If you were asked to describe how you can move through the Universe, you'd probably think of all the different directions you were free to move in. You could go left or right, forwards or backwards, ...

For decades mathematicians have searched for a specific pair of surfaces that can’t be transformed into each other in four-dimensional space. Now they’ve found them. In geometry and the closely ...

Yes, it is possible to create a three-dimensional image of a four-dimensional object: a hypercube is the four-dimensional analogue of a cube, and it has a well-known three-dimensional image that looks ...

In the illustration: A tesseract (a four-dimensional cube) and the "shadow" it casts on a plane—the quasicrystal discovered by Shechtman. According to Prof. Bartal, "The fact that a quasicrystal is a ...

When you are sent to do a bit of work experience in the office of a university science department you don’t normally expect much more than a bit of boring filing and some tedious photocopying. So ...

The central objects of study in topology are spaces called manifolds, which look flat when you zoom in on them. The surface of a sphere, for instance, is a two-dimensional manifold. Topologists ...

Can you imagine the imprint a four-dimensional hexagon might leave as it passes through your three-dimensional kitchen table? Probably not, but some people can. One such person was mathematician ...