Bill Casselman writes about the intriguing amateur mathematician Henry Perigal, who took his elegant proof of Pythagoras' Theorem literally to his grave - by having it carved on his tombstone.

Sometimes a mathematical object can be so big that, however disorderly we make the object, areas of order are bound to emerge. Imre Leader looks at the colourful world of Ramsey Theory.

As customers will tell you, overcrowding is a problem on trains. Fortunately, mathematical modelling techniques can help to analyse the changing demands on services through the day. Tim Gent explains.

Can you imagine objects that you can't measure? Not ones that don't exist, but real things that have no length or area or volume? It might sound weird, but they're out there. Andrew Davies gives us an introduction to Measure Theory.

During World Mathematical Year 2000 a sequence of posters were displayed month by month in the trains of the London Underground aiming to stimulate, fascinate - even infuriate passengers! Keith Moffatt tells us about three of the posters from the series.

Yes, you were right to wish you were in the other lane during this morning's commute! Nick Bostrom tells why we're usually caught in the slow lane.

This is a game played between a team of 3 people (Ann, Bob and Chris, say), and a TV game show host. The team enters the room, and the host places a hat on each of their heads. Each hat is either red or blue at random (the host tosses a coin for each team-member to decide which colour of hat to give them). The players can see each others' hats, but no-one can see their own hat.

The paradoxes of the philosopher Zeno, born approximately 490 BC in southern Italy, have puzzled mathematicians, scientists and philosophers for millennia. Although none of his work survives today, over 40 paradoxes are attributed to him which appeared in a book he wrote as a defense of the philosophies of his teacher Parmenides.

There are many errors that can occur when numbers are written, printed or transferred in any manner. Luckily, there are schemes in place to detect, and in some cases even correct, such errors almost immediately. Emily Dixon takes a break and discovers that codes are not just for sleuths.

The harmonic series is far less widely known than the arithmetic and geometric series. However, it is linked to a good deal of fascinating mathematics, some challenging Olympiad problems, several surprising applications, and even a famous unsolved problem. John Webb applies some divergent thinking, taking in the weather, traffic flow and card shuffling along the way.