group theory

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

Laurent Fargues and Peter Scholze have found a new, more powerful way of connecting number theory and geometry as part of the sweeping Langlands program.

Inside the symmetries of a crystal shape, a postdoctoral researcher has unearthed a counterexample to a basic conjecture about multiplicative inverses.

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

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

In a major mathematical achievement, a small team of researchers has proven Zimmer’s conjecture.

New findings are fueling an old suspicion that fundamental particles and forces spring from strange eight-part numbers called “octonions.”

A type of symmetry so unusual that it was called a “pariah” turns out to have deep connections to number theory.

To begin to understand what mathematicians and physicists see in the abstract structures of symmetries, let’s start with a familiar shape.