Mathematical physics

For a half century, mathematicians have tried to define the exact circumstances under which a black hole is destined to exist. A new proof shows how a cube can help answer the question.

By treating molecules as geometric tessellations, scientists devised a new way to forecast how 2D materials might self-assemble.

Wave-science researcher Ton van den Bremer and Steven Strogatz discuss how rogue waves can form in relatively calm seas and whether their threat can be predicted.

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.