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.

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 ...

In work that has been 30 years in the making, mathematicians have proved a major part of a profound mathematical vision called the Langlands program. A group of nine mathematicians has proved the ...

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

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, ...

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 ...

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

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 ...