Mathematical physics

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

An exercise in pure mathematics has led to a wide-ranging theory of how the world comes together.

It has been thought of as many things: a pointlike object, an excitation of a field, a speck of pure math that has cut into reality. But never has physicists’ conception of a particle changed more than it is changing now.

Renormalization has become perhaps the single most important advance in theoretical physics in 50 years.

Physicists have identified an algebraic structure underlying the messy mathematics of particle collisions. Some hope it will lead to a more elegant theory of the natural world.

Einstein’s equations describe three canonical configurations of space-time. Now one of these three — important in the study of quantum gravity — has been shown to be inherently unstable.

Freeman Dyson — physicist, mathematician, writer and idea factory — died on February 28, but his vitality lives on.

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.