OpenAI claims it solved an 80-year-old math problem — for real this time

OpenAI has announced a groundbreaking development with its latest reasoning model, which it asserts has produced an original mathematical proof that challenges a long-standing conjecture in geometry. This conjecture, famously proposed by mathematician Paul Erdős in 1946, has perplexed scholars for decades. This latest claim comes after a previous instance in which OpenAI's former VP, Kevin Weil, suggested that GPT-5 had solved numerous Erdős problems. However, it was later revealed that those solutions were not original breakthroughs but rather existing findings documented in academic literature. This led to criticism from figures such as Yann LeCun and Demis Hassabis, who pointed out the inaccuracies in Weil's assertions. In a more cautious tone this time, OpenAI has backed its current announcement with endorsements from notable mathematicians, including Noga Alon, Melanie Wood, and Thomas Bloom, who has previously criticized Weil's earlier claims. OpenAI stated on social media that the conventional belief held by mathematicians for nearly eight decades—that optimal solutions resembled square grids—has been upended by its AI model, which has discovered a new family of constructions that outperform the old assumptions. This achievement is touted as a historic moment, marking the first instance of AI independently solving a significant open problem in mathematics. The proof was generated by a general-purpose reasoning model, rather than a specialized math-solving system, underscoring the growing capabilities of AI in linking complex ideas across diverse domains. The implications of this advancement could extend into various fields, including biology, physics, engineering, and medicine. Thomas Bloom remarked, "AI is helping us to more fully explore the cathedral of mathematics we have built over the centuries. What other unseen wonders are waiting in the wings?" This question encapsulates the excitement and potential that lies ahead as AI continues to push the boundaries of mathematical understanding.