Mathematicians regard the Collatz conjecture as a quagmire and warn each other to stay away. But now Terence Tao has made more progress than anyone in decades.

We finally know how big a set of numbers can get before it has to contain a pattern known as a “polynomial progression.”

New work on the problem of “scissors congruence” explains when it’s possible to slice up one shape and reassemble it as another.

Today Google announced that it achieved “quantum supremacy.” Its chief quantum computing rival, IBM, said it hasn’t. The disagreement hinges on what the term really means.

A major advance toward solving the 60-year-old sunflower conjecture is shedding light on how order begins to appear as random systems grow in size.

Two monumental works have led many mathematicians to avoid the equal sign. The process has not always gone smoothly.

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.