combinatorics

For decades, mathematicians have been inching forward on a problem about which sets contain evenly spaced patterns of three numbers. Last month, two computer scientists blew past all of those results.

In a recent paper, two mathematicians showed that a particular pattern is unavoidable when fractions are categorized.

Mathematicians have uncovered a surprising wealth of rock-paper-scissors-like patterns in randomly chosen dice.

On nights and weekends, Justin Gilmer attacked an old question in pure math using the tools of information theory.

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.