## Just A Review: One to Nine – The Inner Life of Numbers by Andrew Hodges

Posted on Friday 1 August 2008 at 9:42 pm by Jacob Aron
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Andrew Hodges’ inspiration for the title One to Nine was Sudoku, the immensely popular number puzzle. Hodges comments that newspapers insist the puzzles require no mathematical knowledge, in order to not scare away an often maths-phobic British public – indeed, Sudoku does not even require numbers, since substituting nine letters or symbols into a puzzle would leave the logic required to solve it unchanged.

Hodges describes logic as one of the most fascinating elements of ‘adult mathematics’, wholly different to the ‘school maths’ that newspapers try to distance themselves from. The book aims to provide an insight into this for those who may have been turned off the subject at school.

Unsurprisingly, the book is split into nine chapters, One through Nine. Each begins with a characterisation of the number; seven ‘needs sifting and sorting out’, whereas three ‘doesn’t just talk’, but ‘thinks big’. The chapter titles are a bit of a gimmick at times. Six is the first perfect number, so-called because 6 = 1 + 2 + 3 = 1 x 2 x 3, and this leads to a discussion of factorials. Six is 3! (pronounced ‘three factorial’) because 3! = 1 x 2 x 3., and the factorial of a number n is simply the product of all numbers from 1 to n. The chapter continues with probabilities, the Enigma machine, and Euler’s equation – all very interesting topics with links to factorials, but do they really relate particularly to six, more so than any other number?

Gimmicks aside, One to Nine is a whistle-stop tour of pop-sci mathematics, with sections ranging from black holes to game theory to musical harmony. Each topic is well described and often accompanied by many useful diagrams, although some appear to have been lifted straight from a .jpg file, complete with ugly compression artefacts – a bit more care could have been take in order to provide high quality images.

Numerous equations may discourage the casual reader, but they are always accompanied by a thorough explanation in the text. Stephen Hawking was told when writing A Brief History of Time that ‘each equation in the book would halve the sales’; I hope this is not the case else I will have already lost 75% of my readership! For those who really will not abide equations, relax – they can for the most part be skipped.

Sprinkled throughout the text are problems rated on a Sudoku-like scale, from GENTLE to DEADLY. I found these to be a welcome addition, but normally skipped over any that I was unable to solve in a minute or two, so as not to slow down the pace of the book. Placing these at the end of each chapter would have made me more inclined to give them a go.

Helpfully, all of the solutions are provided on the website for the book, along with further notes and comments. Unfortunately the book does not feature a bibliography or recommended reading list, so if you do become engrossed in a particular topic you will have to hunt out more information by yourself, but the website does go some way to assisting with this.

If you would like to learn how mathematics is used in a variety of scientific fields and are not too afraid of a few equations, One to Nine is a good place to start. In fact, Hodges’ appropriation of Sudoku is quite apt. If you enjoy the use of logic in a Sudoku puzzle, but have dreaded school memories of multiplication tables, perhaps One to Nine can show you the world through the filter of ‘adult mathematics’.

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