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

Luna: Moon Rising (SF) - Ian McDonald ****

I'm not the natural audience for this book. Game of Thrones l eaves me cold - and it's hard not to feel the influence of GoT (and a whole lot of Dune )   underneath a veneer of science fiction and the trappings of a South American drug cartel in the cod-medieval family power battles and chivalric details. There are even dragons (of a sort). I'd be really sad if the future did involve this sort of throwback feudalism. However, remarkably, despite this I found Luna: Moon Rising kept me engaged. The fact is that Ian McDonald can put together a good plot with intricate machinations, which is enough to carry the reader through what can be a bewildering collection of characters. The two page scene-setter saying who did what to whom at the start was useful, but I could have done with family trees for the main family as I was constantly forgetting who was who - especially easy as McDonald endows many families with characters with the same first initial (e.g. Ariel and Al...
Post a Comment
Read more

Adventures of a Computational Explorer - Stephen Wolfram ***

Stephen Wolfram, the man behind the scientist's mathematical tool of choice, Mathematica, plus a whole host of other software products, including the uncanny Wolfram Alpha knowledge engine, is undoubtedly a genius of the first order. In this book, we get an uncensored excursion into the mind of genius - which is, without doubt, a fascinating prospect. The book consists of a collection of essays and speeches that Wolfram has produced over the last ten to fifteen years, covering an eclectic range of topics. Like all such collections, the result is something that lacks the coherence of a book with a narrative that runs through it, inevitably introducing a degree of repetition and a mix of interesting and not-so-interesting topics - but there's likely to be something to catch the attention anyone who is into computing or mathematics. One of the most interesting pieces is the opening one, where Wolfram describes being a consultant on the SF movie Arrival. He seems to hav...
Post a Comment
Read more

The AI Paradox - Virginia Dignum ****

This is a really important book in the way that Virginia Dignum highlights various ways we can misunderstand AI and its abilities using a series of paradoxes. However, I need to say up front that I'm giving it four stars for the ideas: unfortunately the writing is not great. It reads more like a government report than anything vaguely readable - it really should have co-authored with a professional writer to make it accessible. Even so, I'm recommending it: like some government reports it's significant enough to make it necessary to wade through the bureaucrat speak. Why paradoxes? Dignum identifies two ways we can think about paradoxes (oddly I wrote about paradoxes recently , but with three definitions): a logical paradox such as 'this statement is false', or a paradoxical truth such as 'less is more' - the second of which seems a better to fit to the use here.  We are then presented with eight paradoxes, each of which gives some insights into aspects of t...
Post a Comment
Read more