The ancient Greeks wondered when “irrational” numbers can be approximated by fractions. By proving the longstanding Duffin-Schaeffer conjecture, two mathematicians have provided a complete answer.

Researchers are getting close to building a quantum computer that can perform tasks a classical computer can’t. Here’s what the milestone will mean.

Randomness would seem to make a mathematical statement harder to prove. In fact, it often does the opposite.

Mathematicians have proved that a random process applied to a random surface will yield consistent patterns.

Neven’s law states that quantum computers are improving at a “doubly exponential” rate. If it holds, quantum supremacy is around the corner.

Amie Wilkinson searches for exotic examples of the mathematical structures that describe change.

The universe of problems that a computer can check has grown. The researchers’ secret ingredient? Quantum entanglement.

Mathematicians have found that materials conduct electricity when electrons follow a universal mathematical pattern.

Quantum computers can’t selectively forget information. A new algorithm for multiplication shows a way around that problem.