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One million dollars is waiting to be won by anyone who can solve one of the grand mathematical challenges of the 21st century. In the second of two articles, Chris Budd looks at the wellposedness of the NavierStokes equations.

The Four Colour Theorem  the statement that four colours suffice to fill in any map so that neighbouring countries are always coloured differently  has had a long and controversial history. It was first conjectured 150 years ago, and finally (and infamously) proved in 1976 with much of the work done by a computer. The published proof relied on checking 1432 special cases, which took more than 1,000 hours of computer time.

Geometric dissection is the mathematical art of cutting figures into pieces that can be rearranged to form other figures, preferably using as few pieces as possible. You may already have come across puzzles such as the Aviary Tangram, the pieces of which can be used to form an egg, a chicken and many other shapes; but the ingenuity of the dissections shown here may still be a revelation to you, as they were to this reviewer.

George Szpiro has a most unusual day job for someone writing about the abstract world of pure mathematics. Although he first studied maths at university, he has been a political journalist now for a number of years, working as Israel correspondent for NZZ, a Swiss daily. He wrote this book at night, after the paper's deadline, and as it was being finished lost one of his closest friends in a suicide bombing. The contrast between sphere packings in three dimensions and his daytime subject material must often have struck him.

Many people, when they look back, can pinpoint the precise moment when their interest in mathematics was awakened  it was when they found a puzzle that intrigued them. Perhaps they now realise the puzzle was trivial or insignificant, but at the time something about it captured their imagination and started them on a path that may have led very far  perhaps even into fundamental mathematical research.

Whether you love maths or hate maths, your opinions on the subject were probably formed early. So primary teachers have a vital role to play in promoting mathematical skills. Plus meets primary teacher and maths coordinator Maureen Matthews.


To study a system, mathematicians begin by identifying its most crucial elements, and try to describe them in simple mathematical terms. As Phil Wilson tells us, this simplification is the essence of mathematical modelling.
