Mathematical physics

The math of even the simplest ocean waves is notoriously uncooperative. A team of Italian mathematicians has made major advances toward understanding it.

The amplituhedron, a shape at the heart of particle physics, appears to be deeply connected to the mathematics of paper folding.

The proof, known to be so hard that a mathematician once offered 10 martinis to whoever could figure it out, connects quantum mechanics to infinitely intricate mathematical structures.

For decades, mathematicians have struggled to understand matrices that reflect both order and randomness, like those that model semiconductors. A new method could change that.

A team of mathematicians based in Vienna is developing tools to extend the scope of general relativity.

By mathematically proving how individual molecules create the complex motion of fluids, three mathematicians have illuminated why time can’t flow in reverse.

Turbulence is a notoriously difficult phenomenon to study. Mathematicians are now starting to untangle it at its smallest scales.

Geometry may have its origins thousands of years ago in ancient land surveying, but it has also had a surprising impact on modern physics. In the latest episode of The Joy of Why, Yang-Hui He explores geometry’s evolution and its future potential through AI.

For decades, extremal black holes were considered mathematically impossible. A new proof reveals otherwise.