Carnegie Mellon University computer scientists and mathematicians have resolved the last, stubborn piece of Keller's conjecture, a geometry problem that scientists have puzzled over for 90 years. By ...

On May 20, 2026, OpenAI announced that its internal AI model had disproven a long-held prediction regarding the 'unit distance problem,' a central unsolved problem in discrete geometry. The unit ...

One of the oldest and simplest problems in geometry has caught mathematicians off guard—and not for the first time. Since antiquity, artists and geometers have wondered how shapes can tile the entire ...

OpenAI claims its reasoning model disproved a geometry conjecture unsolved since 1946 — and this time, the mathematicians who exposed its last embarrassing claim are backing it up.

The last dimension of Keller's conjecture has been proven using a computer algorithm. The conjecture involves the way hypercubes in different dimensions share sides when tiled. The proof is ...

On June 18, Adam Marcus and Daniel A. Spielman of Yale University, along with Nikhil Srivastava of Microsoft Research India, announced a proof of the Kadison-Singer conjecture, a question about the ...

The result is correct but challenges core norms of mathematics: checking proofs, crediting ideas and keeping research open to everyone.

Consider a pencil lying on your desk. Try to spin it around so that it points once in every direction, but make sure it sweeps over as little of the desk’s surface as possible. You might twirl the ...

The Collatz conjecture is also known as the “3n + 1” problem. It’s an easy problem to explain and check, and has been tested up into the nineteen figure range. But it’s only now that anyone has come ...

Monstrous moonshine, a quirky pattern of the monster group in theoretical math, has a shadow -- umbral moonshine. Mathematicians have now proved this insight, known as the Umbral Moonshine Conjecture, ...