Skip to main content

Reaching for the Extreme - Ian Stewart ****

Ian Stewart is arguably the UK's best raconteur of mathematics - here he takes on some of the extremes of the mathematical world, and in doing so gives us some real insights into what makes mathematicians tick.

There's a good mix here of the flashy fun aspects of maths - think, for instance of the wonders of infinity or the monster group - and the solid everyday that nonetheless can turn up surprises. The book is littered with little insights. For example, if we think it's easy to work out the area of a rectangle by dividing it up into unit squares, what do you do with one that measures square root of two by pi?

You'll find yourself jumping around from what lies beneath calculus to game theory (rock, paper, scissors anyone? - I hadn't realised a version of this game dates back around 2,000 years). One minute you'll be considering colouring maps and the next finding the shortest distance between two points on a curved surface.

Some of the mathematics here has everyday applications, some can be used in fairly abstruse corners of science and some is pure mathematical puzzle solving with no obvious application ever. You pays your money and you takes your choice.

There were a few points where Stewart lost me. Some of these were simply due to going on too far. I enjoyed the tiling chapter to begin with, but as we got onto more and more obscure aperiodic tiles there was a bit of a feeling of 'we get the point, move on'. In other cases, Stewart had the problem of dealing with mathematics that is well beyond the grasp of a general reader like me. He is clearly aware of this, but rather than avoid it, makes the discussion so vague that it's difficult to feel you are getting anywhere. 

This was particularly the case in the 'weirdest symmetry' chapter, which brings in the aforementioned monster group. There's some nice material on what groups are, but when we get onto that monster, the 'largest sporadic simple group', it's way beyond comprehension, when we're dealing with something it's was difficult even to prove whether or not it existed. It doesn't really help that Stewart then ties this into string theory, an aspect of physics that many believe is more mathematical play than anything connected to physical reality, which has been notably described as 'not even wrong'.

There's a lot to like, though, in this generous meander through eighteen chapters of different mathematical pondering. It'll certainly stretch your mind - and if occasional it leaves us mere mortals behind, that's not always a bad thing.

Hardback:   
Kindle:  
Using these links earns us commission at no cost to you
These articles will always be free - but if you'd like to support my online work, consider buying a virtual coffee or taking out a membership:
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

Mathematics with Love – Mary Stopes-Roe *****

Admittedly it’s early days (this review is written in January), but this, for me, is the surprise hit of the year so far! I approached this book with trepidation, but found it absolutely delightful. It is described on the cover as the “courtship correspondence of Barnes Wallis, inventor of the bouncing bomb”, and contains a series of letters between Wallis and his cousin and eventual wife Molly Bloxham, along with some useful annotation by their daughter, Mary. The courtship itself is not without difficulties, as Wallis was 18 years older than the 17-year-old Molly at the start of the correspondence, and her father, not surprisingly, wasn’t too pleased about the interest of such an elderly suitor, but that isn’t the only reason the letters are interesting – it’s also because of maths, and Wallis’s position in the UK as the engineering hero of the Second World War. (Incidentally, it seemed very strange to see letters addressed to “Barnes” – I had always assumed Barnes Wallis was a ...
Post a Comment
Read more

Why Nobody Understands Quantum Physics - Frank Verstraete and Céline Broeckaert **

It's with a heavy heart that I have to say that I could not get on with this book. The structure is all over the place, while the content veers from childish remarks to unexplained jargon. Frank Versraete is a highly regarded physicist and knows what he’s talking about - but unfortunately, physics professors are not always the best people to explain physics to a general audience and, possibly contributed to by this being a translation, I thought this book simply doesn’t work. A small issue is that there are few historical inaccuracies, but that’s often the case when scientists write history of science, and that’s not the main part of the book so I would have overlooked it. As an example, we are told that Newton's apple story originated with Voltaire. Yet Newton himself mentioned the apple story to William Stukeley in 1726. He may have made it up - but he certainly originated it, not Voltaire. We are also told that ‘Galileo discovered the counterintuitive law behind a swinging o...
Post a Comment
Read more

On Time - Jim Al-Khalili *****

By a small margin Jim Al-Khalili's The World According to Physics is my favourite of his books, both because the 'three pillars' concept at its heart works so well - but also because it's short. On Time is somewhat heavier, but thankfully not a wrist-buster. It might seem at first sight odd that a book on a subset of physics is considerably longer than one covering the whole thing, but time is one of those subjects that inevitably involves considerable complexities and needs depth. As Al-Khalili establishes, it's hard to think of any other scientific concept where our perception of it - what he refers to as manifest time or psychological time - is so different from the view from physics. Some physicists go so far as to suggest that time doesn't exist at all. In the book, Al-Khalili sets out (to my mind quite successfully) both to explain why they think this is the case, but also why it's not the best interpretation of time. I'd certainly note that I...
Post a Comment
Read more