Did you know that you can't average averages? Or that Paris is rainier than London ... but it rains more in London than in Paris? Andrew Stickland explores the dangers that face the unwary when using a single number to summarise complex data.

Mathematician and physicist John Baez declares himself fascinated by exceptions in mathematics. This interest has led him to study the octonions, and, through them, to find out more about the origins of complex numbers and quaternions. In the first of two articles, he talks about connections between algebra and geometry, and the importance of lateral thinking in mathematics.

Regular Plus contributor Lewis Dartnell reports on the scramble for million-dollar prizes that made mathematical headlines at the BA Festival of Science in September 2004.

Frances Elwell looks at the eddies and currents, from the pungent problem of sewage outflow to the search for bodies of people who have fallen into rivers, explaining that fluid mechanics lies behind it all.

The three door problem has become a staple mathematical mindbender, but even if you know the answer, do you really understand it? Phil Wilson lets his imagination run riot in this intergalactic application of Bayes' Theorem.

Are records predictable in any way?

Why do so many people say they hate mathematics, asks David Acheson? The truth, he says, is that most of them have never been anywhere near it, and that mathematicians could do more to change this perception - perhaps by emphasising the element of surprise that so often accompanies mathematics at its best.

Memory is fundamental to the way we think, and we use it in almost every activity. But most of us cannot imagine approaching the level of world record holder Hiroyuki Goto, who memorised and recited 42,195 digits of pi! Rob Eastaway asks if mere mortals can learn anything useful from such incredible feats of memory, and gives some hints on how to remember numbers.