OpenAI makes breakthrough on 80-year-old maths problem

Company says work on Paul Erdős planar unit distance problem shows advance in AI reasoning OpenAI has claimed a further advance in AI reasoning after its technology successfully tackled an 80-year-old maths problem. The company behind ChatGPT said it had made a breakthrough with a challenge first posed by Hungarian mathematician Paul Erdős in 1946: the planar unit distance problem. The question posed by Erdős is simple to explain. If you take a sheet of paper and add some dots, how many pairs can be the same distance apart? Erdős proposed the number would rise only slightly faster than the number of dots themselves. OpenAI’s model concluded otherwise by drawing on different branches of mathematics to uncover a family of arrangements that break the limit in Erdős’s conjecture. “For nearly 80 years, mathematicians believed the best possible solutions looked roughly like square grids,” OpenAI wrote on X. “An OpenAI model has now disproved that belief, discovering an entirely new family of constructions that performs better.” While the work has excited mathematicians, the broader problem remains unsolved because the AI did not come up with a new answer for how fast the pairs of dots ri