Langlands program

The Langlands program provides a beautifully intricate set of connections between various areas of mathematics, pointing the way toward novel solutions for old problems.

Mathematicians and computer scientists answered major questions in topology, set theory and even physics, even as computers continued to grow more capable.

Ana Caraiani seeks to unify mathematics through her work on the ambitious Langlands program.

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.

Even as mathematicians and computer scientists proved big results in computational complexity, number theory and geometry, computers proved themselves increasingly indispensable in mathematics.

The p-adics form an infinite collection of number systems based on prime numbers. They’re at the heart of modern number theory.

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

Mathematicians have figured out how to expand the reach of a mysterious bridge connecting two distant continents in the mathematical world.