Mathematical physics

The accelerating effort to understand the mathematics of quantum field theory will have profound consequences for both math and physics.

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

A mathematical shortcut for analyzing black hole collisions works even in cases where it shouldn’t. As astronomers use it to search for new classes of hidden black holes, others wonder: Why?

A former graduate student reflects on how Isadore Singer, who died on February 11, brought together mathematicians, physicists and anyone else interested in the deeper connections between diverse fields.

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.