This year's Abel Prize goes to Luis A. Caffarelli for a body of work on the maths of change.

PhD student Tamara Grossmann tells us about her work on image analysis.

Change is the only constant in our lives — which is why differential equations are so useful.

Straddling the boundary between pure and applied mathematics.

This year's Abel prize shows you can wrap anything, no matter how weirdly shaped.

A new foam with medical potential

In 1979 decorating work in a house in Vienna revealed a set of medieval frescoes depicting a cycle of songs by a 13th century poet, who was particularly fond of satirising the erotic relationships between knights and peasant maidens. The frescoes are of great historical significance, but they are badly damaged. In this article Carola Schönlieb explores how mathematicians use the heat equation to fill in the gaps.

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.

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.

Nick Crawley had recently set up his own financial consultancy firm in Sydney, Australia, offering advice on large-scale financing deals. He tells Plus about the challenges and rewards of working in an incentive-driven environment.

André Léger studies the fluid mechanics of food travelling through the intestines for consumer goods giant Unilever.