Kevin Hartnett

The twin primes conjecture is one of the most important and difficult questions in mathematics. Two mathematicians have solved a parallel version of the problem for small number systems.

In some ways, machine vision is superior to human vision. In other ways, it may never catch up.

Mathematicians and neuroscientists have created the first anatomically accurate model that explains how vision is possible.

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.