## topology

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?

**Robin Wilson**starts off a four part series on Euler with a look at his life and work.

*Plus*takes an illustrated tour of an extraordinary geometric construction: the

**Klein bottle**.