A $1 million prize awaits anyone who can show where the math of fluid flow breaks down. With specially trained AI systems, researchers have found a slew of new candidates in simpler versions of the problem.

AI is tackling PhD-level math, but can it keep up with the toughest challenges yet?

How did AI help solve a 24-dimensional puzzle in just two weeks? Dive into the world of sphere packing and find out.

Columnist Natalie Wolchover explores whether applied category theory can be “green” math.

Researchers debate motivation, purpose, and the field’s future

With automated proof-checkers, a problem can be broken up into small chunks, solved bit-by-bit, then reassembled with confidence that every piece is correct. For some, this heralds a new area in mathematical research.

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.

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?

Mathematicians at OpenAI showed that the Navier-Stokes equations, which describe how fluids flow, can sometimes “blow up.” But the massive result is not without controversy.

Mathematicians are facing the sudden shift with grief, anger, and a desperate search for fresh ideas: “If we don’t adapt, there’s just no more math in 50 years.”

Unlike other recent AI proofs, this one has been unpacked by human experts. The implications, one mathematician said, are “staggering.”