In the light of recent events, it may appear that attempting to model the behaviour of financial markets is an impossible task. However, there are mathematical models of financial processes that, when applied correctly, have proved remarkably effective. Angus Brown looks at one of these, a simple model for option pricing, and explains how it takes us on the road to the famous Black-Scholes equation of financial mathematics, which won its discoverers the 1997 Nobel Prize in Economics.

Chuck Gill caught the space bug as a child when watching Alan Shepherd launch into space. Since then he's worked as a US Air Force navigator, a satellite operator, and in the US intelligence service. These days he's busy reducing carbon emissions and preparing London for the 2012 Olympics. Plus went to see him to find out more about his career.

Peter Markowich is a mathematician who likes to take pictures. At first his two interests seemed completely separate to him, but then he realised that behind every picture there is a mathematical story to tell. Plus went to see him to find out more, and ended up with a pictorial introduction to partial differential equations.

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.

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.

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.

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Mathematicians explain how plants climb

Learn about the aerodynamics of footballs and perfect your free kick.

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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.