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:  
Using these links earns us commission at no cost to you


Review by Brian Clegg

Comments

Popular posts from this blog

How to Drive a Nuclear Reactor - Colin Tucker ****

How To Drive A Nuclear Reactor does exactly what it says on the tin. The book is a general overview of nuclear reactors. From the basic principles that make them work through to what buttons to press in what order (and of course how and why they can go wrong).Nuclear power could be a good step on the path to a greener energy future, but there is a lot of understandable fear. This book can give some idea of what an incredible feat of both science and engineering one of these machines is and, hopefully, make anyone reading it feel far more comfortable about them.The book presents information about everything, almost down to the literal nuts and bolts, giving you a near complete understanding of how a nuclear works. From putting in the fuel to getting out the power and down from the control panel to the construction material. Everything you could ever want to know is here. By the end you'll likely feel ready to walk into a control room and get started (do not try doing this, nuclear …

Being Mortal - Atul Gawande ****

I heard recently that the local geriatric ward puts a photograph of the patient in his or her prime by each bed. The aim is to help staff to treat their patients as individuals, but it makes me uneasy. Do these people only matter because of what they were, not what they are? Because once they stood proud and handsome in their uniform, or looked lovely on their wedding day?

Professor Atul Gawande has the problem surgically excised and laid out for inspection in one of his unflinching but compassionate case studies:

‘What bothered Shelley was how little curiosity the staff members seemed to have about what Lou cared about in his life and what he had been forced to forfeit... They might have called the service they provided assisted living, but no-one seemed to think it was their job to actually assist him with living – to figure out how to sustain the connection and joys that most mattered to him.’

Gawande is an eminent surgeon. As a young resident he displayed little overt emotion when hi…

Twenty Worlds - Niall Deacon *****

This is a truly entertaining and informative book, but the reason I’m giving it the full five stars has as much to do with the refreshing novelty of the author’s style as anything else. There’s novelty in the subject-matter too – the wide variety of recently discovered exoplanets orbiting other stars – but even so this is the third book on the topic that I’ve read. The first two were a lot less fun to read, and (without naming and shaming the authors) it’s worth a brief diversion to explain why.The first author was a university professor with a vast knowledge of the subject, who seemed determined to convey the entirety of that knowledge without stopping to think whether it was interesting or necessary for a general audience. The second author – another academic – took a different but equally tedious approach, with a plodding chronological account that focused as much on the dull routine of the scientists involved as on their work.Niall Deacon doesn’t make either of those mistakes. He’…