Partial differential equations

A new study shows that extreme black holes could break the famous “no-hair” theorem, and in a way that we could detect.

After translating some of math’s complicated equations, researchers have created an AI system that they hope will answer even bigger questions.

Einstein’s equations describe three canonical configurations of space-time. Now one of these three — important in the study of quantum gravity — has been shown to be inherently unstable.

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.

For the first time, physicists have calculated exactly what kind of singularity lies at the center of a realistic black hole.

A founder of modern geometric analysis who produced “some of the most dramatic advances in mathematics in the last 40 years,” Uhlenbeck is the first woman to be awarded this top honor.