differential equation

Not so long ago, if you had a medical complaint, doctors had to open you up to see what it was. These days they have a range of sophisticated imaging techniques at their disposal, saving you the risk and pain of an operation. Chris Budd and Cathryn Mitchell look at the maths that isn't only responsible for these medical techniques, but also for much of the digital revolution.
The Arctic ice cap is melting fast and the consequences are grim. Mathematical modelling is key to predicting how much longer the ice will be around and assessing the impact of an ice free Arctic on the rest of the planet. Plus spoke to Peter Wadhams from the Polar Ocean Physics Group at the University of Cambridge to get a glimpse of the group's work.
Rupa Patel never wanted to be a financial engineer — she wanted to be a maths teacher. However, her skills in conveying difficult mathematical concepts to others, as well as a love of maths, enticed her into the exciting field of financial mathematics. Now she models risk, travels Europe and occasionally finds time to herself to examine the maths of her job in detail.
Why traffic jams occur for seemingly no reason
Mathematicians explain how plants climb
Learn about the aerodynamics of footballs and perfect your free kick.
What happens to bent pasta?
Riaz Ahmad's mathematical career has led him from the complexities of blood flow to the risks of the financial markets via underwater acoustics. Plus found out how maths can explain all this and more.
Saying that someone is a chaotic thinker might seem like an insult - but, according to Lewis Dartnell, it could be that the mathematical phenomenon of chaos is a crucial part of what makes our brains work.
Peter D Lax wins the Abel Prize 2005.