Rachel Thomas

How calculating the height of a frustum gave a glimpse of the mathematical frontier.

Will computers ever replace human mathematicians?

What makes a number a constant of nature?

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.

By the 1970s physicists had successfully tamed three of the fundamental forces using a sophisticated construct called quantum field theory. The trouble was that the framework seemed to fall apart when you looked at very high or very low energy scales. So how could these be thought of as valid theories? It's a question physicists are still grappling with today.

The early 1950s were an experimental gold mine for physicists, with new particles produced in accelerators almost every week. Yet the strong nuclear force that acted between them defied theoretical description, sending physicists on a long and arduous journey that culminated in several Nobel prizes and the exotic concept of "asymptotic freedom".

The 2013 Nobel prize in physics goes to Peter Higgs and François Englert for proposing the mechanism that gives things mass.