Symmetry

The n-queens problem is about finding how many different ways queens can be placed on a chessboard so that none attack each other. A mathematician has now all but solved it.

By focusing on relationships between solutions to polynomial equations, rather than the exact solutions themselves, Évariste Galois changed the course of modern mathematics.

A group of mathematicians has shown that at critical moments, a symmetry called rotational invariance is a universal property across many physical systems.

Even in an incomplete state, quantum field theory is the most successful physical theory ever discovered. Nathan Seiberg, one of its leading architects, talks about the gaps in QFT and how mathematicians could fill them.

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

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.

Three mathematicians have resolved a fundamental question about straight paths on the 12-sided Platonic solid.

By translating Keller’s conjecture into a computer-friendly search for a type of graph, researchers have finally resolved a problem about covering spaces with tiles.

Representation theory was initially dismissed. Today, it’s central to much of mathematics.