navier-stokes equations

This year's Abel Prize goes to Luis A. Caffarelli for a body of work on the maths of change.

How does your phone know what the weather's going to be like?

Where do the magnetic fields of planets and stars come from?

It's a good question with a fascinating answer.

The mathematical equations governing fluid flow may have no known solutions, but maths still has the answers!

An insightful look at the climate models that predict our future.

The mathematical problem with turbulence.

Few things in nature are as dramatic, and potentially dangerous, as ocean waves. The impact they have on our daily lives extends from shipping to the role they play in driving the global climate. From a theoretical viewpoint water waves pose rich challenges: solutions to the equations that describe fluid motion are elusive, and whether they even exist in the most general case is one of the hardest unanswered questions in mathematics.

Africa isn't a continent that's famous for cutting edge research. But at the University of Stellenbosch, 50km East of Cape Town, South Africa, Kiran Dellimore and his team are engineering medical equipment that will save the lives of people all over the world. Latest projects include replacement heart valves made from kangaroo tissue and equipment to help resuscitate people in emergencies.