Rachel Thomas

What makes a number a constant of nature?

Stanley Osher has won the 2014 Gauss Prize for his revolutionary impact in areas including medical imaging, sonic booms, movie animation and microchip design and manufacture.

Manjul Bhargava is being honoured as a number theorist of "extraordinary creativity," with "a taste for simple problems of timeless beauty."

Artur Avila is being honoured for "formidable technical power, the ingenuity and tenacity of a master problem-solver, and an unerring sense for deep and significant questions."

Martin Hairer's is being honoured for a major breakthrough that gives a way of attacking problems that had previously been impenetrable.

Patterns and structures lie at the heart of mathematics, some even say they are mathematics. But how do they help us do mathematics?

Many materials around us are oxides – such as rocks, window glass and some of the materials used in your computer. These materials may seem hard and rigid, but mathematics reveals a hidden flexibility that can explain many of their properties.

We joined HRH Princess Anne and many great mathematicians to celebrating 50 years of the IMA at the Royal Society.