The Kochen-Specker theorem shows that quantum mechanics is always going to be strange. Its proof is surprisingly simple!

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."

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.