fluid mechanics
Ocean waves are not moving walls of water. Instead, it's some kind of energy that moves along. But then, what happens to the water itself? This isn't just an idle question to ponder while watching the ocean — its answer may help protect us from it too. And it requires some sophisticated maths. 
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. 
Describing the motion of fluids is a huge and unsolved mathematical problem. There are equations that seem to describe it well, but their complete solution is way beyond reach. But could there be a simpler method? The physicist Jerry Gollub tells Plus about a new discovery which combines experiment with sophisticated maths.


Umbrella or no umbrella? New advances in weather forecasting will help us dodge hurricanes and protect against floods.

Can maths help save lives by making more accurate predictions of future volcanic eruptions?

A new mathematical model might explain the strange magnetic fields of Uranus and Neptune.

One million dollars is waiting to be won by anyone who can solve one of the grand mathematical challenges of the 21st century. In the second of two articles, Chris Budd looks at the wellposedness of the NavierStokes equations.

During World Mathematical Year 2000 a sequence of posters were displayed month by month in the trains of the London Underground aiming to stimulate, fascinate  even infuriate passengers! Keith Moffatt tells us about three of the posters from the series.
