Combinatorics

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.

Mathematicians are finding inevitable structures in sufficiently large sets of integers.

In 1973, Paul Erdős asked if it was possible to assemble sets of “triples” — three points on a graph — so that they abide by two seemingly incompatible rules. A new proof shows it can always be done.

With Hugo Duminil-Copin, thinking rarely happens without moving. His insights into the flow-related properties of complex networks have earned him the Fields Medal.

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.

With her homeland mired in war, the sphere-packing number theorist Maryna Viazovska has become the second woman to win a Fields Medal in the award’s 86-year history.

Play this simple math game with your friends to gain insights into fundamental principles of graph theory.

A surprising new solution to Leonhard Euler’s famous “36 officers puzzle” offers a novel way of encoding quantum information.

A new paper shows how to create longer disordered strings than mathematicians had thought possible, proving that a well-known recent conjecture is “spectacularly wrong.”