On May 20, OpenAI said an internal reasoning model had produced a counterexample to Paul Erdős’s 1946 unit distance ...

OpenAI has revealed a breakthrough proof that overturns a nearly 80-year-old geometry conjecture posed by Paul Erdős.

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 ...

Katie has a PhD in maths, specializing in the intersection of dynamical systems and number theory. She reports on topics from maths and history to society and animals. Katie has a PhD in maths, ...

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 ...