What's up in

After decades of effort, mathematicians now have a complete understanding of the complicated equations that model the motion of free boundaries, like the one between ice and water.

A new proof establishes the boundary at which a shape becomes so corrugated, it can be crushed.

Two teams found different ways for quantum computers to process nonlinear systems by first disguising them as linear ones.

Lauren Williams has charted an adventurous mathematical career out of the pieces of a fundamental object called the positive Grassmannian.

Having solved a central mystery about the “twirliness” of tornadoes and other types of vortices, William Irvine has set his sights on turbulence, the white whale of classical physics.

Explore our surprisingly simple, absurdly ambitious and necessarily incomplete guide to the boundless mathematical universe.

Rogue waves — enigmatic giants of the sea — were thought to be caused by two different mechanisms. But a new idea that borrows from the hinterlands of probability theory has the potential to predict them all.

By exploiting randomness, three mathematicians have proved an elegant law that underlies the chaotic motion of turbulent systems.

A startling experimental discovery about how fluids behave started a wave of important mathematical proofs.

Previous