Physicists have wondered for decades whether infinitely dense points known as singularities can ever exist outside black holes, which would expose the mysteries of quantum gravity for all to see.

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 ...

The starting point for rigorous reasoning in mathematics is a system of axioms. An axiom is a statement that is assumed, without demonstration, to be true. It is usually self-evident, for example, ...