Topologists famously think that a doughnut is the same as a coffee cup because one can be deformed into the other without tearing or cutting. In other words, topology doesn't care about exact measurements of quantities like lengths, angles and areas. Instead, it looks only at the overall shape of an object, considering two objects to be the same as long as you can morph one into the other without breaking it. But how do you work with such a slippery concept? One useful tool is what's called the fundamental group of a shape.

The Abel Prize 2011 goes to John Willard Milnor of Stony Brook University, New York for "pioneering discoveries in topology, geometry and algebra".

This is the second in a series of two articles in which Ian Short looks at topology using topographical features of maps. Find out about Jordan curves and winding numbers with the help of hermits, lighthouses and drunken sailors.

Journey to distant islands to discover if topology can overcome topography and bring peace to rival towns.

The world we live in is strictly 3-dimensional: up/down, left/right, and forwards/backwards, these are the only ways to move. For years, scientists and science fiction writers have contemplated the possibilities of higher dimensional spaces. What would a 4- or 5-dimensional universe look like? Or might it even be true that we already inhabit such a space, that our 3-dimensional home is no more than a slice through a higher dimensional realm, just as a slice through a 3-dimensional cube produces a 2-dimensional square?

Lucinda Mathews visualises tricky surfaces
One of science's biggest prizes awarded for research into strings and knots
Mathematicians solve the famous loop's mystery
Leonhard Euler was one of the most prolific mathematicians of all time. This year marks the 300th anniversary of his birth. Robin Wilson starts off a four part series on Euler with a look at his life and work.
The 2004 Abel Prize celebrates one of the great landmarks of 20th century mathematics.
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