Ramsey theory

Four mathematicians have found a new upper limit to the “Ramsey number,” a crucial property describing unavoidable structure in graphs.

It’s been known for thousands of years that the primes go on forever, but new proofs give fresh insights into how theorems depend on one another.

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

A new proof significantly strengthens a decades-old result about the ubiquity of ways to represent whole numbers as sums of unit fractions.

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.”

Researchers have proved a special case of the Erdős-Hajnal conjecture, which shows what happens in graphs that exclude anything resembling a pentagon.

At 21, Ashwin Sah has produced a body of work that senior mathematicians say is nearly unprecedented for a college student.

David Conlon and Asaf Ferber have raised the lower bound for multicolor “Ramsey numbers,” which quantify how big graphs can get before patterns inevitably emerge.

“Rainbow colorings” recently led to a new proof. It’s not the first time they’ve come in handy.