In the mid-19th century, Bernhard Riemann conceived of a new way to think about mathematical spaces, providing the foundation ...

The Poincaré conjecture can be understood by analogy with the case in two dimensions. A two-dimensional space, or surface, is like a bubble made from an infinitely thin film of soap. If the bubble is ...

On its surface, the Kakeya conjecture is a simple statement about rotating needles. But it underlies a wealth of mathematics. In mathematics, a simple problem is often not what it seems. Earlier this ...

Prince Rupert of the Rhine first asked this question in the 17th century, and he soon found out the answer is yes. Later, ...

Can you drill a hole in a cube that an identical cube could fall through? Prince Rupert of the Rhine first asked this ...