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When I was fourteen years old, I started a notebook. A math notebook. Before you write me off as a sad case, I hasten to add that it wasn't a notebook of school math. It was a note- book of every interesting thing I could find out about the math that wasn't taught at school. Which, I discovered, was a lot, because I soon had to buy another notebook.

OK, now you can write me off. But before you do, have you spotted the messages in this sad little tale? The math you did at school is not all of it. Better still: the math you didn't do at school is interesting. In fact, a lot of it is fun--es- pecially when you don't have to pass a test or get the sums right.

My notebook grew to a set of six, which I still have, and then spilled over into a filing cabinet when I discovered the virtues of the photocopier. Curiosities is a sample from my cabinet, a miscellany of intriguing mathematical games, puzzles, stories, and factoids. Most items stand by themselves, so you can dip in at almost any point. A few form short mini-series. I incline to the view that a miscel- lany should be miscellaneous, and this one is. 2 // Start Here

The games and puzzles include some old favorites, which tend to reappear from time to time and often cause renewed excitement when they do--the car and the goats, and the 12-ball weighing puzzle, both caused a huge stir in the me- dia: one in the USA, the other in the UK. A lot of the material is new, specially designed for this book. I've striven for vari- ety, so there are logic puzzles, geometric puzzles, numerical puzzles, probability puzzles, odd items of mathematical cul- ture, things to do, and things to make.

One of the virtues of knowing a bit of math is that you can impress the hell out of your friends. (Be modest about it, though, that's my advice. You can also annoy the hell out of your friends.) A good way to achieve this desirable goal is to be up to speed on the latest buzzwords. So I've scattered some short "essays" here and there, written in an informal, nontechnical style. The essays explain some of the recent breakthroughs that have featured prominently in the media. Things like Fermat's Last Theorem--remem- ber the TV program? And the Four-Color Theorem, the Poincaré Conjecture, Chaos Theory, Fractals, Complexity Science, Penrose Patterns. Oh, and there are also some un- solved questions, just to show that math isn't all done. Some are recreational, some serious--like the P = NP? prob- lem, for which a million-dollar prize is on offer. You may not have heard of the problem, but you need to know about the prize.

Shorter, snappy sections reveal interesting facts and dis- coveries about familiar but fascinating topics: , prime numbers, Pythagoras' Theorem, permutations, tilings. Amusing anecdotes about famous mathematicians add a historical dimension and give us all a chance to chuckle sympathetically at their endearing foibles ...

Now, I did say you could dip in anywhere--and you can, believe me--but to be brutally honest, it's probably better Start Here // 3

to start at the beginning and dip in following much the same order as the pages. A few of the early items help with later ones, you see. And the early ones tend to be a bit eas- ier, while some of the later ones are, well, a bit ... challeng- ing. I've made sure that a lot of easy stuff is mixed in everywhere, though, to avoid wearing your brain out too quickly.

What I'm trying to do is to excite your imagination by showing you lots of amusing and intriguing pieces of mathematics. I want you to have fun, but I'd also be over- joyed if Curiosities encouraged you to engage with mathe- matics, experience the thrill of discovery, and keep yourself informed about important developments--be they from four thousand years ago, last week--or tomorrow.

Ian Stewart

Coventry, January 2008

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