In issue 29 of Plus, we heard how a simple mathematical equation became the subject of a debate in the UK parliament. Chris Budd and Chris Sangwin continue the story of the mighty quadratic equation.
All of science can be regarded as motivated by the search for rules behind the randomness of nature, and attempts to make prediction in the presence of uncertainty. Chris Budd describes the search for pattern and order in chaos.
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.

You play tennis like a champion compared with the best of robots, if you play tennis at all.

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.
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.
In the late 1940s, American painter Jackson Pollock dripped paint from a can on to vast canvases rolled out across the floor of his barn. Richard P. Taylor explains that Pollock's patterns are really fractals - the fingerprint of Nature.
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.
Images based on Lyapunov Exponent fractals are very striking. Andy Burbanks explains what Lyapunov Exponents are, what the much misunderstood phenomenon of chaos really is, and how you can iterate functions to produce marvellous images of chaos from simple mathematics.

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.