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I would be interested to hear what you think of Ian Stewart's list of top 10 popular mathematics books on the Guardian website.

I've heard some discussion that the level might be a little high. What do you think?

What books would you have missed out? What would you have included instead?
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Christian Perfect's profile photoSarah Kavassalis's profile photoPeter Rowlett's profile photoVincent Knight's profile photo
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There's a few that I reckon are missing... Alex's adventures in Numberland is a favorite of mine...
 
I think he's chosen 10 books about his favourite mathematical ideas rather than 10 books which most effectively communicate mathematical ideas to a member of the "populace". The fact that he felt the need to include the Principia points towards this.

I haven't read any of the books on the list to completion, so I don't know about the difficulty level. I can say that I didn't like the chapters of Godel, Escher and Bach that I've read. Not completely sure why, but I think it just took too long to get where it was going.

I've had a look at my bookshelf and I don't know which books I'd rather have in the list.
 
It's an interesting list, although I can't say I've read all of the books included. To add a very different approach to popular mathematics, I'd actually have include Flatland. I do think the inclusion of Newton with the others is a little silly, because it's really not the same kind of read, but I understand the motivation (I'd have gone with one of Poincaré's popular books instead though, for readability).
 
Would agree with Sarah that Flatland is missing, which is strange since Ian Stewart wrote the follow up Flatterland! I know he can't choose his own books but Cabinet and Hoard are fabulous repositories of interesting stuff. Vincent is right about Alex Bellos' Adventures.
I would also include the beautiful Math Book by Clifford Pickover and the wonderfully written Imagining Numbers: (Particularly the Square Root of Minus Fifteen) by Barry Mazur. Finally I would want to include A History of Mathematical Notations by Florian Cajori which covers the history of mathematics through the methods of writing it.
 
I enjoyed Godel Esher Bach when I read it 20 years ago, and Mathenauts is also a good read. I would have on my list the recursive universe by William Poundstone, Ivan Moscovitch's super games, Mandelbrot's fractal geometry of nature, innumeracy by John Allen Paulos, and by Martin Gardner I would pick 'mathematical puzzles and diversions' as the first I bought and the one I go back to most. I also enjoyed Marcus DuSautoys music of the primes. I'd also pick an Ian Stewart - probably Game, Set and Math.
 
I guess there are two types of "popular" - 1) something accessible for people who know no maths and 2) something fun for the math literate. Id say Ian's list is very much the latter. If a lay friend asked me for a maths book suggestion they might understand and enjoy, I would only recommend the first two on his list.

If I was compiling 1) it would have to include Fermat's Last Theorem by Simon Singh and Logicomix and Uncle Petros and Goldbach's Conjecture by Apostolos Doxiadis. The challenge when writing a maths book is to find a strong narrative - and these three books do it better than any others.

If I was compiling 2) it would include a History of Pi by Beckmann, Number by Dantzig, the Man Who Loved Only Numbers by Hoffman and the complete works of Martin Gardner.

A writer like James Gleick sits halfway between the two. His books Chaos and The Information are both utterly brilliant but might lose the casual reader in parts.

(PS thanks for nice comments!)
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