Erdős conjecture

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

A new proof breaks a decades-long drought of progress on the problem of estimating the size of triangles created by cramming points into a square.

A new result shows how much of the plane can be colored by points that are never exactly one unit apart.

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.

No two pairs have the same sum; add three numbers together, and you can get any whole number.

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

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.

Fifty years ago, Paul Erdős and two other mathematicians came up with a graph theory problem that they thought they might solve on the spot. A team of mathematicians has finally settled it.