It’s an educated guess, not a proof. But a good conjecture will guide math forward, pointing the way into the mathematical unknown. Mountain climbing is a beloved metaphor for mathematical research.

Fermat’s last theorem is just one of many examples of innocent-looking problems that can long stymie even the most astute mathematicians. It took about 350 years to prove Fermat’s scribbled conjecture ...

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, ...

A chatbot’s result for the 80-year-old “unit distance” conjecture is the first AI proof that would likely be published in ...

OpenAI says an AI reasoning model disproved an 80-year-old Erdős geometry conjecture, raising new questions about AI’s role ...

MILLENNIUM PRIZE SERIES: The Millennium Prize Problems are seven mathematics problems laid out by the Clay Mathematics Institute in 2000. They’re not easy – a correct solution to any one results in a ...

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 ...

OpenAI makes big splash with AI finding math problem breakthrough. Real lesson is to use AI to find counterexamples. An AI ...