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# mathematical physics

## Latest Articles

### Behold Modular Forms, the ‘Fifth Fundamental Operation’ of Math

Modular forms are one of the most beautiful and mysterious objects in mathematics. What are they?

### Math Proof Draws New Boundaries Around Black Hole Formation

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.

### The Simple Geometry That Predicts Molecular Mosaics

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

### What Causes Giant Rogue Waves?

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.

### New Proof Finds the ‘Ultimate Instability’ in a Solar System Model

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

### A New Symmetry Shakes Up Physics

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

### How to Tame the Infinities Hiding in the Heart of Particle Physics

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

### New Proof Distinguishes Mysterious and Powerful ‘Modular Forms’

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.

### Mathematicians Find an Infinity of Possible Black Hole Shapes

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.