Infinity

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.

A two-player game can reveal whether the universe has an infinite amount of complexity.

Two mathematicians have proved that two different infinities are equal in size, settling a long-standing question. Their proof rests on a surprising link between the sizes of infinities and the complexity of mathematical theories.

What can the mathematical genius Srinivasa Ramanujan teach us about number theory through mathematical structures involving infinity?

Insights from the mathematical genius Srinivasa Ramanujan give us a number of ways to explore the infinite.