Mathematics

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

A mathematical mechanism enables AI models to process language at scale, undergirding the current AI revolution. Our columnist asks: Why is attention the key?

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.”

Maggie Miller explains why our intuition about three dimensions breaks down in four, and how she visualizes 4D spaces as a reel of three-dimensional snapshots.

After a long hiatus, the problem, which was likely inspired by juggling, has finally been resolved by a group of young mathematicians.

The proof of a decades-old conjecture has given researchers a new way to understand complex networks.

By revisiting the famous problem — which was controversially solved in the 1970s with the help of computers — mathematicians have gained important new insights into the nature of graphs.

Hidden correspondences hint at a deeper structure to the mathematical universe. Our columnist unpacks one of those connections and asks mathematicians what they might mean.

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.