“Rainbow colorings” recently led to a new proof. It’s not the first time they’ve come in handy.

Computer scientists established a new boundary on computationally verifiable knowledge. In doing so, they solved major open problems in quantum mechanics and pure mathematics.

Mathematicians have proved that copies of smaller graphs can always be used to perfectly cover larger ones.

Explore our surprisingly simple, absurdly ambitious and necessarily incomplete guide to the boundless mathematical universe.

By exploiting randomness, three mathematicians have proved an elegant law that underlies the chaotic motion of turbulent systems.

A startling experimental discovery about how fluids behave started a wave of important mathematical proofs.

Researchers have spent centuries looking for a scenario in which the Euler fluid equations fail. Now a mathematician has finally found one.

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.”