Mathematical physics

For the first time, mathematicians have proved that planetary orbits in a solar system will always be unstable.

So-called “higher symmetries” are illuminating everything from particle decays to the behavior of complex quantum systems.

In the math of particle physics, every calculation should result in infinity. The set of techniques known as “resurgence” points toward an escape.

Using “refreshingly old” tools, mathematicians resolved a 50-year-old conjecture about how to categorize important functions called modular forms, with consequences for number theory and theoretical physics.

In three-dimensional space, the surface of a black hole must be a sphere. But a new result shows that in higher dimensions, an infinite number of configurations are possible.

For more than 250 years, mathematicians have wondered if the Euler equations might sometimes fail to describe a fluid’s flow. A new computer-assisted proof marks a major breakthrough in that quest.

Svetlana Jitomirskaya was born in Ukraine, but left the Soviet Union to escape sexism and antisemitism. Even though her work in mathematical physics has now been honored with one of the field’s top prizes, she finds herself still fighting old battles.

The solutions to Einstein’s equations that describe a spinning black hole won’t blow up, even when poked or prodded.

Surprising as it may sound, 107 years after the introduction of general relativity, the meanings of basic concepts are still being worked out.