Magnificent Mistakes In Mathematics by Alfred S. Posamentier and Ingmar Lehmann (book review).

I do think the title ‘Magnificent Mistakes In Mathematics’ needs to be qualified as ‘Magnificent Mistakes In Mathematics Made By Mathematicians’ for the first couple of chapters. If you thought those scientists, amongst them, Isaac Newton, Lord Kelvin and Albert Einstein, were perfect mathematicians then I think you’ll be pleasantly surprised by the fact that they make as many mistakes as ourselves and sometimes others didn’t even spot or tell them neither. I hope this book is read by current scientists as a pointer to question everything, even from their peers than think they are perfect. It could mean finding something that was overlooked before.


However, for us other folk, although the authors, Alfred S. Posamentier and Ingmar Lehmann, assure us in the introduction that you don’t need a college degree to understand the maths in this book. Indeed, to a point that’s true. The text is actually an authoritative read but with the proofs also here, you might want to sit down with a piece of paper and a pen to work through. If you’re still of school or college age and grasp what they say, you can probably put some of your maths teachers on the spot with their observations, especially with the examples where you get a zero where you shouldn’t. I haven’t seen or had a use for a Pascal triangle in years. I did have some odd thoughts on this but mostly with these had to be special instances that fail outside of the normal maths and algebraic functions although I can see the point as to why should they happen at all.

Some of them, like calculating percentage of in shop items will make you think, not to mention whether shop owners know that they are actually taking advantage of their customers. There are also examples showing how calculators doing their sums don’t always get it that right beyond the decimal point, mostly because of the way they round up their numbers.

If you thought this book would just deal with numbers, the move into geometry where the authors describe as ‘the visual part of mathematics’ shows a variety of anomalies. For those of you who play with shapes in computer games, I suspect will find some meaning in shape preparation. For the rest of us, there are a lot of other manipulations that don’t make sense but should that are explored which should make you think.

Further into the book, there’s even an examination of Sudoku logic under statistics and probabilities. One thing that I would contest from a different perspective is having thirty-five people in a room and the odds of having two people with the same birthday is helped a long a bit by more people are born during the spring-summer months than winter-autumn where people go to bed much earlier with sex on their minds which must surely enhance the odds. I love the problem of finding out how many pairs of prime numbers equal 999 and the answer is so simple that I can see people attempting this with other numbers as well. Likewise a coin trick which has more to do with probability than sleigh of hand.

I came away from this book thinking that although a lot of people perceive mathematics and numbers as being a perfect medium, around the edges there are areas where they are not. Perhaps it will encourage more discoveries in these areas. After all, from a science perspective what works at our scale, doesn’t do so at quantum level, so maybe we’re seeing things at a matter of scale and that applies to maths as well.

Although I’m not sure this book is for everyone, for those with a mathematical bent and very much those who are still being schooled in mathematics, this book will make you think and try some of these things out and that’s the whole point. Pick a number.

GF Willmetts

September 2013

(pub: Prometheus Books. 296 page illustrated indexed small hardback. Price: $24.00 (US), $25.50 (CAN). ISBN: 978-1-61614-747-1. Ebook: $12.99/ISBN: 978-61614-747-1)

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