It’s been a while since I’ve written anything really meaty on my blog and an entire year since I last wrote a post that reviewed a book on mathematics.
But what I really like about this particular post is that it renders the near to the global. This arose from a Christmas drink that I had with my neighbour across the road, Sarah, who lent me a book, that she never lends, on the proviso I write it up on my blog. So from my neighbour, who literally lives directly opposite me with her 2 sons, Andre and Emelio, to the blogosphere.
Over a bottle of Aussie red (Barossa Valley Shiraz 2008) – yes that’s worth mentioning because we both agreed that it was a bloody good drop (literally and figuratively) – we somehow got into a discussion on mathematics and the teaching of mathematics in particular, which led us to swapping books the next day.
On Christmas Day 2009, I published a post on The Bedside Book of Algebra (Michael Willers), which is the book I swapped with Sarah. The Number Devil; A Mathematical Adventure covers some of the same material but it’s aimed at a younger audience and it has a different approach. The whole purpose of this book it to reveal to young people that mathematics is a world worth exploring and not just a sadistic intellectual exercise designed by teachers to torment young developing minds. Sarah’s book has 2 bookmarks in it: one for her and one for her 7 year-old son; and her son’s bookmark is further advanced than hers.
It is written in novel-form and the premise of the narrative is very simple: the protagonist, Robert, is having tormenting dreams when he is visited by a devil, who calls himself the ‘Number Devil’ and begins to give him lessons in mathematics. It’s extremely clever, because it’s engaging and contains entertaining and informative illustrations, as well as providing exposition on some of the more esoteric mathematical concepts like infinity, transfinite numbers, combinations and permutations, Pascal’s triangle, Fibonacci numbers, prime numbers and Goldbach’s conjecture.
Whilst Enzensberger reveals the relationship between Pascal’s triangle and Fibonacci numbers, he doesn’t explain the relationship between Pascal’s triangle and the binomial theorem, which I learned in high school. He also explains the relationship between Pascal’s triangle and the combination algorithm, but not the way I learned it, which I think is more intuitive and useful. He uses diagonals (within Pascal’s triangle) whereas I learned it by using the rows.
The cleverness is that he provides these expositions without revealing to the reader how advanced these mathematical ‘lessons’ are. In fact, the reader is introduced to the ‘mysteries’ that have fascinated ‘ancients’ from many cultures across the world. Enzensberger’s inspired approach is to reveal the appeal of mathematics (that most mathematicians only find in adulthood) to young people before they are turned off it forever. He demonstrates that esoteric concepts can be taught without emphasising their esoterica.
Even the idea of a ‘number devil’ is inspired because mathematics is considered to be so devilish, and, in some cultures, mathematicians were considered to be devil’s apprentices (refer my recent post on Hypatia). In the second chapter (chapters are sequential nights of dreaming) Robert finds himself in a cave with the Number Devil, and the illustration is an obvious allusion to Plato’s cave, though no mention is made of this in the text.
At the end, the Number Devil takes Robert to ‘Number Heaven’ and ‘Number Hell’, though they appear to be the same place, where he meets some of the ‘masters’ like Russell, Fibonacci, Archimedes and a Chinese man whose name we don’t learn. We don’t meet Pythagoras who lives in a higher realm altogether, up in the clouds.
I’d recommend this book to any parent whose children show the slightest mathematical inclination and also adults who want an introduction to this esoteric world. As Sarah said, it’s like a mathematical version of Jostein Gaarder’s Sophie’s World, which is a high enough recommendation in itself.
Oh, I should mention that the illustrations are by Rotraut Susanne Berner; they augment the text perfectly.