## Articles

**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.

**Phil Wilson**lets his imagination run riot in this intergalactic application of Bayes' Theorem.

**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.

*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.