Tickle your mathematical funnybone and get your own personal Black Chamber

For millennia, puzzles and paradoxes have forced mathematicians to continually rethink their ideas of what proofs actually are. Jon Walthoe explains the tricks involved and how great thinkers like Pythagoras, Newton and Gödel tackled the problems.

Perhaps the most sinister weather phenomenon in the world is the twister - that dark, dangerous funnel drooping from the clouds that weaves its way across the landscape, leaving a narrow trail of devastation in its wake.

Combining the computational powers of modern digital computers with the complex beauty of mathematical fractals has produced some entrancing artwork during the past two decades. Intriguingly, recent research at the University of New South Wales, Australia, has suggested that some works by the American artist Jackson Pollock also reflect a fractal structure.

Dr Yvan Dutil has been losing sleep lately. Why? Because he and his colleague Dr. Stéphane Dumas have proved to be only human.

Tax harmonisation, a common market, EU-wide laws: the trend is for ever-increasing standardisation across Europe. Ironically, there is currently a popular rebellion in France against one of the earliest pan-European standards, the Prime Meridian - the line of longitude from which all time zones are referenced.

Human beings seem to have an inborn mathematical ability. Research has shown that even tiny babies seem to have a built-in awareness of numbers. But is this the only way our brains process mathematics?