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.
As anyone starting out knows, the violin is a difficult instrument. It takes time before the novice player can expect to produce a musical note at the desired pitch, instead of a whistle, screech or graunch. Jim Woodhouse and Paul Galluzzo explain why.

Two people who get on well together can often find their relationship destabilised by the arrival of a third into their orbit.

  • The permanent revolution - The government's response to Adrian Smith's Inquiry into post 14 mathematics education
  • A-levels - Are the ever-improving results a sign of falling standards?
How much evidence would you need before buying into a get rich quick scheme? Do high ice cream sales cause shark attacks? And just how likely was it that you were ever born? Andrew Stickland finds out that, when it comes to probability, our instincts can lead us seriously astray.
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.