Ramsey theory

Decades ago, Paul Erdős used randomness to illuminate the vast and weird world of networks. Now mathematicians are making his technique even more powerful.

Fan Chung, who has an Erdős number of 1, discusses the importance of connection — both human and mathematical.

A new proof marks the first progress in decades on a problem about how order emerges from disorder.

Mathematicians show that graphs of a certain common type must contain a route that visits each point exactly once.

Landmark results in Ramsey theory and a remarkably simple aperiodic tile capped a year of mathematical delight and discovery.

Mathematicians can often figure out what happens as quantities grow infinitely large. What about when they are just a little big?

Mathematicians probe the limits of randomness in new work estimating quantities called Ramsey numbers.

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.