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.

**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.

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.

**Francesca Harris** has always known she wanted to work in the music or film industry, and she has found that her maths skills have stood her in good stead as she works her way up.