The relevance and usefulness of mathematics is most clearly demonstrated in its application to real-world problems, many of which have featured in Plus over the years. To celebrate mathematics at work in the real-world, the International Council for Industrial and Applied Mathematics have announced the winners of the five ICIAM prizes for 2007.

The Pioneer Prize, recognising innovations in applied mathematics, was jointly won by Ingrid Daubechies (Princeton University, USA) and Heinz Engl (Johannes Kepler Universität Linz, Austria). Daubechies' work on wavelets has found widespread use in image processing and frequency analysis. Engl was recognised for his work on inverse problems to the solution of a wide range of industrial problems and for his promotion world-wide of industrial and applied mathematics.

The Collatz Prize is awarded to outstanding applied mathematicians under the age of 42. It was won by Felix Otto (Universität Bonn, Germany) for his fundamental contributions in areas ranging from micromagnetics to mass transportation problems.

Joseph Keller (Stanford University, USA) won the Lagrange Prize for his exceptional contributions to the field. Not only has he influenced the course of modern applied mathematics over the last 50 years, he has also had a great impact in pure mathematics as well. He developed the Geometrical Theory of Diffractions that provided the first systematic description of wave propagation around edges and corners of an obstacle. It has been widely used for radar reflection from targets, elastic wave scattering from defects in solids, acoustic wave propagation in the ocean radar and many other fields. He has also made contributions to quantum mechanics, optics, acoustics, biophysics and biomechanics and transport theory.

Peter Deuflhard (ZIB Berlin, Germany), winner of the Maxwell Prize, is one of the founders of modern scientific computing, and is described as having made a contribution to applied mathematics that is without parallel, including applications in chemical engineering, medicine and biotechnology, microwave technology and nano-optics.

The Su Buchin Prize is more unusual in the field of mathematics, recognising the "application of Mathematics to emerging economies and human development". The winner, Gilbert Strang (MIT, USA), is one of the most recognised mathematicians in the developing world through his promotion of mathematical research and education across the globe. As well as numerous visits himself, he has organised visits by other mathematicians to developing countries, and his educational materials are available on the web, free-of-charge to any user anywhere in the world, through MIT's OpenCourseWare. Alongside his contributions in bringing mathematics to people around the world, his research has made contributions in many areas of pure and applied mathematics.

The prizes will be presented at the International Congress for Industrial and Applied Mathematics in Zürich next year, a major international celebration of mathematics in action. More information on the prizes, and the winners, can be found at the ICIAM website. And you can read more about industrial mathematics on Plus.