The International Mathematical Union has celebrated its 100th anniversary with a conference entitled Mathematics without borders.

How to unjam traffic.

Find out what gravitational waves will tell us about the Universe: from understanding its birth to figuring out whether black holes have hairs.

Find out about the heroic effort that led to the detection of gravitational waves and the excitement of their discovery.

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?

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".

Is the Universe finite or infinite? Is there infinity inside a black hole? Is space infinitely divisible or is there a shortest length? We talk to philosophers and physicists to find out.