"Steve Davis is walking round the table. He has a choice of pots, none of them very difficult. He's decided to go for the red by the middle pocket and screw back for the pink . . . Oh dear, that was a bad mistake, he's left it open for his opponent with all the reds in good positions . . ."

As Steve Davis makes his mistake a million viewers gasp, then wait with knowledgeable anticipation for his opponent to take advantage. Why is snooker so easy to appreciate ? Why is it ideally suited for television? Why do so many people enjoy watching the game? Snooker is extraordinarily visual. You can see so much of what is happening. It's all above board. The only thing you cannot usually see is precisely how the players strike the cue ball with the tip of the cue, the very subtlety that allows them to control the cue ball - but you don't have to see this in order to appreciate the game, especially when a commentator is at hand.

Mathematics is the complete opposite of snooker. Watch a worldclass mathematician doing mathematics and you could see nothing at all, except someone sitting at a desk thinking, or pacing up and down a room, or going for a walk, or reading a book. Even if they were writing or drawing on a blackboard, you probably wouldn't have any idea what they were writing or why, or what it meant.

Mathematics, as teachers are fond of repeating, is not a spectator sport. It's exciting, it's fascinating, it's mysterious, but you can't just put it up in vivid colours on a TV screen and expect viewers to grasp it while sitting back in an easy chair. At least, the reader of a mathematics book must be prepared to think about what the author is saying. At best the reader gets stuck in and becomes involved with the author's ideas. Professional mathematicians do this all the time. When they read a book, or a paper by a colleague, they reach for a pen and paper and they start to work out the ideas for themselves, because they know that "To do is to understand".

This book gives you, the reader, the chance to do just that. Each chapter is interrupted by a number of boxes which pose questions to you, related to the theme of the chapter. Some are easy, some are more difficult, but they will all make you think. Tackle them, and you too will be a Mathematician. Of course, if you don't feel like exercising your grey cells, you can always look up the solutions, but I hope that you will feel drawn to the problems, and experience an irresistible temptation to attempt to solve them! Good luck, and bon voyage on your mathematical journey!

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