Mathematical physics

Columnist Natalie Wolchover examines the latest developments in the “forever war” over whether string theory can describe the world.

A $1 million prize awaits anyone who can show where the math of fluid flow breaks down. With specially trained AI systems, researchers have found a slew of new candidates in simpler versions of the problem.

Quantum mechanics has at last been formulated exclusively with real numbers, bringing a mathematical puzzle at the heart of the theory into a new era of inquiry.

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.