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.

One million dollars is waiting to be won by anyone who can solve one of the grand mathematical challenges of the 21st century. But be warned...these problems are hard. In the first of two articles, Chris Budd explains how to hit the bigtime.

Numbers are bandied around all the time in sports coverage - and cricket is particularly rich in statistics and rankings. It has probably not escaped your attention that the World Cup of cricket has just finished in South Africa (Australia won - again) and so to mark the occasion, Rob Eastaway tells Plus what it takes to be the best.

Some molecules - thalidomide, for example - come in both left and right handed versions, while others are indistinguishable from their reflections. Plus finds out about the role of mathematical symmetry in chemistry.

In 1694, a famous discussion between two of the leading scientists of the day - Isaac Newton and David Gregory - took place on the campus of Cambridge University. The discussion concerned the kissing problem, but it was to be another 260 years before the problem was finally solved.

Imagine stepping inside your favourite painting, walking around the light-filled music room of Vermeer's "The Music Lesson" or exploring the chapel in the "Trinity" painted by Masaccio in the 15th century. Using the mathematics of perspective, researchers are now able to produce three-dimensional reconstructions of the scenes depicted in these works.

Currently, disabled computer users have a hard time inputting text, using laborious word-completion. Plus find out how this is changing, thanks to Dasher, a new open-source text-entry system based on arithmetic coding.

How can a 3 hour long film like the Lord of the Rings fit on a single DVD? Hw cn U rd txt msgs? How do MP3s make music files smaller, so they can be downloaded faster off the Internet? All these things rely on the mathematics of data compression.