life. He is a full-time author, edits fiction for other writers and was a professional librarian for over twenty-five years. He has degrees in English, Classics and Information Science. When he isn't writing, he loves exercise, guitars, computer and board games, the natural environment, animals, social justice, cake and zombies - not necessarily in that order. His latest novel is Lost Solace.

Why science fiction?

My favourite books have always been any form of speculative fiction. As a child I began with ghost stories, which were the first books to make me completely forget I was reading. By my teenage years I was obsessed with fantasy, science fiction, and horror. Although I read literary and contemporary books, non-fiction, historical works, classics and so on, it is speculative fiction that I return to when I want escape and wonder. When I read reviews of my last book, the fast-paced novella Harvest Fe…