Mathematical physics

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.

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.