Alpöge’s discovery is the latest in a string of high-profile mathematical breakthroughs made by large language models. Recent examples include OpenAI’s disproof of the unit distance conjecture, and ...

Yet another longstanding mathematical question has been resolved by AI – and it feels a little different from the ones that ...

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 ...

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 ...

Let's be totally honest, when you hear that AI has cracked a 80-year-old math problem, your first instinct is probably to yawn and swipe away. It sounds like a headline strictly for the coding nerds ...

The Poincaré conjecture can be understood by analogy with the case in two dimensions. A two-dimensional space, or surface, is like a bubble made from an infinitely thin film of soap. If the bubble is ...

They made some progress, re-proving the conjecture in two dimensions using different techniques—ones they hoped would be applicable to the three-dimensional case. But then they hit a wall. “At some ...