combinatorics

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.”

New work establishes a tighter connection between the rank of a polynomial and the extent to which it favors particular outputs.

The n-queens problem is about finding how many different ways queens can be placed on a chessboard so that none attack each other. A mathematician has now all but solved it.