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.

More than a century ago, an American astronomer named Seth Carlo Chandler discovered that, as the earth spun on its axis, it also wobbled. This wobble, now known as the Chandler wobble in honour of its discoverer, didn't disappear over time, as would have been expected if no further force reactivated it. The source of the continuing activating force has remained a mystery ever since - until now.

Four mathematicians have finally confirmed that the familiar double soap bubble is indeed the best way to enclose two separate volumes of air.

Solitaire is a game played with pegs in a rectangular grid. A peg may jump horizontally or vertically, but not diagonally, over a peg in an adjacent square into a vacant square immediately beyond. The peg which was jumped over is then removed.

The Millennium Bridge across the Thames opened in June 2000 and was subsequently closed two days later because of the now-famous "wobbles". Given that, at any instant, two thousand people were suspended above a very dangerous river, this presented a serious problem.

Have you ever noticed what happens when you spin a coin on a table? As the coin starts to fall over and roll on its edge, its spin gets faster and faster until it suddenly stops altogether.

More than a century after the death of its inventor, the world's first computer printer has finally been constructed at the Science Museum in London.

In 1998, Goldbach's Conjecture was shown by computer to be true for even numbers up to 400,000,000,000,000. In addition, some progress has been made towards formally proving the conjecture. As of this year, mathematicians with Goldbach fever have some extra incentive for their labours.

Maths A-levels are "too easy"

One of the most striking and powerful means of presenting numbers is completely ignored in the mathematics that is taught in schools, and it rarely makes an appearance in university courses. Yet the continued fraction is one of the most revealing representations of many numbers, sometimes containing extraordinary patterns and symmetries. John D. Barrow explains.