Skip to main content

The Mathematics Lover's Companion - Edward Scheinerman ****

The worrying thing about this title is that I'm not sure I am a maths lover. I find some parts of mathematics interesting - infinity and probability, for example - but a lot of it is just a means to an end for me. The good news is that, even if you are like me, there's a lot to like here, though you may find yourself skipping through some parts.

Edward Scheinerman takes us through 23 mathematical areas, so should you find a particular one doesn't work for you, it's easy enough to move onto another that does. Sometimes it wasn't the obvious ones that intrigued - where I found the section on infinity, for example, a little underwhelming, I really enjoyed the section on factorials. The book opens with prime numbers, which while not the most exciting of its contents, gives the reader a solid introduction to the level of mathematical thought they will be dealing with. It's enough to get the brain working - this isn't a pure fun read and you have to think - but not so challenging that you feel obliged to give up.

Along the way, Scheinerman is enthusiastic and encouraging with a light, informative style. Each page has side bars (meaning there's a lot of white space), which contain occasional comments and asides. I found these rather irritating for two reasons. In part because it really breaks up the reading process - if it's worth saying, say it in the main text - and partly because (in good Fermat fashion) there's not a lot of room so, for example, when we are told the origin of the RSA algorithm in the side bar, there's space to say it's named after Rivest, Shamir and Adelman but not to say that Cocks came up with it before them.

Occasionally, as often seems the case with mathematicians, the author seemed to be in a slightly different world. He says that the angle trisection problem is more famous that squaring the circle - which seems very unlikely - and though he notes that pi day is usually considered to be 14 March (when written as 3/14) he doesn't point out it makes much more sense in the non-US world for it to be the 22 July (22/7).

A typical section for me was the one the constant e (like pi, a number that crops up in nature and is valuable in a number of mathematical applications). There were parts of the section that I found really interesting: I'd never really seen the point of e before, the compound interest example was an eye-opener and there's the beautiful e= -1. The two other examples, though, I did have to skip as they were a little dull. 

My favourite part was at the end - the sections on uncertainty, including non-transitive dice (where you can have a series of dice, each of which can beat one of the others) and equivalent poker hands, Bayesian statistics, how to have a fair election and a fascinating game (Newcomb's paradox) - where it seems that you should choose what's not best for you to come out best - were all great. It would have been even better if the election section had used terms like 'first past the post' and 'single transferable vote' to make a clearer parallel with real election systems - and the Newcomb's paradox section should have made more of the difficulty of predicting an individual's choice - but these are small concerns.

So will anyone love all of it? Probably not. If you truly do love maths, you'll know a lot of this already. If you aren't sure about your relationship with the field, the book won't all work for you - but that bits that do should be enough to show that mathematics can make an entertaining and stimulating companion.


Review by Brian Clegg


Popular posts from this blog

The Feed (SF) - Nick Clark Windo ****

Ever since The War of the Worlds, the post-apocalyptic disaster novel has been a firm fixture in the Science Fiction universe. What's more, such books are often among the few SF titles that are shown any interest by the literati, probably because many future disaster novels feature very little science. With a few exceptions, though (I'm thinking, for instance, The Chrysalids) they can make for pretty miserable reading unless you enjoy a diet of page after page of literary agonising.

The Feed is a real mixture. Large chunks of it are exactly that - page after page of self-examining misery with an occasional bit of action thrown in. But, there are parts where the writing really comes alive and shows its quality. This happens when we get the references back to pre-disaster, when we discover the Feed, which takes The Circle's premise to a whole new level with a mega-connected society where all human interaction is through directly-wired connections… until the whole thing fails …

Everything You Know About Space Is Wrong - Matt Brown ****

What we have here is a feast of assertions some people make about space that are satisfyingly incorrect, with pithy, entertaining explanations of what the true picture is. Matt Brown admits in his introduction that a lot of these incorrect facts are nitpicking - more on that in a moment - but it doesn't stop them being delightful. I particularly enjoyed the ones about animals in space and about the Moon.

Along the way, we take in space exploration, the Earth's place in space, the Moon, the solar system, the universe and a collection of random oddities, such as the fact that Mozart didn't write Twinkle, Twinkle Little Star. Sometimes the wrongness comes from a frequent misunderstanding. So, for example, Brown corrects the idea that Copernicus was the first to say that the Earth moves around the Sun. Sometimes there's some very careful wording. This is used when Brown challenges the idea that the Russian dog Laika was the first animal in space. What we discover is that, i…

Dark Matter and the Dinosaurs - Lisa Randall ****

I did my PhD in galactic dynamics - which is an awkward subject when people want to know what its relevance to the 'real world' is. So I was excited when Clube and Napier's book The Cosmic Serpent came out, around the same time, because it provided me with a ready-made answer. It argued that the comets which occasionally crash into Earth with disastrous results - such as the extinction of the dinosaurs - are perturbed from their normal orbits by interactions with the large-scale structure of the galaxy.

I was reminded of this idea a few years ago when there was a flurry of media interest in Lisa Randall's "dark matter and the dinosaurs" conjecture. I was sufficiently enthusiastic about it to write an article on the subject for Fortean Times - though my enthusiasm didn't quite extend to purchasing her hardback book at the time. However, now that it's out in paperback I've remedied the situation - and I'm glad I did.

Dark matter is believed to exi…