After a series of novels, time for something factual and an exercise for the brain. Ian Stewart was Professor of Mathematics at The University of Warwick when he wrote this book in 2008 and still holds that title although now Emeritus since he retired. He has written numerous books on mathematics, several of which I own so this was chosen as the first one I picked off the shelf, he was also the third person to write the recreational mathematics column for the periodical Scientific American, taking the reins from 1991 to 2001. This column was started by Martin Gardner back in 1956 and he wrote it until the mid 1980’s and this was the true start of my love of mathematics so it has been a pleasure over the years to have sat in a few bars with Ian and discuss maths and also to enjoy his very readable books.

This book, along with it’s sequels Professor Stewart’s Hoard of Mathematical Treasures’ from 2009 and ‘Professor Stewart’s Casebook of Mathematical Mysteries’ from 2014, are an interesting mix of puzzles and mathematical history and are partly built upon notebooks that Ian started whilst still at school and more snippets that he has gathered over his long career of anything that looked fun or interesting in the field of mathematics. I had come across roughly half of the puzzles before and it’s surprising it was so few as I have lots of maths puzzle books but the 249 pages of puzzles and essays plus 60 pages of solutions and/or further further discussions on points raised contained a lot that was new to me. Of the essays I particularly liked his short summary of Fermat’s Last Theorem and how Andrew Wiles finally came to solve it centuries later. Ian demonstrates his skill as a good teacher in these essays, not simplistic, after all anyone picking this book up will have an interest in mathematics but not too complex either. The solution relies on a whole new branch of mathematics so he doesn’t try to explain how the solution works but instead explains why it is important and hints at the complexity involved. There are also essays on fractals, chaos theory, various famous mathematicians and numerous important conjectures and theorems spread throughout the book.

It is in the puzzles though that Ian allows his wit to shine through, even if sometimes that is just a series of bad puns as in ‘The Shaggy Dog Story’ which is a fun rewriting of a really old puzzle that would be familiar to almost all readers of the book so he dresses it up to still make it fun and then in the solutions section introduces a variant of the puzzle which I hadn’t come across before. The puzzle involves the terms of a will where the eldest son is to have a half of his fathers dogs, the middle son a third and the youngest a ninth. Unfortunately when the father dies he has seventeen dogs so the division looks like it could be quite messy if the will is to be executed exactly. The solution is actually quite easy and I first saw this puzzle over forty years ago but I’d never seen the follow up question which can also be solved where the legacy of the first two sons remains the same but the third son gets a seventh of the dogs and the puzzle is reversed because you have to work out how many dogs the father had in order for there to be a solution with no dogs harmed. If you haven’t seen the original puzzle before I’ll put the answer at the end of this blog.

I’d recommend this book to anyone with an interest in maths, the essays are fascinating, the puzzles fun and you’re guaranteed to learn something new.

I also have both the subsequent books in this style and there is an interesting part to the introduction of the second book, I’ll reproduce it here.

Cabinet was published in 2008, and, as Christmas loomed it began to defy the law of gravity. Or perhaps to obey the law of levity. Anyway, by Boxing Day it had risen to number 16 in a well known national best seller list, and by late January it had peaked at number 6. A mathematics book was sharing company with Stephanie Meyer, Barack Obama, Jamie Oliver and Paul McKenna.

This was, of course, completely impossible, everyone knows that there aren’t that many people interested in mathematics.

Ian therefore unexpectedly received an email from the publisher wanting a sequel which did well, but not as well as the first hence the longer delay before the third book. The Casebook is easily the weakest of the three as too many puzzles are dressed up in cod Sherlock Holmes stories which frankly only serve to pad out the puzzle and it appears to have been remaindered as I didn’t know it existed until planning to write about the first two and got a brand new still shrink wrapped first edition copy for a third the original price seven years after it originally came out.

Dogs problem solution – You just need to borrow a dog from somebody else. This will mean you have 18 dogs, half of that is 9, a third is 6 and a ninth is 2. As 9 + 6 + 2 = 17 you can then give the borrowed dog back, Now try the follow up question…