1107 words on Books

Being in maths myself means that I’m naturally curious about the coverage mathematics get in the ‘normal’ public. It’s not a lot, and mostly it involves some distasteful remark about the general geekiness of it all and how the person reporting it ‘never understood maths’ anyway. An interesting area are whole books about mathematical subjects – books which are aimed at the public. Generally I think it is very hard to write a book that is both suitable for the general public and yet covers non-trivial areas of mathematics. There seem to be two approaches to this: The first is to not write about the mathematics at all but rather focus on the mathematicians. You can always find a story of some maths professor sitting in a library looking like a bum or – in older times – more respectful stories. Alternatively, you can write about first and second year maths topics, which potentially are amazing for people not into maths, but far from the new and exciting areas.

Some years back there was the BBC documentary on Fermat’s last theorem by Simon Singh and John Lynch. It’s a great documentary because it captures the drama involved in finding the proof. Wiles worked for years and found a proof but then – poof! – there was a gap which sent him back to his desk and almost made him give up.

It also managed to show mathematicians in their odd and geeky way but without being derogatory or otherwise patronising. In fact, when seeing the documentary I was amazed that the makers managed to get quite a number of mathematicians to cooperate with them so well.

Singh went on to write a book about Fermat’s last theorem which has become a bestseller. It contains the contents of the documentary plus endless sidenotes on the history of the problem and all the stories surrounding it. But I didn’t like it at all. Too much jumping around between the ‘current’ story of Wiles doing his work and all the historical prerequisites with endless notes on the mathematical background scattered througout. If you are mildly interested in mathematics you will know those tidbits anyway and if you aren’t then they’ll just distract you from the book’s main attraction. I can see how this is a clever way to sneak some mathematical knowledge to people who bought the book for the big names and the drama, but I still disagree with that technique.

And needless to mention that no matter how often the words Taniyama Shimura conjecture are mentioned in the book, the actual proof will remain inaccessible to the reader. That’s not Singh’s fault but rather the fault of the proof being very hard. ‘Very hard’ in this case meaning that having a university degree in mathematics won’t be good enough to understand it.

In this context I won’t forget what Miles Reid (a professor at Warwick university and one of the smartest people I’ve ever met) said when opening a course on elliptic curves that he taught. Of course he did mention that elliptic curves played a role in proving Fermat’s last theorem. But to put our hopes on a realistic level he went on to explain that we’ll have to finish his course, then stay in the area to do our PhD and then spend a number of years doing research in the area before we’d be able to understand the proof…

Another mathematician who *may* be known to the public – in the UK at least – is Ian Stewart. With all the columns he has written for mathematics magazines, all the general interest books he has written and all the public lectures he has given he certainly is well known for a mathematician. Possibly as close to being a well-known ‘celebrity’ as you can get in that area – with people asking him to autograph books which were going to be christmas presents and so on.

He doesn’t go down the road of indulging in stories about mathematicians, but tackles the mathematical topics head on. And his writing is excellent. Not only does he introduce problems in a generally understandable way but in some of his columns he’ll also enrich those by intermediate questions and exercises and hints on how to take the problems further – to a territory where they become harder and may not even have been solved so far. And while often his tone sounds like he’s writing for kids, with a lot or wordplay and childish themes being in there, the content isn’t childish at all.

I can recommend his recent book Math Hysteria which collects a number of his columns and contains some fun classical problems which served well to tease maths freshers or my flatmates alike. For example a variant of the following classical puzzle is treated: Someone is stranded on an island full of unfriendly natives. Those natives behave in a strictly logical way and some of them have a dot on their forehead. There aren’t any mirrors on the island and their culture demands that anybody who knows whether or not he/she has a dot on his/her forehead has to kill him/herself in the following night. When the stranded guy leaves the island he tells the natives Some people here have dots on their foreheads

. The big question then is to figure out what will happen.

The older book Another fine math you’ve got me into has the punniness built into its name and goes along similar line. It even contains a chapter on group theory and bell-ringing. But my absolute favourite is Flatterland. A book about the girl Victoria Line who lives in Flatterland, a world that is two dimensional. She is taken out of her world by a creature that is called (and looks like a) Space Hopper and gets to explore other dimensions and geometries with him.

If you ever wanted to take a journey of many aspects of geometry, ranging from dimensions to topology, from projective to hyperbolic geometry, from symmetries ot fractals and even including a stint into physics, this is the book to read. No formulas just little stories of Victoria discovering the differences between those spaces and first bumping into and then surmounting the difficulties of seeing and understanding them. The only thing I didn’t like was the constant punniness, as in writing about Planiturthian people or Vicky missing Crisp Moose day at home. But otherwise I was amazed how many mathematical concepts could be crammed into a single book. Not in a formal way of course, but to give the ideas and motivations nonetheless. Excellent!

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