Erdős conjecture

In this special live recording from the International Congress of Mathematicians in Philadelphia, July 2026, the central question discussed was what do mathematicians really value about doing mathematics in the first place?

AI’s greatest mathematical successes have come from answers to problems posed by a mid-20th century iconoclast. By examining what makes the Erdős problems unique, mathematicians are trying to understand how AI might change the rest of math.

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

A new proof illuminates the hidden patterns that emerge when addition becomes impossible.

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.