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

Data Empire - Roopika Risam ****

The central thesis presented by Roopika Risam is that information gives us (and particularly countries) the power to organise, control and dominate others. Although I have a couple of issues with the presentation, this is a genuinely interesting trip through the history of our use of stored information from the earliest tallies to the latest information technology. I loved a quote from Lisa Gitelman that data is is always 'cooked' so 'raw data is an oxymoron'. This neatly underlines Risam's thesis that data and information are not neutral facts, but rather tools that (like everything from fire to electronics) can be used for good or evil. As we are taken through the historical context, it can sometimes be a little difficult to judge whether Risam regards a particular example as bad or good, even when the outcome is disastrous. One thing I didn't like too much is the adherence to a popular science writing approach that has got distinctly hackneyed: opening chapte...
Post a Comment
Read more

Andrew Jaffe - Five way interview

Andrew Jaffe is professor of astrophysics and cosmology at Imperial College, London and director of the Imperial Centre for Inference and Cosmology. His new book is The Random Universe. Why science? I’ve always been interested in science, in particular in  astronomy, astrophysics, and space. One of my earliest memories - back in nursery school in New Jersey, I think - was watching one of the moon launches. I wanted that excitement to be part of my life! I never got to be an astronaut, but I did get to be part of the Planck Satellite team, and was privileged to be able to travel to the ESA Spaceport in French Guiana to watch the launch.  In between, I was lucky enough to have a supportive family, get a good education, and find inspiring teachers, mentors, and collaborators. They helped me model the universe, and helped me learn how to refine those models in the face of experimental and observational evidence. That is, they taught me to be a scientist. Why this book? The Random...
Post a Comment
Read more