Algebraic geometry

Four Fields Medals were awarded for major breakthroughs in geometry, combinatorics, statistical physics and number theory, even as mathematicians continued to wrestle with how computers are changing the discipline.

Wei Ho, the first director of the Women and Mathematics program at the Institute for Advanced Study, combines algebra and geometry in her work on an ancient class of curves.

A simple geometric idea has been used to power advances in information theory, cryptography and even blockchain technology.

Eric Larson and Isabel Vogt have solved the interpolation problem — a centuries-old question about some of the most basic objects in geometry. Some credit goes to the chalkboard in their living room.

June Huh wasn’t interested in mathematics until a chance encounter during his sixth year of college. Now his profound insights connecting combinatorics and geometry have led to math’s highest honor.

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.

Lauren Williams has charted an adventurous mathematical career out of the pieces of a fundamental object called the positive Grassmannian.

Emily Riehl is rewriting the foundations of higher category theory while also working to make mathematics more inclusive.

Why do mathematicians enjoy proving the same results in different ways?