Mathematical physics

Hidden correspondences hint at a deeper structure to the mathematical universe. Our columnist unpacks one of those connections and asks mathematicians what they might mean.

Mathematicians at OpenAI showed that the Navier-Stokes equations, which describe how fluids flow, can sometimes “blow up.” But the massive result is not without controversy.

From the 1800s to the early 2000s, physicists used the same theory to understand the behavior of fluids. Now, using a modern insight, they have redefined fluids from the bottom up.

Lauren Williams tells 'The Joy of Why' how studying a fundamental object in algebraic combinatorics led to a career full of surprises.

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.