Infinity

Useful mathematical concepts, like the number line, can linger for millennia before they are rigorously defined.

Transcendental numbers include famous examples like e and π, but it took mathematicians centuries to understand them.

All infinities go on forever, so how is it possible for some infinities to be larger than others? The mathematician Justin Moore discusses the mysteries of infinity with Steven Strogatz.

Of all the endless questions children and mathematicians have asked about infinity, one of the biggest has to do with its size.

Mathematicians and computer scientists answered major questions in topology, set theory and even physics, even as computers continued to grow more capable.

One of the strangest results in mathematics explains how it’s possible to turn one sphere into two identical copies, simply by rearranging its pieces.

A pair of researchers has shown that trying to classify groups of numbers called “torsion-free abelian groups” is as hard as it can possibly be.

For 50 years, mathematicians have believed that the total number of real numbers is unknowable. A new proof suggests otherwise.

These games combine quantum entanglement, infinity and impossible-to-calculate winning probabilities. But if researchers can crack them, they’ll reveal deep mathematical secrets.