Alex's Adventures in Numberland

Last time I looked Alex Bellos was The Guardian's correspondent in Brazil and his one published book was a wonderfully idiosyncratic and entertaining look at Brazilian football (or futebol as the Brazilians would say) which actually turned out to be a pretty good historical and sociological primer for the whole country. Read along with Peter Robb's A Death in Brazil there probably isn't much more that you need to know about this most intriguing (at least to me) country.

So, getting back to the point, I was mildly surprised to find out last year that he had written a book about mathematics called Alex's Adventures in Numberland. However, it turns out he has a degree in philosophy and mathematics (they didn't mention that in the blurb on the football book!) and a boundless enthusiasm for seeking out the quirky and fascinating amongst the numbers and equations.

Starting out with Munduruku people living deep in the Brazilian Amazon who still lead a hunter-gatherer existence and have no words for numbers greater than five. Mainly because, as Alex demonstrates, they don't have any need for them. And even these five numbers aren't a precise match for the quantities one to five translating more correctly into one, two, threeish, fourish and a handful. This leads into a fascinating discussion on how children learn to count and understand numbers. Studying young children and isolated indigenous peoples gives a fascinating insight into innate mathematical intuition compared against taught concepts. (The numerical equivalent of Steven Pinker's The Language Instinct.)

From there we move through number systems, numerology, Vedic mathematics, Pi, algebra, number games, the golden ratio, probability, statistics and on to infinity (the concept not the size of the book ...). He has a journalist's eye for an interesting story and the writing is always clear and intelligent, even when he gets into some fairly high level concepts. Pleasingly, the text is also accompanied by plenty of well-drawn diagrams, illustrations and photos which help with the explanations and let you see what mathematicians really look like. There are also plenty of equations, but what did you expect? It is about maths after all.

Along the way he tracks down some fascinating characters, some well known, most not. For example Wayne Gould, a retired judge from New Zealand who found a Sudoku book in a Tokyo bookshop and although he couldn't read any of the instructions he managed to work out how to solve the puzzle. He then spent six years writing a computer program to generate Sudokus and went on to sell the idea to newspapers in the USA and UK sparking a craze which now has over 100 million regular players. I had always presumed that Sudoku was an ancient Japanese puzzle which was just popularised recently in the West, but it turns out to have been invented by Maki Kaji, a Japanese puzzle-maker who refined a puzzle that he had seen in an American puzzle magazine which had in turn been created by Howard Garns, a retired architect from Indiana.

At 450 pages he covers a lot of ground, but it flys past and I was very sad to see it finish, although my head was hurting a bit by the end. By the last chapter we are up to non-Euclidean geometry, hyperbolic crochet, Georg Cantor's 'set theory' and the Hilbert Hotel. Luckily he also has an excellent blog where he updates some of the stories that appear in the book and any other interesting mathematics that he finds.