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.

Hardback:  


Review by Brian Clegg

Comments

Popular posts from this blog

Where are the chemistry popular science books?

by Brian Clegg
There has never been more emphasis on the importance of public engagement. We need both to encourage a deeper interest in science and to counter anti-scientific views that seem to go hand-in-hand with some types of politics. Getting the public interested in science both helps recruit new scientists of the future and spreads an understanding of why an area of scientific research deserves funding. Yet it is possible that chemistry lags behind the other sciences in outreach. As a science writer, and editor of this website, I believe that chemistry is under-represented in popular science. I'd like to establish if this is the case, if so why it is happening - and what can be done to change things. 


An easy straw poll is provided by the topic tags on the site. At the time of writing, there are 22 books under 'chemistry' as opposed to 97 maths, 126 biology and 182 physics. The distribution is inevitably influenced by editorial bias - but as the editor, I can confirm …

The Case Against Reality - Donald Hoffman ***

It's not exactly news that our perception of the world around us can be a misleading confection of the brain, rather than a precise picture of reality - everything from optical illusions to the apparent motion of video confirms this - but professor of cognitive science Donald Hoffman goes far beyond this. He wants us to believe that spacetime and the objects in it are not real: that they only exist when we perceive them. It's not that he believes everything to be totally illusory, but suggests that the whole framework of the physical world is a construction of our minds.

To ease us into this viewpoint, Hoffman gives the example of the Necker cube - the clever two-dimensional drawing apparently of a cube which can be seen in two totally different orientations. Calling these orientations 'Cube A and Cube B' he remarks that our changing perceptions suggest that 'neither Cube A nor Cube B is there when no one looks, and there is no objective cube that exists unobserve…

The Universe Speaks in Numbers - Graham Farmelo ****

Theoretical physics has taken something of a hammering lately with books such as Sabine Hossenfelder's Lost in Math. The suggestion from these earlier titles is that theoretical physics is so obsessed with mathematics that many theoretical physicists spend their careers working on theory that doesn't actually apply to the universe, because the maths is interesting. Even experimental physics can be tainted, as the driver for new expenditure in experiments, such as the proposed new collider at CERN, is not driven by discoveries but by these mathematically-directed theories. Graham Farmelo presents the opposite view here: that this speculative mathematical work is, in fact, a great success.
As I am very much in the Hossenfelder camp, I expected to find Farmelo's book rather irritating, as it's effectively a love letter to mathematically-obsessed theoretical physics - but in reality (an entertaining phrase, given the context) I found it both interesting and enjoyable. Far…