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.

Akshay Venkatesh, a former prodigy who struggled with the genius stereotype, has won a Fields Medal for his “profound contributions to an exceptionally broad range of subjects in mathematics.”

The 30-year-old math sensation Peter Scholze is now one of the youngest Fields medalists for “the revolution that he launched in arithmetic geometry.”

Generations of researchers have pursued his “Langlands program,” which seeks to create a grand unified theory of mathematics.