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.”

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.