topology

The paths of billiard balls on a table can be long and complicated. To understand them mathematicians use a beautiful trick, turning tables into surfaces.

How to make a hard problem easy by changing the way you look at it.

The London Underground turns 150 today! It's probably the most famous rail network in the world and much of that fame is due to the iconic London Underground map. But what makes this map so special?

Progress in pure mathematics has its own tempo. Major questions may remain open for decades, even centuries, and once an answer has been found, it can take a collaborative effort of many mathematicians in the field to check that it is correct. The New Contexts for Stable Homotopy Theory programme, held at the Institute in 2002, is a prime example of how its research programmes can benefit researchers and its lead to landmark results.
Data, data, data — 21st century life provides tons of it. It's paradise for researchers, or at least it would be if we knew how to make sense of it all. This year's AAAS annual meeting in Vancouver devoted plenty of time to the question of how to understand large amounts of data. And there's one method we particularly liked. It's based on the kind of idea that gave us the London tube map.

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?

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